Forms of justification for inductive machine learning techniques are discussed and classified into four types. This is done with a view to introduce some of these techniques and their justificatory guarantees to the attention of philosophers, and to initiate a discussion as to whether they must be treated separately or rather can be viewed consistently from within a single framework.

In this age of post-Moorean modesty, many of us are inclined to doubt that philosophy is in possession of arguments that might genuinely serve to undermine what we ordinarily believe. It may perhaps be conceded that the arguments of the skeptic appear to be utterly compelling; but the Mooreans among us will hold that the very plausibility of our ordinary beliefs is reason enough for supposing that there must be something wrong in the skeptic’s arguments, even if we are unable (...) to say what it is. In so far then, as the pretensions of philosophy to provide a world view rest upon its.. (shrink)

Formal learning theory is the mathematical embodiment of a normative epistemology. It deals with the question of how an agent should use observations about her environment to arrive at correct and informative conclusions. Philosophers such as Putnam, Glymour and Kelly have developed learning theory as a normative framework for scientific reasoning and inductive inference.

Goodman sustentou que o ajuste mútuo entre inferências indutivas particulares e princípios indutivos constitui a única justificação necessária para ambos. Porém, a sua caracterização desse ajuste, posteriormente denominado de “equilíbrio reflexivo”, foi superficial. Isso levantou dúvida sobre a sua adequação. Neste artigo, argumento que o equilíbrio reflexivo, corretamente caracterizado, fornece a única justificação necessária e a melhor que podemos dar para a prática indutiva.

Issues of reliability are claiming center-stage in the epistemology of machine learning. This paper unifies different branches in the literature and points to promising research directions, whilst also providing an accessible introduction to key concepts in statistics and machine learning – as far as they are concerned with reliability.

The idea that “simplicity is a sign of truth”, and the related “Occam’s razor” principle, stating that, all other things being equal, simpler models should be preferred to more complex ones, have been long discussed in philosophy and science. We explore these ideas in the context of supervised machine learning, namely the branch of artificial intelligence that studies algorithms which balance simplicity and accuracy in order to effectively learn about the features of the underlying domain. Focusing on statistical learning theory, (...) we show that situations exist for which a preference for simpler models provably slows down, instead of favoring, the supervised learning process. Our results shed new light on the relations between simplicity and truth approximation, which are briefly discussed in the context of both machine learning and the philosophy of science. (shrink)

The modern abundance and prominence of data has led to the development of “data science” as a new field of enquiry, along with a body of epistemological reflections upon its foundations, methods, and consequences. This article provides a systematic analysis and critical review of significant open problems and debates in the epistemology of data science. We propose a partition of the epistemology of data science into the following five domains: (i) the constitution of data science; (ii) the kind of enquiry (...) that it identifies; (iii) the kinds of knowledge that data science generates; (iv) the nature and epistemological significance of “black box” problems; and (v) the relationship between data science and the philosophy of science more generally. (shrink)

As our epistemic ambitions grow, the common and scientific endeavours are becoming increasingly dependent on Machine Learning (ML). The field rests on a single experimental paradigm, which consists of splitting the available data into a training and testing set and using the latter to measure how well the trained ML model generalises to unseen samples. If the model reaches acceptable accuracy, an a posteriori contract comes into effect between humans and the model, supposedly allowing its deployment to target environments. Yet (...) the latter part of the contract depends on human inductive predictions or generalisations, which infer a uniformity between the trained ML model and the targets. The paper asks how we justify the contract between human and machine learning. It is argued that the justification becomes a pressing issue when we use ML to reach ‘elsewheres’ in space and time or deploy ML models in non-benign environments. The paper argues that the only viable version of the contract can be based on optimality (instead of on reliability which cannot be justified without circularity) and aligns this position with Schurz’s optimality justification. It is shown that when dealing with inaccessible/unstable ground-truths (‘elsewheres’ and non-benign targets), the optimality justification undergoes a slight change, which should reflect critically on our epistemic ambitions. Therefore, the study of ML robustness should involve not only heuristics that lead to acceptable accuracies on testing sets. The justification of human inductive predictions or generalisations about the uniformity between ML models and targets should be included as well. Without it, the assumptions about inductive risk minimisation in ML are not addressed in full. (shrink)

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)

For computer simulation models to usefully inform climate risk management, uncertainties in model projections must be explored and characterized. Because doing so requires running the model many ti...

At its strongest, Hume's problem of induction denies the existence of any well justified assumptionless inductive inference rule. At the weakest, it challenges our ability to articulate and apply good inductive inference rules. This paper examines an analysis that is closer to the latter camp. It reviews one answer to this problem drawn from the VC theorem in statistical learning theory and argues for its inadequacy. In particular, I show that it cannot be computed, in general, whether we are in (...) a situation where the VC theorem can be applied for the purpose we want it to. (shrink)

The present paper shows how statistical learning theory and machine learning models can be used to enhance understanding of AI-related epistemological issues regarding inductive reasoning and reliability of generalisations. Towards this aim, the paper proceeds as follows. First, it expounds Price’s dual image of representation in terms of the notions of e-representations and i-representations that constitute subject naturalism. For Price, this is not a strictly anti-representationalist position but rather a dualist one (e- and i-representations). Second, the paper links this debate (...) with machine learning in terms of statistical learning theory becoming more viable epistemological tool when it abandons the perspective of object naturalism. The paper then argues that machine learning grounds a form of knowing that can be understood in terms of e- and i-representation learning. Third, this synthesis shows a way of analysing inductive reasoning in terms of reliability of generalisations stemming from a structure of e- and i-representations. In the age of Artificial Intelligence, connecting Price’s dual view of representation with Deep Learning provides an epistemological way forward and even perhaps an approach to how knowing is possible. (shrink)

We compare Karl Popper’s ideas concerning the falsifiability of a theory with similar notions from the part of statistical learning theory known as VC-theory . Popper’s notion of the dimension of a theory is contrasted with the apparently very similar VC-dimension. Having located some divergences, we discuss how best to view Popper’s work from the perspective of statistical learning theory, either as a precursor or as aiming to capture a different learning activity.

Nelson Goodman's new riddle of induction forcefully illustrates a challenge that must be confronted by any adequate theory of inductive inference: provide some basis for choosing among alternative hypotheses that fit past data but make divergent predictions. One response to this challenge is to distinguish among alternatives by means of some epistemically significant characteristic beyond fit with the data. Statistical learning theory takes this approach by showing how a concept similar to Popper's notion of degrees of testability is linked to (...) minimizing expected predictive error. In contrast, formal learning theory appeals to Ockham's razor, which it justifies by reference to the goal of enhancing efficient convergence to the truth. In this essay, I show that, despite their differences, statistical and formal learning theory yield precisely the same result for a class of inductive problems that I call strongly VC ordered, of which Goodman's riddle is just one example. (shrink)

Talk of linguistic universals has given cognitive scientists the impression that languages are all built to a common pattern. In fact, there are vanishingly few universals of language in the direct sense that all languages exhibit them. Instead, diversity can be found at almost every level of linguistic organization. This fundamentally changes the object of enquiry from a cognitive science perspective. This target article summarizes decades of cross-linguistic work by typologists and descriptive linguists, showing just how few and unprofound the (...) universal characteristics of language are, once we honestly confront the diversity offered to us by the world's 6,000 to 8,000 languages. After surveying the various uses of “universal,” we illustrate the ways languages vary radically in sound, meaning, and syntactic organization, and then we examine in more detail the core grammatical machinery of recursion, constituency, and grammatical relations. Although there are significant recurrent patterns in organization, these are better explained as stable engineering solutions satisfying multiple design constraints, reflecting both cultural-historical factors and the constraints of human cognition.Linguistic diversity then becomes the crucial datum for cognitive science: we are the only species with a communication system that is fundamentally variable at all levels. Recognizing the true extent of structural diversity in human language opens up exciting new research directions for cognitive scientists, offering thousands of different natural experiments given by different languages, with new opportunities for dialogue with biological paradigms concerned with change and diversity, and confronting us with the extraordinary plasticity of the highest human skills. (shrink)

Our response takes advantage of the wide-ranging commentary to clarify some aspects of our original proposal and augment others. We argue against the generative critics of our coevolutionary program for the language sciences, defend the use of close-to-surface models as minimizing cross-linguistic data distortion, and stress the growing role of stochastic simulations in making generalized historical accounts testable. These methods lead the search for general principles away from idealized representations and towards selective processes. Putting cultural evolution central in understanding language (...) diversity makes learning fundamental in the cognition of language: increasingly powerful models of general learning, paired with channelled caregiver input, seem set to manage language acquisition without recourse to any innate “universal grammar.” Understanding why human language has no clear parallels in the animal world requires a cross-species perspective: crucial ingredients are vocal learning (for which there are clear non-primate parallels) and an intention-attributing cognitive infrastructure that provides a universal base for language evolution. We conclude by situating linguistic diversity within a broader trend towards understanding human cognition through the study of variation in, for example, human genetics, neurocognition, and psycholinguistic processing. (shrink)

In this article, we provide a tutorial overview of some aspects of statistical learning theory, which also goes by other names such as statistical pattern recognition, nonparametric classification and estimation, and supervised learning. We focus on the problem of two-class pattern classification for various reasons. This problem is rich enough to capture many of the interesting aspects that are present in the cases of more than two classes and in the problem of estimation, and many of the results can be (...) extended to these cases. Focusing on two-class pattern classification simplifies our discussion, and yet it is directly applicable to a wide range of practical settings. (shrink)

Ockham’s razor is the principle that, all other things being equal, scientists ought to prefer simpler theories. In recent years, philosophers have argued that simpler theories make better predictions, possess theoretical virtues like explanatory power, and have other pragmatic virtues like computational tractability. However, such arguments fail to explain how and why a preference for simplicity can help one find true theories in scientific inquiry, unless one already assumes that the truth is simple. One new solution to that problem is (...) the Ockham efficiency theorem, which states that scientists who heed Ockham’s razor retract their opinions less often and sooner than do their non-Ockham competitors. The theorem neglects, however, to consider competitors following random strategies and in many applications random strategies are known to achieve better worst-case loss than deterministic strategies. In this paper, we describe two ways to extend the result to a very general class of random, empirical strategies. The first extension concerns expected retractions, retraction times, and errors and the second extension concerns retractions in chance, times of retractions in chance, and chances of errors. (shrink)

The modern abundance and prominence of data have led to the development of “data science” as a new field of enquiry, along with a body of epistemological reflections upon its foundations, methods, and consequences. This article provides a systematic analysis and critical review of significant open problems and debates in the epistemology of data science. We propose a partition of the epistemology of data science into the following five domains: (i) the constitution of data science; (ii) the kind of enquiry (...) that it identifies; (iii) the kinds of knowledge that data science generates; (iv) the nature and epistemological significance of “black box” problems; and (v) the relationship between data science and the philosophy of science more generally. (shrink)

Contrary to common views that philosophy is extraneous to cognitive science, this paper argues that philosophy has a crucial role to play in cognitive science with respect to generality and normativity. General questions include the nature of theories and explanations, the role of computer simulation in cognitive theorizing, and the relations among the different fields of cognitive science. Normative questions include whether human thinking should be Bayesian, whether decision making should maximize expected utility, and how norms should be established. These (...) kinds of general and normative questions make philosophical reflection an important part of progress in cognitive science. Philosophy operates best, however, not with a priori reasoning or conceptual analysis, but rather with empirically informed reflection on a wide range of findings in cognitive science. (shrink)

Statistical Learning Theory (e.g., Hastie et al., 2001; Vapnik, 1998, 2000, 2006) is the basic theory behind contemporary machine learning and data-mining. We suggest that the theory provides an excellent framework for philosophical thinking about inductive inference.

This essay defends the view that inductive reasoning involves following inductive rules against objections that inductive rules are undesirable because they ignore background knowledge and unnecessary because Bayesianism is not an inductive rule. I propose that inductive rules be understood as sets of functions from data to hypotheses that are intended as solutions to inductive problems. According to this proposal, background knowledge is important in the application of inductive rules and Bayesianism qualifies as an inductive rule. Finally, I consider a (...) Bayesian formulation of inductive skepticism suggested by Lange. I argue that while there is no good Bayesian reason for judging this inductive skeptic irrational, the approach I advocate indicates a straightforward reason not to be an inductive skeptic. (shrink)

Although machine learning has been successful in recent years and is increasingly being deployed in the sciences, enterprises or administrations, it has rarely been discussed in philosophy beyond the philosophy of mathematics and machine learning. The present contribution addresses the resulting lack of conceptual tools for an epistemological discussion of machine learning by conceiving of deep learning networks as ‘judging machines’ and using the Kantian analysis of judgments for specifying the type of judgment they are capable of. At the center (...) of the argument is the fact that the functionality of deep learning networks is established by training and cannot be explained and justified by reference to a predefined rule-based procedure. Instead, the computational process of a deep learning network is barely explainable and needs further justification, as is shown in reference to the current research literature. Thus, it requires a new form of justification, that is to be specified with the help of Kant’s epistemology. (shrink)

The distinction between distributive and non-distributive profiles figures prominently in current evaluations of the ethical and epistemological risks that are associated with automated profiling practices. The diagnosis that non-distributive profiles may coincidentally situate an individual in the wrong category is often perceived as the central shortcoming of such profiles. According to this diagnosis, most risks can be retraced to the use of non-universal generalisations and various other statistical associations. This article develops a top-down analysis of non-distributive profiles in which this (...) fallibility of non-distributive profiles is no longer central. Instead, it focuses on how profiling creates various asymmetries between an individual data-subject and a profiler. The emergence of informational, interest, and perspectival asymmetries between data-subject and profiler explains how non-distributive profiles weaken the epistemic position of a profiled individual. This alternative analysis provides a more balanced assessment of the epistemic risks associated with non-distributive profiles. (shrink)

In these notes, I will use the word “reasoning” to refer to something people do. The general category includes both internal reasoning, reasoning things out by oneself—inference and deliberation—and external reasoning with others—arguing, discussing and negotiating.

Harman and Kulkarni provide a rigorous and informative discussion of reliable reasoning, drawing philosophical conclusions from the elegant formal results of statistical learning theory. They have presented a strong case that statistical learning theory is highly relevant to issues in philosophy and psychology concerning inductive inferences. Although I agree with their general thrust, I want to take issue with some of the philosophical and psychological conclusions they reach. I will first discuss the general problem of assessing norms and propose a (...) metanormative decision procedure that can then be applied to the assessment of inductive methods. In particular, I will apply it to the assessment of the method of inference that Harman and Kulkarni call transduction. (shrink)

Reliable Reasoning is a simple, accessible, beautifully explained introduction to Vapnik and Chervonenkis’s statistical learning theory. It includes a modest discussion of the application of the theory to the philosophy of induction; the purpose of these remarks is to say something more. 27.

This essay defends the view that inductive reasoning involves following inductive rules against objections that inductive rules are undesirable because they ignore background knowledge and unnecessary because Bayesianism is not an inductive rule. I propose that inductive rules be understood as sets of functions from data to hypotheses that are intended as solutions to inductive problems. According to this proposal, background knowledge is important in the application of inductive rules and Bayesianism qualifies as an inductive rule. Finally, I consider a (...) Bayesian formulation of inductive skepticism suggested by Lange. I argue that while there is no good Bayesian reason for judging this inductive skeptic irrational, the approach I advocate indicates a straightforward reason not to be an inductive skeptic. (shrink)

Like Glenn Shafer, we are nostalgic for the time when “philosophers, mathematicians, and scientists interested in probability, induction, and scientific methodology talked with each other more than they do now”, [p.10]. 1 Shafer goes on to mention other relevant contemporary communities. He himself has been at the interface of many of these communities while at the same time making major contributions to them and this very symposium represents something of that desired discussion. We begin with a couple of general points (...) about issues several commentators have raised and then discuss other more particular issues. (shrink)

"What Is Cognitive Access?" PDF. Behavioral and Brain Sciences 30 (2007 [published 2008]): 505. Brief comments on a paper of Ned Block's. "Mechanical Mind," a review of Mind as Machine: A History of Cognitive Science by Margaret Boden. Online Published Version . From American Scientist (2008): 76-81.