We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

Scientists depend on complex computational systems that are often ineliminably opaque, to the detriment of our ability to give scientific explanations and detect artifacts. Some philosophers have s...

This article considers the issue of opacity as a problem for socially consequential mechanisms of classification and ranking, such as spam filters, credit card fraud detection, search engines, news trends, market segmentation and advertising, insurance or loan qualification, and credit scoring. These mechanisms of classification all frequently rely on computational algorithms, and in many cases on machine learning algorithms to do this work. In this article, I draw a distinction between three forms of opacity: opacity as intentional corporate or state (...) secrecy, opacity as technical illiteracy, and an opacity that arises from the characteristics of machine learning algorithms and the scale required to apply them usefully. The analysis in this article gets inside the algorithms themselves. I cite existing literatures in computer science, known industry practices, and do some testing and manipulation of code as a form of lightweight code audit. I argue that recognizing the distinct forms of opacity that may be coming into play in a given application is a key to determining which of a variety of technical and non-technical solutions could help to prevent harm. (shrink)

Offering a new approach to scientific explanation, this book focuses initially on the explaining act itself.

First published in 1713, this work was designed as a vivid and persuasive presentation of the remarkable picture of reality that Berkeley had first presented two years earlier in his Principles of Human Knowledge. His central claim there, as here, was that physical things consist of nothing but ideas in minds--that the world is not material but mental. Berkeley uses this thesis as the ground for a new argument for the existence of God, and the dialogue form enables him to (...) raise and respond to many of the natural objections to his position. The text printed in this volume is that of the 1734 edition of the Dialogues. (shrink)

Semantic information is usually supposed to satisfy the veridicality thesis: p qualifies as semantic information only if p is true. However, what it means for semantic information to be true is often left implicit, with correspondentist interpretations representing the most popular, default option. The article develops an alternative approach, namely a correctness theory of truth (CTT) for semantic information. This is meant as a contribution not only to the philosophy of information but also to the philosophical debate on the nature (...) of truth. After the introduction, in Sect. 2, semantic information is shown to be translatable into propositional semantic information (i). In Sect. 3, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in Sect. 4, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + A]. This completes the reduction of the truth of i to the correctness of A. In Sects. 5 and 6, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates Q by verifying and validating it (in the computer science’s sense of “verification” and “validation”); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of “proxy”) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of “commutation”); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. Sect. 7 provides some further clarifications about CTT, in the light of semantic paradoxes. Section 8 draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. In the course of the article all technical expressions from computer science are explained. (shrink)

The aim of this paper is to sketch a theory of justified belief. What I have in mind is an explanatory theory, one that explains in a general way why certain beliefs are counted as justified and others as unjustified. Unlike some traditional approaches, I do not try to prescribe standards for justification that differ from, or improve upon, our ordinary standards. I merely try to explicate the ordinary standards, which are, I believe, quite different from those of many classical, (...) e. g., ‘Cartesian’, accounts. (shrink)

Issues concerning scientific explanation have been a focus of philosophical attention from Pre- Socratic times through the modern period. However, recent discussion really begins with the development of the Deductive-Nomological (DN) model. This model has had many advocates (including Popper 1935, 1959, Braithwaite 1953, Gardiner, 1959, Nagel 1961) but unquestionably the most detailed and influential statement is due to Carl Hempel (Hempel 1942, 1965, and Hempel & Oppenheim 1948). These papers and the reaction to them have structured subsequent discussion concerning (...) scientific explanation to an extraordinary degree. After some general remarks by way of background and orientation (Section 1), this entry describes the DN model and its extensions, and then turns to some well-known objections (Section 2). It next describes a variety of subsequent attempts to develop alternative models of explanation, including Wesley Salmon's Statistical Relevance (Section 3) and Causal Mechanical (Section 4) models and the Unificationist models due to Michael Friedman and Philip Kitcher (Section 5). Section 6 provides a summary and discusses directions for future work. (shrink)

Provides comprehensive coverage of logical structure as well as the techniques of formal reasoning.

<Hylas> It is indeed something unusual; but my thoughts were so taken up with a subject I was discoursing of last night, that finding I could not sleep, ...

The final work of a distinguished physicist, this remarkable volume examines the emotive significance of time, the time order of mechanics, the time direction of thermodynamics and microstatistics, the time direction of macrostatistics, and the time of quantum physics. Coherent discussions include accounts of analytic methods of scientific philosophy in the investigation of probability, quantum mechanics, the theory of relativity, and causality. "[Reichenbach’s] best by a good deal."—Physics Today. 1971 ed.

A key to modern studies of 18th century Western philosophy, the Treatise considers numerous classic philosophical issues, including causation, existence, freedom and necessity and morality. This abridged edition has an introduction which explain's Hume's thought and places it in the context of its times.

The influence of J. L. Austin on contemporary philosophy was substantial during his lifetime, and has grown greatly since his death, at the height of his powers, in 1960. Philosophical Papers, first published in 1961, was the first of three volumes of Austin's work to be edited by J. O. Urmson and G. J. Warnock. Together with Sense and Sensibilia and How to do things with Words, it has extended Austin's influence far beyond the circle who knew him or read (...) the handful of papers he published in journals. (shrink)

Thomas S. Kuhn's classic book is now available with a new index.

This text provides a critique of the subjective Bayesian view of statistical inference, and proposes the author's own error-statistical approach as an alternative framework for the epistemology of experiment. It seeks to address the needs of researchers who work with statistical analysis.

We are sceptical of concerns over the opacity of algorithmic decision tools. While transparency and explainability are certainly important desiderata in algorithmic governance, we worry that automated decision-making is being held to an unrealistically high standard, possibly owing to an unrealistically high estimate of the degree of transparency attainable from human decision-makers. In this paper, we review evidence demonstrating that much human decision-making is fraught with transparency problems, show in what respects AI fares little worse or better and argue that (...) at least some regulatory proposals for explainable AI could end up setting the bar higher than is necessary or indeed helpful. The demands of practical reason require the justification of action to be pitched at the level of practical reason. Decision tools that support or supplant practical reasoning should not be expected to aim higher than this. We cast this desideratum in terms of Daniel Dennett’s theory of the “intentional stance” and argue that since the justification of action for human purposes takes the form of intentional stance explanation, the justification of algorithmic decisions should take the same form. In practice, this means that the sorts of explanations for algorithmic decisions that are analogous to intentional stance explanations should be preferred over ones that aim at the architectural innards of a decision tool. (shrink)

Many of the computing systems programmed using Machine Learning are opaque: it is difficult to know why they do what they do or how they work. Explainable Artificial Intelligence aims to develop analytic techniques that render opaque computing systems transparent, but lacks a normative framework with which to evaluate these techniques’ explanatory successes. The aim of the present discussion is to develop such a framework, paying particular attention to different stakeholders’ distinct explanatory requirements. Building on an analysis of “opacity” from (...) philosophy of science, this framework is modeled after accounts of explanation in cognitive science. The framework distinguishes between the explanation-seeking questions that are likely to be asked by different stakeholders, and specifies the general ways in which these questions should be answered so as to allow these stakeholders to perform their roles in the Machine Learning ecosystem. By applying the normative framework to recently developed techniques such as input heatmapping, feature-detector visualization, and diagnostic classification, it is possible to determine whether and to what extent techniques from Explainable Artificial Intelligence can be used to render opaque computing systems transparent and, thus, whether they can be used to solve the Black Box Problem. (shrink)

The evidence from randomized controlled trials (RCTs) is widely regarded as supplying the ‘gold standard’ in medicine—we may sometimes have to settle for other forms of evidence, but this is always epistemically second-best. But how well justified is the epistemic claim about the superiority of RCTs? This paper adds to my earlier (predominantly negative) analyses of the claims produced in favour of the idea that randomization plays a uniquely privileged epistemic role, by closely inspecting three related arguments from leading contributors (...) to the burgeoning field of probabilistic causality—Papineau, Cartwright and Pearl. It concludes that none of these further arguments supplies any practical reason for thinking of randomization as having unique epistemic power. IntroductionWhy the issue is of great practical importance—the ECMO casePapineau on the ‘virtues of randomization’Cartwright on causality and the ‘ideal’ randomized experimentPearl on randomization, nets and causesConclusion. (shrink)

Woodward's long awaited book is an attempt to construct a comprehensive account of causation explanation that applies to a wide variety of causal and explanatory claims in different areas of science and everyday life. The book engages some of the relevant literature from other disciplines, as Woodward weaves together examples, counterexamples, criticisms, defenses, objections, and replies into a convincing defense of the core of his theory, which is that we can analyze causation by appeal to the notion of manipulation.

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealisedexplanation gamein which players collaborate to find the best explanation(s) for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal patterns of (...) variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a (conditionally) optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence, a fast-growing research area that is so far lacking in firm theoretical foundations. In this article, an expanded version of a paper originally presented at the 37th Conference on Uncertainty in Artificial Intelligence, we attempt to fill this gap. Building on work in logic, probability, and causality, we establish the central role of (...) necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We propose a novel formulation of these concepts, and demonstrate its advantages over leading alternatives. We present a sound and complete algorithm for computing explanatory factors with respect to a given context and set of agentive preferences, allowing users to identify necessary and sufficient conditions for desired outcomes at minimal cost. Experiments on real and simulated data confirm our method’s competitive performance against state of the art XAI tools on a diverse array of tasks. (shrink)

This paper offers a dialogue theory of explanation. A successful explanation is defined as a transfer of understanding in a dialogue system in which a questioner and a respondent take part. The questioner asks a special sort of why-question that asks for understanding of something and the respondent provides a reply that transfers understanding to the questioner. The theory is drawn from recent work on explanation in artificial intelligence (AI), especially in expert systems, but applies to scientific, legal and everyday (...) conversational explanations. (shrink)

This paper builds a dialectical system of explanation with speech act rules that define the kinds of moves allowed, like requesting and offering an explanation. Pre and post-condition rules for the speech acts determine when a particular speech act can be put forward as a move in the dialogue, and what type of move or moves must follow it. A successful explanation has been achieved when there has been a transfer of understanding from the party giving the explanation to the (...) party asking for it. The dialogue has an opening stage, an explanation stage and a closing stage. Whether a transfer of understanding has taken place is tested by a dialectical shift to an examination dialogue. (shrink)

Simple idealized models seem to provide more understanding than opaque, complex, and hyper-realistic models. However, an increasing number of scientists are going in the opposite direction by utilizing opaque machine learning models to make predictions and draw inferences, suggesting that scientists are opting for models that have less potential for understanding. Are scientists trading understanding for some other epistemic or pragmatic good when they choose a machine learning model? Or are the assumptions behind why minimal models provide understanding misguided? In (...) this paper, using the case of deep neural networks, I argue that it is not the complexity or black box nature of a model that limits how much understanding the model provides. Instead, it is a lack of scientific and empirical evidence supporting the link that connects a model to the target phenomenon that primarily prohibits understanding. (shrink)

The philosophical theory of scientific explanation proposed here involves a radically new treatment of causality that accords with the pervasively statistical character of contemporary science. Wesley C. Salmon describes three fundamental conceptions of scientific explanation--the epistemic, modal, and ontic. He argues that the prevailing view is untenable and that the modal conception is scientifically out-dated. Significantly revising aspects of his earlier work, he defends a causal/mechanical theory that is a version of the ontic conception. Professor Salmon's theory furnishes a robust (...) argument for scientific realism akin to the argument that convinced twentieth-century physical scientists of the existence of atoms and molecules. To do justice to such notions as irreducibly statistical laws and statistical explanation, he offers a novel account of physical randomness. The transition from the "reviewed view" of scientific explanation to the causal/mechanical model requires fundamental rethinking of basic explanatory concepts. (shrink)

In this paper I argue that the search for explainable models and interpretable decisions in AI must be reformulated in terms of the broader project of offering a pragmatic and naturalistic account of understanding in AI. Intuitively, the purpose of providing an explanation of a model or a decision is to make it understandable to its stakeholders. But without a previous grasp of what it means to say that an agent understands a model or a decision, the explanatory strategies will (...) lack a well-defined goal. Aside from providing a clearer objective for XAI, focusing on understanding also allows us to relax the factivity condition on explanation, which is impossible to fulfill in many machine learning models, and to focus instead on the pragmatic conditions that determine the best fit between a model and the methods and devices deployed to understand it. After an examination of the different types of understanding discussed in the philosophical and psychological literature, I conclude that interpretative or approximation models not only provide the best way to achieve the objectual understanding of a machine learning model, but are also a necessary condition to achieve post hoc interpretability. This conclusion is partly based on the shortcomings of the purely functionalist approach to post hoc interpretability that seems to be predominant in most recent literature. (shrink)

In this paper I argue that the search for explainable models and interpretable decisions in AI must be reformulated in terms of the broader project of offering a pragmatic and naturalistic account of understanding in AI. Intuitively, the purpose of providing an explanation of a model or a decision is to make it understandable to its stakeholders. But without a previous grasp of what it means to say that an agent understands a model or a decision, the explanatory strategies will (...) lack a well-defined goal. Aside from providing a clearer objective for XAI, focusing on understanding also allows us to relax the factivity condition on explanation, which is impossible to fulfill in many machine learning models, and to focus instead on the pragmatic conditions that determine the best fit between a model and the methods and devices deployed to understand it. After an examination of the different types of understanding discussed in the philosophical and psychological literature, I conclude that interpretative or approximation models not only provide the best way to achieve the objectual understanding of a machine learning model, but are also a necessary condition to achieve post hoc interpretability. This conclusion is partly based on the shortcomings of the purely functionalist approach to post hoc interpretability that seems to be predominant in most recent literature. (shrink)

Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of philosophical controversy and debate for over 60 years. Both current and long-standing problems of N–P tests stem from unclarity and confusion, even among N–P adherents, as to how a test's (pre-data) error probabilities are to be used for (post-data) inductive inference as opposed to inductive behavior. We argue that the relevance of error probabilities (...) is to ensure that only statistical hypotheses that have passed severe or probative tests are inferred from the data. The severity criterion supplies a meta-statistical principle for evaluating proposed statistical inferences, avoiding classic fallacies from tests that are overly sensitive, as well as those not sensitive enough to particular errors and discrepancies. Introduction and overview 1.1 Behavioristic and inferential rationales for Neyman–Pearson (N–P) tests 1.2 Severity rationale: induction as severe testing 1.3 Severity as a meta-statistical concept: three required restrictions on the N–P paradigm Error statistical tests from the severity perspective 2.1 N–P test T(): type I, II error probabilities and power 2.2 Specifying test T() using p-values Neyman's post-data use of power 3.1 Neyman: does failure to reject H warrant confirming H? Severe testing as a basic concept for an adequate post-data inference 4.1 The severity interpretation of acceptance (SIA) for test T() 4.2 The fallacy of acceptance (i.e., an insignificant difference): Ms Rosy 4.3 Severity and power Fallacy of rejection: statistical vs. substantive significance 5.1 Taking a rejection of H0 as evidence for a substantive claim or theory 5.2 A statistically significant difference from H0 may fail to indicate a substantively important magnitude 5.3 Principle for the severity interpretation of a rejection (SIR) 5.4 Comparing significant results with different sample sizes in T(): large n problem 5.5 General testing rules for T(), using the severe testing concept The severe testing concept and confidence intervals 6.1 Dualities between one and two-sided intervals and tests 6.2 Avoiding shortcomings of confidence intervals Beyond the N–P paradigm: pure significance, and misspecification tests Concluding comments: have we shown severity to be a basic concept in a N–P philosophy of induction? (shrink)

The growing availability of computer power and statistical software has greatly increased the ease with which practitioners apply statistical methods, but this has not been accompanied by attention to checking the assumptions on which these methods are based. At the same time, disagreements about inferences based on statistical research frequently revolve around whether the assumptions are actually met in the studies available, e.g., in psychology, ecology, biology, risk assessment. Philosophical scrutiny can help disentangle 'practical' problems of model validation, and conversely, (...) a methodology of statistical model validation can shed light on a number of issues of interest to philosophers of science. (shrink)

The usefulness of machine learning algorithms has led to their widespread adoption prior to the development of a conceptual framework for making sense of them. One common response to this situation is to say that machine learning suffers from a “black box problem.” That is, machine learning algorithms are “opaque” to human users, failing to be “interpretable” or “explicable” in terms that would render categorization procedures “understandable.” The purpose of this paper is to challenge the widespread agreement about the existence (...) and importance of a black box problem. The first section argues that “interpretability” and cognates lack precise meanings when applied to algorithms. This makes the concepts difficult to use when trying to solve the problems that have motivated the call for interpretability. Furthermore, since there is no adequate account of the concepts themselves, it is not possible to assess whether particular technical features supply formal definitions of those concepts. The second section argues that there are ways of being a responsible user of these algorithms that do not require interpretability. In many cases in which a black box problem is cited, interpretability is a means to a further end such as justification or non-discrimination. Since addressing these problems need not involve something that looks like an “interpretation” of an algorithm, the focus on interpretability artificially constrains the solution space by characterizing one possible solution as the problem itself. Where possible, discussion should be reformulated in terms of the ends of interpretability. (shrink)

Published research findings are sometimes refuted by subsequent evidence, says Ioannidis, with ensuing confusion and disappointment.

Semantic information is usually supposed to satisfy the veridicality thesis: p qualifies as semantic information only if p is true. However, what it means for semantic information to be true is often left implicit, with correspondentist interpretations representing the most popular, default option. The article develops an alternative approach, namely a correctness theory of truth (CTT) for semantic information. This is meant as a contribution not only to the philosophy of information but also to the philosophical debate on the nature (...) of truth. After the introduction, in Sect. 2, semantic information is shown to be translatable into propositional semantic information (i). In Sect. 3, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in Sect. 4, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + A]. This completes the reduction of the truth of i to the correctness of A. In Sects. 5 and 6, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates Q by verifying and validating it (in the computer science’s sense of verification and validation ); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of proxy ) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of commutation ); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. Sect. 7 provides some further clarifications about CTT, in the light of semantic paradoxes. Section 8 draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. In the course of the article all technical expressions from computer science are explained. (shrink)

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes’s original paper to contemporary formal learning theory.In (...) a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh. (shrink)

This classic work in the philosophy of physical science is an incisive and readable account of the scientific method. Pierre Duhem was one of the great figures in French science, a devoted teacher, and a distinguished scholar of the history and philosophy of science. This book represents his most mature thought on a wide range of topics.

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes's original paper to contemporary formal learning theory. (...) In a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh. (shrink)