Posted:July 13, 2015

‘Natural Classes’ in the Knowledge Web

Gleaning Clues from Aristotle to Charles S. Peirce

We have recently talked much of the use of knowledge bases in areas such as artificial intelligence and knowledge supervision. The idea is to leverage the knowledge codified in these knowledge bases, Wikipedia being the most prominent exemplar, to guide feature selection or the creation of positive and negative training sets to be used by machine learners.

The pivotal piece of information that enables knowledge bases to perform in this way is a coherent knowledge graph of concepts and entity types. As I have discussed many times, the native category structure of Wikipedia (and all other commonly used KBs) leaves much to be desired. It is one of the major reasons we are re-organizing KB content using the UMBEL reference knowledge graph [1]. The ultimate requirement for the governing knowledge graph (ontology) is that it be logical, consistent and coherent. It is from this logical structure that we can provide the rich semsets [2] for semantic matches, make inferences, understand relatedness, and make disjointedness assertions. In the context of knowledge-based artificial intelligence (KBAI) applications [3], the disjointedness assertions are especially important to aiding the creation of negative training sets based on knowledge supervision.

Coherent and logical graphs first require natural groupings or classes of concepts and entity types by which to characterize the domain at hand, situated with respect to one another with testable relations. Entity types are further characterized by a similar graph of descriptive attributes. Concepts and entity types thus represent the nodes in the graph, with relations being the connecting infrastructure.

Going back at least to Aristotle, how to properly define and bound categories and concepts has been a topic of much philosophical discussion. If the nodes in our knowledge graph are not scoped and defined in a consistent way, then it is virtually impossible to construct a logical and coherent way to reason over this structure. This inconsistency is the root source of the problem that Wikipedia can not presently act as a computable knowledge graph, for example.

This article thus describes how Structured Dynamics informs its graph-construction efforts built around the notion of “natural classes.” Our use and notion of “natural classes” hews closely to how we understand the great American logician, Charles S. Peirce, came to define the concept [3]. Natural classes were a key underpinning to Peirce’s own efforts to provide a uniform classification system related to inquiry and the sciences.

Humanity’s Constant Effort to Define and Organize Our World

Aristotle set the foundational basis for understanding what we now call natural kinds and categories. The universal desire by all of us to be able to understand and describe our world has meant that philosophers have argued these splits and their bases ever since. In very broad terms we have realists, who believe things have independent order in the natural world and can be described as such; we have nominalists, who believe that humans provide the basis for how things are organized in part by how we name them; and we have idealists, or anti-realists, who believe “natural” classes are generalized ones that conform to human ideals of how the world is organized, but are not independently real [4]. These categories, too, shade into one another, such that these beliefs become strains in various degrees for how any one individual might be defined.The realist strain, also closely tied to the sciences and the scientific method, is what most guides the logic basis behind semantic technologies and SD’s view of how to organize the world.

Aristotle believed that the world could be characterized into categories, that categories were hierarchical in nature, and what defined a particular class or category was its essence, or the attributes that uniquely define what a given thing is. A mammal has the essences of being hairy, warm-blooded, and live births. These essences distinguish from other types of animals such as birds or reptiles or fishes or insects. Essential properties are different than accidental or artificial distinctions, such as whether a man has a beard or not or whether he is gray- or red-haired or of a certain age or country. A natural classification system is one that is based on these real differences and not artificial or single ones. Hierarchies arise from the shared generalizations of such essences amongst categories or classes. Under the Aristotelian approach, classification is the testing and logical clustering of such essences into more general or more specific categories of shared attributes. Because these essences are inherent to nature, natural clusterings are an expression of true relationships in the real world.

By the age of the Enlightenment, these long-held philosophies began to be questioned by some. Descartes famously grounded the perception of the world into innate ideas in the human mind. This philosophy built upon that of William of Ockham, who maintained the world is populated by individuals, and no such things as universals exist. In various guises, thinkers from Locke to Hume questioned a solely realistic organization of concepts in the world [5]. While there may be “natural kinds”, categorization is also an expression of the innate drive by humans to name and organize their world.

Relatedness of shared attributes can create ontological structures that enable inference and a host of graph analytics techniques for understanding meaning and connections. For such a structure to be coherent, the nodes (classes) of the structure should be as natural as possible, with uniformly applied relations defining the structure.

Thus, leaving behind metaphysical arguments, and relying solely on what is pragmatic, effectively built ontologies compel the use of a realistic viewpoint for how classes should be bounded and organized. Science and technology are producing knowledge at unprecedented amounts, and realism is the best approach for testing the trueness of new assertions. We think realism is the most efficacious approach to ontology design. One of the reasons that semantics are so important is that language used to capture the diversity of the real world must be able to be meaningfully related. Being explicit about the philosophy in how we construct ontologies helps decide sometimes sticky design questions.

Unnatural Classifications Instruct What is Natural

These points are not academic. The central failing, for example, of Wikipedia has been its category structure [7]. Categories have strayed from a natural classification scheme, and many categories are “artificial” in that they are compound or distinguished by a single attribute.“Compound” (or artificial) categories (such as Films directed by Pedro Almodóvar or Ambassadors of the United States to Mexico) are not “natural” categories, and including them in a logical evaluation only acts to confuse attributes from classification. To be sure, such existing categories should be decomposed into their attribute and concept components, but should not be included in constructing a schema of the domain.

“Artificial” categories may be identified in the Wikipedia category structure by both syntactical and heuristic signals. One syntactical rule is to look for the head of a title; one heuristic signal is to select out any category with prepositions. Across all rules, “compound” categories actually account for most of what is removed in order to produce “cleaned” categories.

We can combine these thoughts to show what a “cleaned” version of the Wikipedia category structure might look like. The 12/15/10 column in the table below reflects the approach used for determining the candidates for SuperTypes in the UMBEL ontology, last analyzed in 2010 [8]. The second column is from a current effort mapping Wikipedia to Cyc [9]:

	12/15/10	3/1/15
Total Categories	100%	100%

Administrative Categories	14%	15%

Orphaned Categories	10%	20%

Working Categories	76%	66%

“Artificial” Categories	44%	34%

Single Head		23%
	33%
Plural Head		24%

“Clean” Categories	33%	46%

Two implications can be drawn from this table. First, without cleaning, there is considerable “noise” in the Wikipedia category structure, equivalent to about half to two-thirds of all categories. Without cleaning these categories, any analysis or classification that ensues is fighting unnecessary noise and has likely introduced substantial assignment errors.

Second, the power that comes from a coherent schema of categories and concepts — especially inference and graph analysis — can not be applied to a structure that is not constructed along realistic lines. We can expand on this observation by bringing in our best logician on information, semeiosis and categories, Charles S. Peirce.

Peirce’s Refined Arguments of a Natural Class

Peirce was the first, by my reading, who looked at the question of “natural classes” sufficient to provide design guidance, and which may be sometimes contraposed against what are called “artificial classes” (we tend to use the term “compound” classes instead). A “natural class” is a set with members that share the same set of attributes, though with different values (such as differences in age or hair color for humans, for example). Some of those attributes are also more essential to define the “type” of that class (such as humans being warm-blooded with live births and hair and use of symbolic languages). Artificial classes tend to only add one or a few shared attributes, and do not reflect the essence of the type [6].

The most comprehensive treatment of Peirce’s thinking on natural classes was provided by Menno Hulswit in 1997. He first explains the genesis of Peirce’s thinking [6]:

“The idea that things belong to natural kinds seems to involve a commitment to essentialism: what makes a thing a member of a particular natural kind is that it possesses a certain essential property (or a cluster of essential properties), a property both necessary and sufficient for a thing to belong to that kind.”

“According to Mill, every thing in the world belongs to some natural class or real kind. Mill made a distinction between natural classes and non-natural or artificial classes (Mill did not use the latter term). The main difference is that the things that compose a natural class have innumerous properties in common, whereas the things that belong to an artificial class resemble one another in but a few respects.”

“Accordingly, a natural or real class is defined as a class ‘of which all the members owe their existence to a common final cause’ (CP 1.204), or as a class the ‘existence of whose members is due to a common and peculiar final cause’ (CP1.211). The final cause is described in this context as ‘a common cause by virtue of which those things that have the essential characters of the class are enabled to exist’ (CP 1.204).”

“Peirce concluded from these observations that the objects that belong to the same natural class, need not have all the characters that seem to belong to the class. After thus having criticized Mill, Peirce gave the following definition of natural class (or real kind):

“Any class which, in addition to its defining character, has another that is of permanent interest and is common and peculiar to its members, is destined to be conserved in that ultimate conception of the universe at which we aim, and is accordingly to be called ‘real.’ (CP6.384; 1901)”

“. . . natural classification of artificial objects is a classification according to the purpose for which they were made.”

“The problem of natural kinds is important because it is inextricably linked to several philosophical notions, such as induction, universals, scientific realism, explanation, causation, and natural law.”

This background sets up Hulswit’s interpretation of then how Peirce’s views on natural classification evolved [6]:

“Peirce’s approach was broadly Aristotelian inasmuch as natural classification always concerns the form of things (which is that by virtue of which things are what they are) and not their matter. This entails that Peirce borrowed Aristotle’s idea that the form was identical to the intrinsic final cause. Therefore it was obvious that natural classification concerns the final causes of the things. From the natural sciences, Peirce had learned that the forms of chemical substances and biological species are the expression of a particular internal structure. He recognized that it was precisely this internal structure that was the final cause by virtue of which the members of the natural class exist.”

“Accordingly, Peirce’s view may be summarized as follows: Things belong to the same natural class on account of a metaphysical essence and a number of class characters. The metaphysical essence is a general principle by virtue of which the members of the class have a tendency to behave in a specific way; this is what Peirce meant by final cause. This finality may be expressed in some sort of microstructure. The class characters which by themselves are neither necessary nor sufficient conditions for membership of a class, are nevertheless concomitant. In the case of a chair, the metaphysical essence is the purpose for which chairs are made, while its having chair-legs is a class character. The fuzziness of boundary lines between natural classes is due to the fuzziness of the class characters. Natural classes, though very real, are not existing entities; their reality is of the nature of possibility, not of actuality. The primary instances of natural classes are the objects of scientific taxonomy, such as elementary particles in physics, gold in chemistry, and species in biology, but also artificial objects and social classes.”

“By denying that final causes are static, unchangeable entities, Peirce avoided the problems attached to classical essentialism. On the other hand, by eliminating arbitrariness, Peirce also avoided pluralistic anarchism. Though Peircean natural classes only come into being as a result of the abstractive and selective activities of the people who classify, they reflect objectively real general principles. Thus, there is not the slightest sense in which they are arbitrary: “there are artificial classifications in profusion, but [there is] only one natural classification” (C P 1.275; 1902).”

Importantly, note that “natural kinds” or “natural classes” are not limited to things only found in nature. Perice’s semiotics (theory of signs) also recognizes “natural” distinctions in arenas such as social classes, the sciences, and man-made products [6]. Again, the key discriminators are the essences of things that distinguish them from other things, and the degree of sharing of attributes contains the basis for understanding relationships and hierarchies.

Natural Classes Can be Tested, Reasoned Over and Are Mutable

Though all of this sounds somewhat abstract and philosophical, these distinctions are not merely metaphysical. The ability to organize our representations of the world into natural classes also carries with it the ability to organize that world, reason over it, draw inferences from it, and truth test it. Indeed, as we may discover through knowledge acquisition or the scientific method, this world representation is itself mutable. Our understanding of species relationships, for example, has changed markedly, especially most recently, as the basis for our classifications shifts from morphology to DNA. Einstein’s challenges to Newtonian physics similarly changed the “natural” way by which we need to organize our understanding of the world.

When we conjoin ideas such as Shannon’s theory of information [10] with Peirce’s sophisticated and nuanced theory of signs [11], other insights begin to emerge about how the natural classification of things (“information”) can produce leveraged benefits. In linking these concepts together, de Tienne has provided some explanations for how Peirce’s view of information relates to information theory and efficient information messaging and processing [12]:

“For a propositional term to be a predicate, it must have ‘informed breadth’, that is, it must be predicable of real things, ‘with logical truth on the whole in a supposed state of information.’ . . . . For a propositional term to be a subject, it must have ‘informed depth’, that is, it must have real characters that can be predicated of it also ‘with logical truth on the whole in a supposed state of information’.”

“Peirce indeed shows that induction, by enlarging the breadth of predicate terms, actually increases the depth of subject terms—by boldly generalizing the attribution of a character from selected objects to their collection—while hypothesis, by enlarging the depth of subject terms, actually increases the breadth of predicate terms—by boldly enlarging their attribution to new individuals. Both types of amplicative inferences thus generate information.”

“. . . information is not a mere sum of quantities, but a product, and this distinction harbors a profound insight. When Peirce began defining, in 1865, information as the multiplication of two logical quantities, breadth and depth (or connotation and denotation, or comprehension and extension), it was in recognition of the fact that information was itself a higher-order logical quantity not reducible to either multiplier or multiplicand. Unlike addition, multiplication changes dimensionality—at least when it is not reduced, as is often the case in schoolbooks, to a mere additive repetition. Information belongs to a different logical dimension, and this entails that, experientially, it manifests itself on a higher plane as well. Attributing a predicate to a subject within a judgment of experience is to acknowledge that the two multiplied ingredients, one the fruit of denotation, the other of connotation, in their very multiplication or copulative conjunction, engender a new kind of logical entity, one that is not merely a fruit or effect of their union, but one whose anticipation actually caused the union.”

The essence of knowledge is that it is ever-growing and expandable. New insights bring new relations and new truths. The structures we use to represent this knowledge must themselves adapt and reflect the best of our current, testable understandings. Keeping in mind the need for all of our classes to be “natural” — that is, consistent with testable, knowable truth — is a key building block in how we should organize our knowledge graphs. Similar inspection can be applied to the relations used in the knowledge graph [13], but I will leave that discussion to another day.

Though hardly simple, the re-classification of Wikipedia’s content into a structure based on “natural classes” will bring heretofore unseen capabilities in coherence and computability to the knowledge base. Similar benefits can be obtained from any knowledge base that is presently characterized by an unnatural structure.

We now have both tests and guidelines — granted, still being discerned from Peirce’s writings or its logic — for what constitutes a “natural class”. “Natural classes” are testable; we not only know it when we see it, we can systematize the use of them. In classifying a class as a “natural” one does entail aspects of judgment and world view. But, so long as the logics and perspectives behind these decisions are consistent, I believe we can create computable knowledge graphs that cohere following these tests and guidelines.

Some may question whether any given structure is more “natural” than another one. But, through such guideposts as coherence, inference, testability and truthfulness, these structural arrangements are testable propositions. As Peirce, I think, would admonish us, failure to meet these tests are grounds for re-jiggering our structures and classes. In the end, coherence and computability become the hurdles that our knowledge graphs must clear in order to be reliable structures.

[1] For the latest release of UMBEL and its knowledge graph and associated links, see M.K. Bergman, 2015. “UMBEL version 1.20 Released,” in AI3:::Adaptive Information blog, April 21, 2015.

[2] A semset is the use of a series of alternate labels and terms to describe a concept or entity. These alternatives include true synonyms, but may also be more expansive and include jargon, slang, acronyms or alternative terms that usage suggests refers to the same concept. See further http://wiki.opensemanticframework.org/index.php/Semset_Concept.

[3] I first discussed Charles S. Peirce at length in M.K. Bergman, 2012. “Give Me a Sign: What Do Things Mean on the Semantic Web,” in AI3:::Adaptive Information blog, January 24, 2012.

[4] See, for example, John Michael Steiner, 2011. “An Anti-Realist Theory of Natural Kinds.” PhD dissertation, University of Calgary, September 2011, 245 pp.

[5] Michael R. Ayers, 1981. “Locke versus Aristotle on Natural Kinds.” The Journal of Philosophy (1981): 247-272.

[6] Menno Hulswit, 1997. “Peirce’s Teleological Approach to Natural Classes,” in Transactions of the Charles S. Peirce Society (1997): 722-772.

[7] See M.K. Bergman, 2015. “Shaping Wikipedia into a Computable Knowledge Base,” in AI3:::Adaptive Information blog, March 31, 2015.

[8] Upper Mapping and Binding Exchange Layer (UMBEL) Specification, Annex G: UMBEL SuperTypes Documentation, UMBEL.org, retrieved February 16, 2015.

[9] Aleksander Smywinski-Pohl, Krzysztof Wróbel, Michael K. Bergman and Bartosz Ziółko, 2015. “cycloped.io: An Interoperable Framework for Web Knowledge Bases,” manuscript in preparation.

[10] Claude E. Shannon, 1948. “A Mathematical Theory of Communication”, Bell System Technical Journal, 27: 379–423, 623-656, July, October, 1948. See http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf.

[11] Charles Sanders Peirce, 1894. “What is in a Sign?”, see http://www.iupui.edu/~peirce/ep/ep2/ep2book/ch02/ep2ch2.htm.

[12] André de Tienne, 2006. “Peirce’s Logic of Information.” Seminario del Grupo de Estudios Peirceanos, Universidad de Navarra 28 (2006).

[13] See, as one example, this discussion for the need for consistent and foundational relationship types, Giancarlo Guizzardi and Gerd Wagner, 2008. “What’s in a Relationship: An Ontological Analysis” In Conceptual Modeling-ER 2008, pp. 83-97. Springer Berlin Heidelberg, 2008.

Posted:June 23, 2015

Knowledge Supervision as a Grounding for Machine Learning

Providing the Method behind Knowledge-based Artificial Intelligence

One of the central engines behind artificial intelligence is machine learning. ML involves various ways that data is used to train or teach machines to classify, predict or perform complicated tasks, such as I captured in an earlier diagram. The methods used in machine learning may be statistical, based on rules, or recognizing or discovering patterns.

The name machine learning begs the question of to learn what? In the context of images, audio, video or sensory perception, machine learning is trained for the recognition of patterns, which can be layered into learning manifolds called deep learning. In my realm — that is, knowledge bases and semantics — machine learning can be applied to topic or entity clustering or classification; entity, attribute or relation identification and extraction; disambiguation; mapping and linking multiple sources; language translation; duplicates removal; reasoning; semantic relatedness; phrase identification; recommendation systems; and, question answering. Significant results can be obtained in these areas without the need for deep learning, though that can and is being usefully applied in areas like machine translation or artificial writing.

Machine learning can be either supervised or unsupervised. In supervised learning, positive and (often) negative training examples are presented to the learning algorithm in order to create a model to produce the desired results for the given context. No training examples are presented in unsupervised learning; rather, the model is derived from patterns discovered in the absence of training examples, sometimes described as finding hidden patterns in unlabeled data. Supervised methods are generally more accurate than unsupervised methods, and nearly universally so in the realm of content information and knowledge.

There is effort and expense associated with creating positive or negative training examples (sets). This effort can span from the maximum of ones completely constructed manually to ones that are semi-automatic (semi-supervised) or to ones informed by knowledge bases (weakly supervised or distant supervised [1], [2]). Creation of manual training sets may consume as much as 80% of overall efforts in some cases, and is always a time-consuming task whenever employed. The accuracy of the eventual models is only as good as the trueness of the input training sets, with traditionally the best results coming from manually determined training sets; the best of those are known as “gold standards.” The field of machine learning is thus broad and multiple methods span these spectra of effort and accuracy.

The Spectrum of Machine Learning

To date, the state-of-the-art in machine learning for natural language processing and semantics, my realm, has been in distant supervision using knowledge bases like Freebase or Wikipedia to extract training sets for supervised learning [1]. Relatively clean positive and negative training sets may be created with much reduced effort over manually created ones. This is the current “sweet spot” in the accuracy v. effort trade-off for machine learning in my realm.

However, as employed to date, distant supervision has mostly been a case-by-case, problem-by-problem approach, and most often applied to entity or relation extraction. Yes, knowledge bases may be inspected and manipulated to create the positive and negative training examples needed, but this effort has heretofore not been systematic in approach nor purposefully applied across a range of ML applications. How to structure and use knowledge bases across a range of machine learning applications with maximum accuracy and minimum effort, what we call knowledge supervision, is the focus of this article. The methods of knowledge supervision are how we make operational the objectives of knowledge-based artificial intelligence. This article is thus one of the foundations to my recent series on KBAI [3].

Features and Training Sets

Features and training sets, in relation to the specific machine learning approaches that are applied, are the major determinants to how successful the learning actually is. We already touched upon the trade-offs in effort and accuracy associated with training sets, and will provide further detail on this question below. But features also pose trade-offs and require similar skill in selection and use.

In machine learning, a feature is a measurable property of the system being analyzed. A feature is equivalent to what is known as an explanatory variable in statistics. A feature, stated another way, is a measurable aspect of the system that provides predictive value for the state the system.

Features with high explanatory power independent of other features are favored, because each added feature adds a computational cost of some manner. Many features are correlated with one another; in these cases it is helpful to find the strongest signals and exclude the other correlates. Too many features also make tuning and refinement more difficult, what has sometimes been called the curse of dimensionality. Overfitting is also often a problem, which limits the ability of the model to generalize to other data.

Yet too few features and there is inadequate explanatory power to achieve the analysis objectives.

Though it is hard to find discussion of best practices in feature extraction, striking this balance is an art [4]. Multiple learners might also be needed in order to capture the smallest, independent (non-correlated) feature set with the highest explanatory power [5].

When knowledge bases are used in distant supervision, only a portion of their structure or content is used as features. Still other distant supervision efforts may be geared to other needs and use a different set of features. Indeed, broadly considered, knowledge bases (potentially) have a rich diversity of possible features arising from:

text, and its content, syntax, semantics and morphology
use vectors of co-occurring terms or concepts
categories
conventions
synonyms
linkages
mappings
relations
attributes
content placement within its knowledge graph, and
disjointednesses.

An understanding of the features potential for knowledge bases is the first mindset of moving toward more purposeful knowledge supervision. At Structured Dynamics we stage the structured information as RDF triples and OWL ontologies, which we can select and manipulate via APIs and SPARQL. We also stage the graph structure and text in Lucene, which gives us powerful faceted search and other advanced NLP manipulations and analyses. These same features may also be utilized to extend the features set available from the knowledge base through such actions as new entity, attribute, or relation extractions; fine-grained entity typing [6]; creation of word vectors or tensors; results of graph analytics; forward or backward chaining; efficient processing structures; etc.

Because all features are selectable via either structured SPARQL query or faceted search, it is also possible to more automatically extract positive and negative training sets. Attention to proper coverage and testing of disjointedness assertions is another purposeful step useful to knowledge supervision, since it aids identification of negative examples for the training.

Whatever the combination of ML method, feature set, or positive or negative training sets, the ultimate precision and accuracy of knowledge supervision requires the utmost degree of true results in both positive and negative training sets. Training to inaccurate information merely perpetuates inaccurate information. As anyone who has worked extensively with source knowledge bases such as Freebase, DBpedia or Wikipedia may attest, assignment errors and incomplete typing and characterizations are all too common. Further, none provide disjointedness assertions.

Thus, the system should be self-learning with results so characterized as to be fed automatically to further testing and refinement. As better quality and more features are added to the system, we produce what we have shown before [3], as the virtuous circle of KBAI:

Features and training sets may thus be based on the syntax, morphology, semantics (meaning of the data) or relationships (connections) of the source data in the knowledge base. Continuous testing and the application of the system’s own machine learners creates a virtuous feedback where the accuracy of the overall system is constantly and incrementally improved.

Manifest Applications for Knowledge Supervision

The artificial intelligence applications to which knowledge supervision may be applied are manifest. Here is a brief listing of some of those areas as evidenced by distant supervision applied to machine learning in academic research, or others not yet exploited:

entity identification (recognition) and extraction
attribute identification and extraction (“slot filling”)
relation identification and extraction
event identification and extraction
entity classifiers
phrase (n-gram) identification
entity linkers
mappers
topic clusterers
topic classifiers
disambiguators
duplicates removal
semantic relatedness
inference and reasoning
sub-graph extraction
ontology matchers
ontology mappers
sentiment analysis
question answering
recommendation systems
language translation
multi-language versions
artificial writing, and
ongoing knowledge base improvements and extensions.

These areas are listed in rough order from the simpler to the more complex analyses. Most distant supervision efforts to date have concentrated on information extraction, the first items shown on the list. But all of these are amenable to knowledge supervision with ML. Since 2009, many of the insights regarding these potentials have arisen from the Knowledge Base Population initiative of the Text Analysis Conference [7].

Mapping and linkage are essential areas on this list since they add greatly to the available feature set and provide the bases for greater information interoperability. This is the current emphasis of Structured Dynamics.

Knowledge Supervision is Purposeful and Systematic

Knowledge supervision is the purposeful structuring and use of knowledge bases to provide features and training sets for multiple kinds of machine learners, which in combination can be applied to multiple artificial intelligence outcomes. Knowledge supervision is the method by which knowledge-based artificial intelligence, or KBAI, is achieved.

None of this is free, of course. Much purposeful work is necessary to configure and stage the data structures and systems that support the broad application of knowledge supervision. And other questions and challenges related to KBAI also remain. Yet, as Pedro Domingos has stated [4]:

“And the organizations that make the most of machine learning are those that have in place an infrastructure that makes experimenting with many different learners, data sources and learning problems easy and efficient, and where there is a close collaboration between machine learning experts and application domain ones.”

Having the mindset and applying the methods of knowledge supervision produces an efficient, repeatable, improvable infrastructure for active learning about the enterprise’s information assets.

As noted, we are just at the beginnings of knowledge supervision, and best practices and guidelines are still in the formative stages. We also have open questions and challenges in how features can be effectively selected; how KB-trained classifiers can be adopted to the wild; how we can best select and combine existing machine learners to provide an ML infrastructure; where and how deep learning should most effectively be applied; and how other emerging insights in computational linguistics can be combined with knowledge supervision [8].

But we can already see that a purposeful mindset coupled with appropriate metadata and structured RDF data is a necessary grounding to the system. We can see broad patterns across the areas of information extraction involving concepts, entities, relations, attributes and events that can share infrastructure and methods. We realize that linkage and mapping are key enabling portions of the system. The need for continuous improvement and codification of self-learning are the means by which our systems will get more accurate.

So, with the what of knowledge-based artificial intelligence, we can now add some broad understandings of the how based on knowledge supervision. None of these ideas are unique or new unto themselves. But the central role of knowledge bases in KBAI and knowledge supervision represents an important advance of artificial intelligence to deal with real-world challenges in content and information.

[1] Distant supervision was earlier or alternatively called self-supervision, indirect supervision or weakly-supervised. It is a method to use knowledge bases to label entities automatically in text, which is then used to extract features and train a machine learning classifier. The knowledge bases provide coherent positive training examples and avoid the high cost and effort of manual labelling. The method is generally more effective than unsupervised learning, though with similar reduced upfront effort. Large knowledge bases such as Wikipedia or Freebase are often used as the KB basis.

The first acknowledged use of distant supervision was Craven and Kumlien in 1999 (Mark Craven and Johan Kumlien. 1999. “Constructing Biological Knowledge Bases by Extracting Information from Text Sources,” in ISMB, vol. 1999, pp. 77-86. 1999; source of weak supervision term.)); the first use of the formal term distant supervision was in Mintz et al. in 2009 (Mike Mintz, Steven Bills, Rion Snow, Dan Jurafsky, 2009. “Distant Supervision for Relation Extraction without Labeled Data,” in Proceedings of the 47th Annual Meeting of the ACL and the 4th IJCNLP of the AFNLP, pages 1003–1011, Suntec, Singapore, 2-7 August 2009). Since then, the field has been a very active area of research; see next reference.

[2] See M. K. Bergman, 2015. “Forty Seminal Distant Supervision Articles,” from AI3:::Adaptive Information blog, November 17, 2014, as supplemented by [3].

[3] See M. K. Bergman, 2014. “Knowledge-based Artificial Intelligence,” from AI3:::Adaptive Information blog, November 17, 2014.

[4] Pedro Domingos, 2012. “A Few Useful Things to Know About Machine Learning.” Communications of the ACM 55, no. 10 (2012): 78-87.

[5] There is a rich literature providing guidance on feature selection and feature extraction. Feature extraction creates new features from functions of the original features, whereas feature selection returns a subset of the available features. It is also possible to apply methods, the best known and simplest being principal component analysis, among many, to reduce feature size (dimensionality) with acceptable loss in accuracy.

[6] As a good introduction and overview, see Xiao Ling and Daniel S. Weld, 2012. “Fine-Grained Entity Recognition,” in Proceedings of the 26th AAAI Conference on Artificial Intelligence, 2012. You can also search on the topic in Google Scholar.

[7] TAC is organized by the National Institute of Standards and Technology (NIST). Initiated in 2008, TAC grew out of NIST’s Document Understanding Conference (DUC) for text summarization, and the Question Answering Track of the Text Retrieval Conference (TREC). TAC is overseen by representatives from government, industry, and academia. The Knowledge Base Population tracks of TAC were started in 2009 and continue to today.

[8] See, for example, Percy Liang and Christopher Potts, 2015. “Bringing Machine Learning and Compositional Semantics Together.” Annu. Rev. Linguist. 1, no. 1 (2015): 355-376.

Posted:June 8, 2015

Logical Implications of Interoperability

What Began as Data Integration Implies So Much More

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Oh, it was probably two or three years ago that one of our clients asked us to look into single-source authoring, or more broadly what has come to be known as COPE (create once, publish everywhere), as made prominent by Daniel Jacobson of NPR, now Netflix. We also looked closely at the question of formats and workflows that might increase efficiencies or lower costs in the quest to grab and publish content.

Then, of course, about the same time, it was becoming apparent that standard desktop and laptop screens were being augmented with smartphones and tablets. Smaller screen aspects require a different interface layout and interaction; but, writing for specific devices was a losing proposition. Responsive Web design and grid layout templates that could bridge different device aspects have now come to the fore.

Though it has been true for some time that different publishing venues — from the Web to paper documents or PDFs — have posed a challenge, these other requirements point to a broader imperative. I have intuitively felt there is a consistent thread at the core of these emerging device, use and publishing demands, but the common element has heretofore eluded me.

For years — decades, actually — I have been focused on the idea of data interoperability. My first quest was to find a model that could integrate text stories and documents with structured data from conventional databases and spreadsheets. My next quest was to find a framework that could relate context and meaning across multiple perspectives and world views. Though it took awhile, and which only began to really take shape about a decade ago, I began to focus on RDF and general semantic Web principles for providing this model.

Data integration though open, semantic Web standards has been a real beacon for how I have pursued this quest. The ideal of being able to relate disparate information from multiple sources and viewpoints to each other has been a driving motivation in my professional interests. In analyzing the benefits of a more connected world of information I could see efficiencies, reduced costs, more global understandings, and insights from previously hidden connections.

Yet here is the funny thing. I began to realize that other drivers for how to improve knowledge worker efficiencies or to deploy results to different devices and venues share the same justifications as data integration. Might there not be some common bases and logic underlying the interoperability imperative? Is not data interoperability but a part of a broader mindset? Are there some universal principles to derive from an inspection of interoperability, broadly construed?

In this article I try to follow these questions to some logical ends. This investigation raises questions and tests from the global — that is, information interoperability — to the local and practical in terms of notions such as create once, use everywhere, and have it staged for relating and interoperability. I think we see that the same motivators and arguments for relating information apply to the efficient ways to organize and publish that information. I think we also see that the idea of interoperability is systemic. Fortunately, meaningful interoperability can be achieved across-the-board today with application of the right mindsets and approaches. Below, I also try to set the predicates for how these benefits might be realized by exploring some first principles of interoperability.

What is Interoperability?

So, what is interoperability and why is it important?

So-called enterprise information integration and interoperability seem to sprout from the same basic reality. Information gets created and codifed across multiple organizations, formats, storage systems and locations. Each source of this information gets created with its own scope, perspective, language, characteristics and world view. Even in the same organization, information gets generated and characterized according to its local circumstances.

In the wild, and even within single organizations, information gets captured, represented, and characterized according to multiple formats and viewpoints. Without bridges between sources that make explicit the differences in format and interpretation, we end up with what — in fact — is today’s reality of information stovepipes. The reality of our digital information being in isolated silos and moats results in duplicate efforts, inefficiencies, and lost understandings. Despite all of the years and resources thrown at information generation, use and consumption, our digital assets are unexploited to a shocking extent. The overarching cause for this dereliction of fiscal stewardship is the lack of interoperability.

By the idea of interoperability we are getting at the concept of working together. Together means things are connected in some manner. Working means we can mesh the information across sources to do more things, or do them better or more cheaply. Interoperability does not necessarily imply integration, since our sources can reside in distributed locations and formats. What is important is not the physical location — or, indeed, even format and representations — but that we have bridges across sources that enable the source information to work together.

In working backwards from this observation, then, we need certain capabilities to fulfill these interoperability objectives. We need to be able to ingest multiple encodings, serializations and formats. Because we need to work with this information, and tools for doing so are diverse, we also need the ability to export information in multiple encodings, serializations and formats. Human circumstance means we need to ingest and encode this information in multiple human languages. Some of our information is more structured, and describes relationships between things or the attributes or characterizations of particular types of things. Since all of this source information has context and provenance, we need to capture these aspects as well in order to ascertain the meaning and trustworthiness of the information.

This set of requirements is a lot of work, which can most efficiently be done against one or a few canonical representations of the input information. From a data integration perspective, then, the core system to support, store and manage this information should be based on only a few central data representations and models, with many connectors for ingesting native information in the wild and tools to support the core representations:

A Data Flow Perspective on Interoperability

In our approach at Structured Dynamics we have chosen the Resource Description Framework (RDF) as the structured data model at the core of the system [1], supported by the Lucene text engine for full-text search and efficient facet searching. Because all of the information is given unique Web identifiers (URIs), and the whole system resides on the Web accessible via the HTTP protocol, our information may reside anywhere the Internet connects.

This gives us a data model and a uniform way to represent the input data across structured, semi-structured and unstructured sources. Further, we have a structure that can capture the relations or attributes (including metadata and provenance) of the input information. However, one more step is required to achieve data interoperability: an understanding of the context and meaning of the source information.

To achieve the next layer in the data interoperability pyramid [2] it is thus necessary to employ semantic technologies. The structure of the RDF data model has an inherent expressiveness to capture meaning and context. To this foundation we must add a coherent view of the concepts and entity types in our domain of interest, which also enables us to capture the entities within this system and their characteristics and relationships to other entities and concepts. These properties applied to the classes and instances in our domain of interest can be expressed as a knowledge graph, which provides the logical schema and inferential framework for our domain. This stack of semantic building blocks gets formally expressed as ontologies (the technical term for a working graph) that should putatively provide a coherent representation of the domain at hand.

We can visualize this semantic stack as follows:

A Semantics Perspective of Interoperability

We have been using the spoke-and-hub diagram above for data flows for some years and have used the semantic stack representation before, too. I believe in my bones the importance of data interoperability to competitive advantage for enterprises, and therefore its business worth as a focus of my company’s technology. But, once so considered, some more fundamental questions emerge. What makes data interoperability a worthwhile objective? Can an understanding of those objectives bring us more fundamental understandings of fundamental benefits? Does a grounding in more fundamental benefits suggest any change in our development priorities?

Drivers of Interoperability

I think we can boil the drivers of interoperability down to four. These are:

Efficiency — literally trillions are spent globally each year in the research, creation, re-use, publishing, storing and browsing of information [3]. Yet relevant information is hard to find, and sometimes obscure information is overlooked. The lack of reuse of prior good content because it is not discoverable is unconscionable given today’s technologies. The base productivity of information use is low;
Cost — missed information or lack of awareness of relevant information leads to increased time, increased direct costs (labor and material), and increased indirect costs. Awareness, understanding and re-use of existing information would save millions or more for brand-name firms [3] annually if these interoperability gaps were overcome;
Insight — drawing connections between previously unconnected things and enabling discovery are essential inputs to innovation, itself the overall driver of productivity (and, therefore, wealth) gains. The reinforcing leverage of interoperability resides in its ability to bring new understandings and insights; and
Capture — simply being able to include the 80% of extant information contained in text is a huge first step to interoperability, but grounding the system in the inherent connectedness of the Web means that all kinds of fields + streams, APIs, mappings, DBs, datasets, Web content, on-the-fly discoveries, and device sensors through the Internet of things (IoT) can be captured to contribute to our insights.

To be sure, data interoperability is focused on insight. But data interoperability also brings efficiency and cost reductions. As we add other aspects of interoperability — say, responsive design for mobile — we may see comparatively fewer benefits in insight, but more in efficiency, cost, and, even, capture. Anything done to increase benefits from any of these drivers contributes to the net benefits and rationale for interoperability.

Principles of Interoperability

The general goodness arising from interoperability suggests it is important to understand the first principles underlying the concept. By understanding these principles, we can also tease out the fundamental areas deserving attention and improvement in our interoperability developments and efforts. These principles help us cut through the crap in order to see what is important and deserves attention.

I think the first of the first principles for interoperability is reusability. Once we have put the effort into the creation of new valuable data or content, we want to be able to use and apply that knowledge in all applicable venues. Some of this reuse might be in chunking or splitting the source information into parts that can be used and deployed for many purposes. Some of this reuse might be in repurposing the source data and content for different presentations, expressions or devices. These considerations imply the importance of storing, characterizing, structuring and retrieving information in one or a few canonical ways.

Interoperable content and forms should also aspire to an ideal of “onceness“. The ideal is that the efforts to gather, create or analyze information be done as few times as possible. This ideal clearly ties into the principle of reusabilty because that must be in place to minimize duplication and overlooking what exists. The reason to focus on onceness is that it forces an explication of the workflows and bottlenecks inherent to our current work practices. These are critical areas to attack since, unattended, such inefficiencies provide the “death by a thousand cuts” to interoperability. Onceness is at the center of such compelling ideas as COPE and the role of APIs in a flexible architecture (see below) to promote interoperability.

A respect for workflows is also a first principle, expressed in two different ways. The first way is that existing workflows can not be unduly disrupted when introducing interoperability improvements. While workflows can be improved or streamlined over time — and should — initial introduction and acceptance of new tools and practices must fit with existing ways of doing tasks in order to see adoption. Jarring changes to existing work practices are mostly resisted. The second way that workflows are a first principle is in the importance of being aware of, explicitly modeling, and then codifying how we do tasks. This becomes the “language” of our work, and helps define the tooling points or points of interaction as we merge activities from multiple disciplines in our domain. These workflow understandings also help us identify useful points for APIs in our overall interoperability architecture.

These considerations provide the rationale for assigning metadata [4] that characterize our information objects and structure, based on controlled vocabularies and relationships as established by domain and administrative ontologies [5]. In the broadest interoperability perspective, these vocabularies and the tagging of information objects with them are a first principle for ensuring how we can find and transition states of information. These vocabularies need not be complex or elaborate, but they need to be constant and consistent across the entire content lifecycle. There are backbone aspects to these vocabularies that capture the overall information workflow, as well as very specific steps for individual tasks. As a complement to such administrative ontologies, domain ontologies provide the context and meaning (semantics) for what our information is about.

The common grounding of data model and semantics means we can connect our sources of information. The properties that define the relationships between things determine the structure of our knowledge graph. Seeking commonalities for how our information sources relate to one another helps provide a coherent graph for drawing inferences. How we describe our entities with attributes provides a second type of property. Attribute profiles are also a good signal for testing entity relatedness. Properties — either relations or attributes — provide another filter to draw insight from available information.

If the above sounds like a dynamic and fluid environment, you would be right. Ultimately, interoperability is a knowledge challenge in a technology environment that is rapidly changing. New facts, perspectives, devices and circumstances are constantly arising. For these very reasons an interoperability framework must embrace the open world assumption [6], wherein the underlying logic structure and its vocabulary and data can be grown and extended at will. We are seeing some breakaway from conventional closed-world thinking of relational databases with NoSQL and graph databases, but a coherent logic based on description logics, such as is found with open standard semantic technologies like RDF and OWL and SPARQL, is even more responsive.

Though perhaps not quite at the level of a first principle, I also think interoperability improvements should be easy to use, easy to share, and easy to learn. Tooling is clearly implied in this, but also it is important we be able to develop a language and framing for what constitutes interoperability. We need to be able to talk about and inspect the question of interoperability in order to discover insights and gain efficiencies.

Aspects of Interoperability

The thing about interoperability is that it extends over all aspects of the information lifecycle, from capturing and creating information, to characterizing and vetting it, to analyzing it, or publishing or distributing it. Eventually, information and content already developed becomes input to new plans or requirements. These aspects extend across multiple individuals and departments and even organizations, with portions of the lifecycle governed (or not) by their own set of tools and practices. We can envision this overall interoperability workflow something like the following [7]:

A Generalized Workflow Perspective of Interoperability

Overall, only pieces of this cycle are represented in most daily workflows. Actually, in daily work, parts of this workflow are much more detailed and involved than what this simplistic overview implies. Editorial review and approvals, or database administration and management, or citation gathering or reference checking, or data cleaning, or ontology creation and management, or ETL activities, or hundreds of other specific tasks, sit astride this general backbone.

Besides showing that interoperability is a systemic activity for any organization (or should be), we can also derive a couple of other insights from this figure. First, we can see that some form of canonical representation and management is central to interoperability. As noted, this need not be a central storage system, but can be distributed using Web identifiers (URIs) and protocols (HTTP). Second, we characterize and tag our information objects using ontologies, both from structural and administrative viewpoints, but also by domain and meaning. Characterizing our information by a common semantics of meaning enables us to combine and analyze our information.

A third insight is that a global schema specific to workflows and information interoperability is the key for linking and combining activities at any point within the cycle. A common vocabulary for stages and interoperability tasks, included as a best practice for our standard tagging efforts, provides the conventions for how batons can get passed between activities at any stage in this cycle. The challenge of making this insight operational is one more of practice and governance than of technology. Inspecting and characterizing our information workflows with a common vocabulary and understanding needs to be a purposeful activity in its own right, backed with appropriate management attention and incentives.

A final insight is that such a perspective on interoperability is a bit of a fractal. As we get more specific in our workflows and activities, we can apply these same insights in order to help those new, more specific workflows become interoperable. We can learn where to plug into this structure. And, we can learn how our specific activities through the application of explicit metadata and tags with canonical representations can work to interact well with other aspects of the content lifecycle.

Interoperability can be achieved today with the right mindsets and approaches. Fortunately, because of the open world first principle, this challenge can be tackled in an incremental, piecemeal manner. While the overall framework provides guidance for where comprehensive efforts across the organization may go, we can also cleave off only parts of this cycle for immediate attention, following a “pay as you benefit” approach [8]. A global schema and a consistent approach to workflows and information characterizations can help ensure the baton is properly passed as we extend our interoperability guidance to other reaches of the enterprise.

General Architecture and a Sample Path

We can provide a similar high-level view for what an enterprise information architecture supporting interoperability might look like. We can broadly layer this architecture into content acquisition, representation and repository, and content consumption:

An Architectural Perspective of Interoperability

Content of all forms — structured, semi-structured and unstructured — is brought into the system and tagged or mapped into the governing domain or administrative schema. Text content is marked up with reduced versions of HTML (such as RASH [9] or Markdown [10]) in order to retain the author’s voice and intent in areas such as emphasis, titles or section headers; the structure of the content is also characterized by patterned areas such as abstracts, body and references. All structured data is characterized according to the RDF data model, with vocabularies as provided by OWL in some cases.

We already have an exemplar repository in the Open Semantic Framework [11] that shows the way (along with other possible riffs on this theme) for how just a few common representations and conventions can work to distribute both schema and information (data) across a potentially distributed network. Further, by not stopping at the water’s edge of data interoperability, we can also embrace further, structural characterization of our content. Adding this wrinkle enables us to efficiently support a variety of venues for content consumption simultaneously.

This architecture is quite consistent with what is known as WOA (for Web-oriented architecture) [12]. Like the Internet itself, WOA has the advantage of being scalable and distributed, all (mostly) based on open standards. The interfaces between architectural components are also provided though mostly RESTful application programming interfaces (APIs), which extends interoperability to outside systems and provides flexibility for swapping in new features or functionality as new components or developments arise. Under this design, all components and engines become in effect “black boxes”, with information exchange via standard vocabularies and formats using APIs as the interface for interoperability.

A Global Context for Interoperability

Though data interoperability is a large and central piece, I hope I have demonstrated that interoperability is a much broader and far-reaching concept. We can see that “global interoperability” extends into all aspects of the information lifecycle. By expanding our viewpoint of what constitutes interoperability, we have discovered some more general principles and mindsets that can promise efficiencies, lower costs and greater insights across the enterprise.

An explicit attention to workflows and common vocabularies for those flows and the information objects they govern is a key to a more general understanding of interoperability and the realization of its benefits. Putting this kind of infrastructure in place is also a prerequisite to greater tooling and automation in processing information.

We can already put in place chains of tooling and workflows governed by these common vocabularies and canonical representations to achieve a degree of this interoperability. We do not need to tackle the whole enchilada at once or mount some form of “big bang” initiative. We can start piecemeal, and expand as we benefit. The biggest gaps remain codification of workflows in relation to the overall information lifecycle, and the application of taggers to provide the workflow and structure metadata at each stage in the cycle. Again, these are not matters so much of technology or tooling, but policy and information governance.

What I have outlined here provides the basic scaffolding for how such an infrastructure to promote interoperability may evolve. We know how we do our current tasks; we need to understand and codify those workflows. Then, we need to express our processing of information at any point along the content lifecycle. A number of years back I discussed climbing the data interoperability pyramid [2]. We have made much progress over the past five years and stand ready to take our emphasis on interoperability to the next level.

To be sure there is much additional tooling still needed, mostly in the form of mappers and taggers. But the basic principles, core concepts and backbone tools for supporting greater interoperability are known and relatively easy to put in place. Embracing the mindset and inculcating this process into our general information management routines is the next challenge. Working to obtain the ideal is doable today.

[1] See M. K. Bergman, 2009. “Advantages and Myths of RDF,” from AI3:::Adaptive Information blog, April 8, 2009.

[2] See M. K. Bergman, 2006. “Climbing the Data Federation Pyramid,” from AI3:::Adaptive Information blog, April 8, 2009.

[3] See M. K. Bergman, 2005. “Untapped Assets: The $3 Trillion Value of U.S. Enterprise Documents,” from AI3:::Adaptive Information blog, July 20, 2005.

[4] See M. K. Bergman, 2010. “I Have Yet to Metadata I Did’t Like,” from AI3:::Adaptive Information blog, August 16, 2010.

[5] See M. K. Bergman, 2011. “An Ontologies Architecture for Ontology-driven Apps,” from AI3:::Adaptive Information blog, December 5, 2011. Ontologies

[6] See M. K. Bergman, 2009. “The Open World Assumption: Elephant in the Room,” from AI3:::Adaptive Information blog, December 21, 2009.

[7] Some sources that helped form my thoughts on the information lifecycle include Backbone Media and Piktochart.

[8] See M. K. Bergman, 2010. “‘Pay as You Benefit’: A New Enterprise IT Strategy,” from AI3:::Adaptive Information blog, July 12, 2010.

[9] See Silvio Peroni, 2015. “RASH: Research Articles in Simplified HTML,” March 15, 2015.

[10] Many Markdown options exist for a reduced subset of HTML; one in this vein is Scholarly Markdown.

[11] The Open Semantic Framework has its own Web site (http://opensemanticframework.org/), supported by a wiki of more than 500 supporting technical articles (http://wiki.opensemanticframework.org/index.php/Main_Page).

[12] See M. K. Bergman, 2009. “A Generalized Web-oriented Architecture (WOA) for Structured Data,” from AI3:::Adaptive Information blog, May 3, 2009.

Posted:May 28, 2015

Pulse: Articles Chosen for Text Analytics

I was pleasantly surprised to discover that a diversity of my writings has been chosen for the syllabus for a text analytics course by Dr. Alianna Maren in Northwestern University’s master program in predictive analytics. Dr. Maren has chosen to feature some of my writings in NLP statistics, ontologies, and the open world assumption.

Dr. Maren has stated her intention is to present text analytics from a “top-down ontological perspective.” The syllabus looks very interesting.

I appreciate the recognition and wish the students and Dr. Maren a great course!

Posted:May 18, 2015

A Primer on Knowledge Statistics

Trying to Cut Through the Terminology Confusion and Offer Simple Guidelines

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Semantics is a funny thing. All professionals come to know that communication with their peers and outside audiences requires accuracy in how to express things. Yet, even with such attentiveness, communications sometimes go awry. It turns out that background, perspective and context can all act to switch circuits at the point of communication. Despite, and probably because of, our predilection as a species to classify and describe things, all from different viewpoints, we can often exhort in earnest a thought that is communicated to others as something different from what we intended. Alas!

This reality is why, I suspect, we have embraced as a species things like dictionaries, thesauri, encyclopedias, specifications, standards, sacred tracts, and such, in order to help codify what our expressions mean in a given context. So, yes, while sometimes there is sloppiness in language and elocution, many misunderstandings between parties are also a result of difference in context and perspective.

It is important when we process information in order to identify relations or extract entities, to type them or classify them, or to fill out their attributes, that we have measures to gauge how well our algorithms and tests work, all attentive to providing adequate context and perspective. These very same measures can also tell us whether our attempts to improve them are working or not. These measures, in turn, also are the keys for establishing effective gold standards and creating positive and negative training sets for machine learning. Still, despite their importance, these measures are not always easy to explain or understand. And, truth is, sometimes these measures may also be mis-explained or mis-calculated. Aiding the understanding of important measures in improving the precision, completeness, and accuracy of communications is my purpose in this article.

Some Basic Statistics as Typically Described

The most common scoring methods for gauging the “accuracy” of natural language communications involves statistical tests based on the nomenclature of negatives and positives, true or false. Sometimes it can be a bit confusing about how to interpret these terms, a confusion which can be made all the more difficult in what kind of statistical environment is at play. Let me try to first confuse, and then more simply explain these possible nuances.

Standard science is based on a branch of statistics known as statistical hypothesis testing. This is likely the statistics that you were taught in school. In hypothesis testing, we begin with a hypothesis about what might be going on with respect to a problem or issue, but for which we do not know the cause or truth. After reviewing some observations, we formulate a hypothesis that some factor A is affecting or influencing factor B. We then formulate a mirror-image null hypothesis that specifies that factor A does not affect factor B; this is what we will actually test. The null hypothesis is what we assume the world in our problem context looks like, absent our test. If the test of our formulated hypothesis does not affect that assumed distribution, then we reject our alternative (meaning our initial hypothesis fails, and we keep the null explanation).

We make assumptions from our sample about how the entire population is distributed, which enables us to choose a statistical model that captures the shape of assumed probable results for our measurement sample. These shapes or distributions may be normal (bell-shaped or Gaussian), binomial, power law, or many others. These assumptions about populations and distribution shapes then tell us what kind of statistical test(s) to perform. (Misunderstanding the true shape of the distribution of a population is one of the major sources of error in statistical analysis.) Different tests may also give us more or less statistical power to test the null hypothesis, which is that chance results will match the assumed distribution. Different tests may also give us more than one test statistic to measure variance from the null hypothesis.

We then apply our test and measure and collect our sample from the population, with random or other statistical sampling important so as not to skew results, and compare the distribution of these results to our assumed model and test statistic(s). The null hypothesis is confirmed or not by whether the shape of our sampled results matches the assumed distribution or not. The significance of the variance from the assumed shape, along with a confidence interval based on our sample size and the test at hand, provides the information necessary to either accept or reject the null hypothesis.

Rejection of the null hypothesis generally requires both significant difference from the expected shape in our sample and a high level of confidence. Absent those results, we likely need to accept the null hypothesis, thus rejecting the alternative hypothesis that some factor A is affecting or influencing factor B. Alternatively, with significant differences and a high level of confidence, we can reject the null hypothesis, thereby accepting the alternative hypothesis (our actual starting hypothesis, which prompted the null) that factor A is affecting or influencing factor B.

This is all well and good except for the fact that either the sampling method or our test may be in error. There are two types of errors that are possible: Type I errors, where a positive result corresponds to rejecting the null hypothesis; and Type II errors, where a negative result corresponds to not rejecting the null hypothesis.

We can combine all of these thoughts into what is the standard presentation for capturing these true and false, positive and negative, results [1]:

		Null hypothesis (H₀) is
		Valid/True	Invalid/False
Judgment of Null Hypothesis (H₀)	Reject	False Positive Type I error	True Positive Correct inference
Judgment of Null Hypothesis (H₀)	Fail to reject (accept)	True negative Correct inference	False negative Type II error

Clear as mud, huh?

Let’s Apply Some Simplifications

Fortunately, there are a couple of ways to sharpen this standard story in the context of information retrieval (IR), natural language processing (NLP) and machine learning (ML) — the domains of direct interest to us at Structured Dynamics — to make understanding all of this much simpler. Statistical tests will always involve a trade off between the level of false positives (in which a non-match is declared to be a match) and the level of false negatives (in which an actual match is not detected) [1]. Let’s see if we can simplify our recognition and understanding of these conditions.

First, let’s start with a recent explanation from the KDNuggets Web site [2]:

“Imagine there are 100 positive cases among 10,000 cases. You want to predict which ones are positive, and you pick 200 to have a better chance of catching many of the 100 positive cases. You record the IDs of your predictions, and when you get the actual results you sum up how many times you were right or wrong. There are four ways of being right or wrong:

TN / True Negative: case was negative and predicted negative
TP / True Positive: case was positive and predicted positive
FN / False Negative: case was positive but predicted negative
FP / False Positive: case was negative but predicted positive.”

The use of ‘case’ and ‘predictions’ help, but are still a bit confusing. Let’s hear another explanation from Benjamin Roth from his recently completed thesis [3]:

“There are two error cases when extracting training data: false positive and false negative errors. A false positive match is produced if a sentence contains an entity pair for which a relation holds according to the knowledge base, but for which the sentence does not express the relation. The sentence is marked as a positive training example for the relation, however it does not contain a valid signal for it. False positives introduce errors in the training data from which the relational model is to be generalized. For most models false positive errors are the most critical error type, for qualitative and quantitative reasons, as will be explained in the following.

“A false negative error can occur if a sentence and argument pair is marked as a negative training example for a relation (the knowledge base does not contain the argument pair for that relation), but the sentence actually expresses the relation, and the knowledge base was incomplete. This type of error may negatively influence model learning by omitting potentially useful positive examples or by negatively weighting valid signals for a relation.”

In our context, we can see a couple of differences from traditional scientific hypothesis testing. First, the problems we are dealing with in IR, NLP and ML are all statistical classification problems, specifically in binary classification. For example, is a given text token an entity or not? What type amongst a discrete set is it? Does the token belong to a given classification or not? This makes it considerably easier to posit an alternative hypothesis and the shape of its distribution. What makes it binary is the decision as to whether a given result is correct or not. We now have a different set of distributions and tests from more common normal distributions.

Second, we can measure our correct ‘hits’ by applying our given tests to a “gold standard” of known results. This gold standard provides a representative sample of what our actual population looks like, one we have characterized in advance whether all results in the sample are true or not for the question at hand. Further, we can use this same gold standard over and over again to gauge improvements in our test procedures.

Combining these thoughts leads to a much simpler matrix, sometimes called a confusion matrix in this context, for laying out the true and false, positive and negative characterizations:

Correctness	Test Assertion
Correctness	Positive	Negative
True	TP True Positive	TN True Negative
False	FP False Positive	FN False Negative

As we can see, ‘positive’ and ‘negative’ are simply the assertions (predictions) arising from our test algorithm of whether or not there is a match or a ‘hit’. ‘True’ and ‘false’ merely indicate whether these assertions proved to be correct or not as determined by gold standards or training sets. A false positive is a false alarm, a “crying wolf”; a false negative is a missed result. Thus, all true results are correct; all false are incorrect.

Key Information Retrieval Statistics

Armed with these four characterizations — true positive, false positive, true negative, false negative — we now have the ability to calculate some important statistical measures. Most of these IR measures also have exact analogs in standard statistics, which I also note.

The first metric captures the concept of coverage. In standard statistics, this measure is called sensitivity; in IR and NLP contexts it is called recall. Basically it measures the ‘hit’ rate for identifying true positives out of all potential positives, and is also called the true positive rate, or TPR:

$\mathit{TPR} = \mathit{TP} / P = \mathit{TP} / (\mathit{TP}+\mathit{FN})$

Expressed as a fraction of 1.00 or a percentage, a high recall value means the test has a high “yield” for identifying positive results.

Precision is the complementary measure to recall, in that it is a measure for how efficient whether positive identifications are true or not:

$\text{precision}=\frac{\text{number of true positives}}{\text{number of true positives}+\text{false positives}}$

Precision is something, then, of a “quality” measure, also expressed as a fraction of 1.00 or a percentage. It provides a positive predictive value, as defined as the proportion of the true positives against all the positive results (both true positives and false positives).

So, we can see that recall gives us a measure as to the breadth of the hits captured, while precision is a statement of whether our hits are correct or not. We also see, as in the Roth quote above, why false positives need to be a focus of attention in test development, because they directly lower precision and efficiency of the test.

This recognition that precision and recall are complementary and linked is reflected in one of the preferred overall measures of IR and NLP statistics, the F-score, which is the adjusted (beta) mean of precision and recall. The general formula for positive real β is:

$F_\beta = (1 + \beta^2) \cdot \frac{\mathrm{precision} \cdot \mathrm{recall}}{(\beta^2 \cdot \mathrm{precision}) + \mathrm{recall}}$ .

which can be expressed in terms of TP, FN and FP as:

$F_\beta = \frac {(1 + \beta^2) \cdot \mathrm{true\ positive} }{(1 + \beta^2) \cdot \mathrm{true\ positive} + \beta^2 \cdot \mathrm{false\ negative} + \mathrm{false\ positive}}\,$

In many cases, the harmonic mean is used, which means a beta of 1, which is called the F₁ statistic:

$F_1 = 2 \cdot \frac{\mathrm{precision} \cdot \mathrm{recall}}{\mathrm{precision} + \mathrm{recall}}$

But F1 displays a tension. Either precision or recall may be improved to achieve an improvement in F₁, but with divergent benefits or effects. What is more highly valued? Yield? Quality? These choices dictate what kinds of tests and areas of improvement need to receive focus. As a result, the weight of beta can be adjusted to favor either precision or recall. Two other commonly used F measures are the F₂ measure, which weights recall higher than precision, and the F_0.5 measure, which puts more emphasis on precision than recall [4].

Another metric can factor into this equation, though accuracy is a less referenced measure in the IR and NLP realm. Accuracy is the statistical measure of how well a binary classification test correctly identifies or excludes a condition:

$\text{accuracy}=\frac{\text{number of true positives}+\text{number of true negatives}}{\text{number of true positives}+\text{false positives} + \text{false negatives} + \text{true negatives}}$

An accuracy of 100% means that the measured values are exactly the same as the given values.

All of the measures above simply require the measurement of false and true, positive and negative, as do a variety of predictive values and likelihood ratios. Relevance, prevalence and specificity are some of the other notable measures that depend solely on these metrics in combination with total population.

By bringing in some other rather simple metrics, it is also possible to expand beyond this statistical base to cover such measures as information entropy, statistical inference, pointwise mutual information, variation of information, uncertainty coefficients, information gain, AUCs and ROCs. But we’ll leave discussion of some of those options until another day.

Bringing It All Together

Courtesy of one of the major templates in Wikipedia in the statistics domain [5], for which I have taken liberties, expansions and deletions, we can envision the universe of statistical measures in IR and NLP, based solely on population and positives and negatives, true and false, as being:

		Condition (as determined by “Gold standard“)
	Total population	Condition positive	Condition negative	Prevalence = Σ Condition positive Σ Total population
Test Assertion	Test assertion positive	TP True positive	FP False positive (Type I error)	Positive predictive value (PPV), Precision = Σ True positive Σ Test outcome positive	False discovery rate (FDR) = Σ False positive Σ Test outcome positive
Test Assertion	Test assertion negative	FN False negative (Type II error)	TN True negative	False omission rate (FOR) = Σ False negative Σ Test outcome negative	Negative predictive value (NPV) = Σ True negative Σ Test outcome negative
	Accuracy (ACC) = Σ True positive + Σ True negative Σ Total population	True positive rate (TPR), Sensitivity, Recall = Σ True positive Σ Condition positive	False positive rate (FPR),Fall-out = Σ False positive Σ Condition negative	Positive likelihood ratio (LR+) = TPR FPR	F-score (F₁ case) = 2 x (Precision * Recall) (Precision + Recall)
		False negative rate (FNR) = Σ False negative Σ Condition positive	True negative rate (TNR), Specificity (SPC) = Σ True negative Σ Condition negative	Negative likelihood ratio (LR−) = FNR TNR

Please note that the order and location of TP, FP, FN and TN differs from my simple layout presented in the confusion matrix above. In the confusion matrix, we are gauging whether the assertion of the test is correct or not as established by the gold standard. In this current figure, we are instead using the positive or negative status of the gold standard as the organizing dimension. Use the shorthand identifiers of TP, etc., to make the cross reference between “correct” and “condition”.

Relationships to Gold Standards and Training Sets

These basic measures and understandings have two further important roles beyond informing how to improve the accuracy and peformance of IR and NLP algorithms and tests. The first is gold standards. The second is training sets.

Gold standards that themselves contain false positives and false negatives, by definition, immediately introduce errors. These errors make it difficult to test and refine existing IR and NLP algorithms, because the baseline is skewed. And, because gold standards also often inform training sets, errors there propagate into errors in machine learning. It is also important to include true negatives in a gold standard, in the likely ratio expected by the overall population, so that this complement of the accuracy measurement is not overlooked.

Once a gold standard is created, you then run your current test regime against it when you run your same tests againt unknowns. Preferably, of course, the gold standard only includes true positives and true negatives (that is, the gold standard is the basis for judging “correctness’; see confusion matrix above). In the case of running an entity recognizer, your results against the gold standard can take one of three forms: you either have open slots (no entity asserted); slots with correct entities; or slots with incorrect entities. Thus, here is how you would create the basis for your statistical scores:

TP = test identifies the same entity as in the gold standard
FP = test identifies a different entity than what is in the gold standard (including no entity)
TN = test identifies no entity; gold standard has no entity, and
FN = test identifies no entity, but gold standard has one.

As noted before, these measures are sufficient to calculate the precision, recall, F-score and accuracy statistics. Also note that the F v T and P v N correspond to the gold standard “correctness” and what is asserted by the test(s), per the confusion matrix.

We can apply this same mindset to the second additional, important role in creating and evaluating training sets. Both positive and negative training sets are recommended for machine learning. Negative training sets are often overlooked. Again, if the learning is not based on true positives and negatives, then significant error may be introduced into the learning.

Clean, vetted gold standards and training sets are thus a critical component to improving our knowledge bases going forward [6]. The very practice of creating gold standards and training sets needs to receive as much attention as algorithm development because, without it, we are optimizing algorithms to fuzzy objectives.

The virtuous circle that occurs between more accurate standards and training sets and improved IR and ML algorithms is a central argument for knowledge-based artificial intelligence (KBAI). Continuing to iterate better knowledge bases and validation datasets is a driving factor in improving both the yield and quality from our rapidly expanding knowledge bases.

[1] See http://en.wikipedia.org/wiki/Type_I_and_type_II_errors.

[2] Tilmann Bruckhaus, 2015. “How Are Precision and Recall Calculated?” from the KDNuggets Web site, retrieved May 10, 2015.

[3] Benjamin Roth, 2014. “Effective Distant Supervision for End-To-End Knowledge Base Population Systems,” D Engineering Thesis, Saarland University; quote is on p 33.

[4] See http://en.wikipedia.org/wiki/F1_score.

[5] See http://en.wikipedia.org/wiki/Template:DiagnosticTesting_Diagram.

[6] Some would also argue for adequate gold standards in the ontology realm. See Dellschaft, Klaas, and Steffen Staab. “On how to perform a gold standard based evaluation of ontology learning.” In The Semantic Web-ISWC 2006, pp. 228-241. Springer Berlin Heidelberg, 2006. For ontologies, they state it “. . . is apparent that there does not exist a canonical way of performing gold-standard based evaluations of ontology learning. Moreover, we argue in this paper that existing gold-standard based evaluations are faulty and that a well-founded evaluation model is largely missing.”

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Author: Mike Bergman