The paper examines constraints and preferences employed by people in learning decision rules from preclassified examples. Results from four experiments with human subjects were analyzed and compared with artificial intelligence (AI) inductive learning programs. The results showed the people's rule inductions tended to emphasize category validity (probability of some property, given a category) more than cue validity (probability that an entity is a member of a category given that it has some property) to a greater extent than (...) did the AI programs. Although the relative proportions of different rule types (e.g., conjunctive vs. disjunctive) changed across experiments, a single process model provided a good account of the data from each study. These observations are used to argue for describing constraints in terms of processes embodied in models rather than in terms of products or outputs. Thus AI induction programs become candidate psychological process models and results from inductive learning experiments can suggest new algorithms. More generally, the results show that human inductive generalizations tend toward greater specificity than would be expected if conceptual simplicity were the key constraint on inductions. This bias toward specificity may be due to the fact that this criterion both maximizes inferences that may be drawn from category membership and protects rule induction systems from developing over‐generalizations. (shrink)

This paper presents a computational model of the way humans inductively identify and aggregate concepts from the low-level stimuli they are exposed to. Based on the idea that humans tend to select the simplest structures, it implements a dynamic hierarchical chunking mechanism in which the decision whether to create a new chunk is based on an information-theoretic criterion, the Minimum Description Length (MDL) principle. We present theoretical justifications for this approach together with results of an experiment in which participants, exposed (...) to meaningless symbols, have been implicitly encouraged to create high-level concepts by grouping them. Results show that the designed model, called hereafter MDLChunker, makes precise quantitative predictions both on the kind of chunks created by the participants and also on the moment at which these creations occur. They suggest that the simplicity principle used to design MDLChunker is particularly efficient to model chunking mechanisms. The main interest of this model over existing ones is that it does not require any adjustable parameter. (shrink)

We study a simple game theoretic model of information transfer which we consider to be a baseline model for capturing strategic aspects of epistemological questions. In particular, we focus on the question whether simple learning rules lead to an efficient transfer of information. We find that reinforcement learning, which is based exclusively on payoff experiences, is inadequate to generate efficient networks of information transfer. Fictitious play, the game theoretic counterpart to Carnapian inductive logic and a more sophisticated (...) kind of learning, suffices to produce efficiency in information transfer. (shrink)

The inductive category formation framework, an influential set of theories of learning in psychology and artificial intelligence, is deeply flawed. In this framework a set of necessary and sufficient features is taken to define a category. Such definitions are not functionally justified, are not used by people, and are not inducible by a learning system. Inductive theories depend on having access to all and only relevant features, which is not only impossible but begs a key question (...) in learning. The crucial roles of other cognitive processes (such as explanation and credit assignment) are ignored or oversimplified. Learning necessarily involves pragmatic considerations that can only be handled by complex cognitive processes.We provide an alternative framework for learning according to which category definitions must be based on category function. The learning system invokes other cognitive processes to accomplish difficult tasks, makes inferences, analyses and decides among potential features, and specifies how and when categories are to be generated and modified. We also examine the methodological underpinnings of the two approaches and compare their motivations. (shrink)

Under what conditions does machine learning (ML) model opacity inhibit the possibility of explaining and understanding phenomena? In this article, I argue that nonepistemic values give shape to the ML opacity problem even if we keep researcher interests fixed. Treating ML models as an instance of doing model-based science to explain and understand phenomena reveals that there is (i) an external opacity problem, where the presence of inductive risk imposes higher standards on externally validating models, and (ii) an (...) internal opacity problem, where greater inductive risk demands a higher level of transparency regarding the inferences the model makes. (shrink)

This paper starts by summarizing work that philosophers have done in the fields of inductive logic since 1950s and truth approximation since 1970s. It then proceeds to interpret and critically evaluate the studies on machine learning within artificial intelligence since 1980s. Parallels are drawn between identifiability results within formal learning theory and convergence results within Hintikka’s inductive logic. Another comparison is made between the PAC-learning of concepts and the notion of probable approximate truth.

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)

The problem of valid induction could be stated as follows: are we justified in accepting a given hypothesis on the basis of observations that frequently confirm it? The present paper argues that this question is relevant for the understanding of Machine Learning, but insufficient. Recent research in inductive reasoning has prompted another, more fundamental question: there is not just one given rule to be tested, there are a large number of possible rules, and many of these are somehow (...) confirmed by the data — how are we to restrict the space of inductive hypotheses and choose effectively some rules that will probably perform well on future examples? We analyze if and how this problem is approached in standard accounts of induction and show the difficulties that are present. Finally, we suggest that the explanation-based learning approach and related methods of knowledge intensive induction could be, if not a solution, at least a tool for solving some of these problems. (shrink)

Vanderschraaf develops a new theory of game theory equilibrium selection in this book. The new theory defends general correlated equilibrium concepts and suggests a new analysis of convention.

As scientists start to adopt machine learning (ML) as one research tool, the security of ML and the knowledge generated become a concern. In this paper, I explain how supervised ML can be improved with better data ontology, or the way we make categories and turn information into data. More specifically, we should design data ontology in such a way that is consistent with the knowledge that we have about the target phenomenon so that such ontology can help us (...) make the inductive leap. I do so by thinking through a thought experiment, Goodman’s New Riddle of Induction (Fact, fiction, and forecast, Harvard University Press, 1955). Goodman’s riddle helps flesh out three problems of induction: (1) the problem of equal goodies, that there are often too many equally good inductive results given the same data; (2) the problem of diverging performance, that these equally good results can give opposite predictions in the future; and (3) the problem of mediocrity, that when averaged across all equally possible datasets and tasks, no inductive algorithm outperforms any other. I show that all these three problems are manifested as real obstacles in ML practice, namely, the Rashomon effect (Breiman in Stat Sci 16(3):199–231, 2001), the problem of underspecification (D’Amour et al. in J Mach Learn Res, 2020, https://doi.org/10.48550/arXiv.2011.03395 ), and the No Free Lunch theorem (Wolpert in Neural Comput 8(7):1341–90, 1996, https://doi.org/10.1162/neco.1996.8.7.1341 ). Lastly, I argue that proper data ontology can help mitigate these problems and I demonstrate how using concrete examples from climate science. This research highlights the links between philosophers’ discussions of induction and implications in ML practice. (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)

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.

In this chapter we consider unsupervised learning from two perspectives. First, we briefly look at its advantages and disadvantages as an engineering technique applied to large corpora in natural language processing. While supervised learning generally achieves greater accuracy with less data, unsupervised learning offers significant savings in the intensive labour required for annotating text. Second, we discuss the possible relevance of unsupervised learning to debates on the cognitive basis of human language acquisition. In this context we (...) explore the implications of recent work on grammar induction for poverty of stimulus arguments that purport to motivate a strong bias model of language learning, commonly formulated as a theory of Universal Grammar (UG). We examine the second issue both as a problem in computational learning theory, and with reference to empirical work on unsupervised Machine Learning (ML) of syntactic structure. We compare two models of learning theory and the place of unsupervised learning within each of them. Looking at recent work on part of speech tagging and the recognition of syntactic structure, we see how far unsupervised ML methods have come in acquiring different kinds of grammatical knowledge from raw text. (shrink)

Using the Chinese Ring Puzzle (Kotovsky & Simon, Citation1990; P. J. Reber & Kotovsky, Citation1997), we studied the effect on rule discovery of having to plan actions or not in order to reach a goal state. This was done by asking participants to predict legal moves as in implicit learning tasks (Experiment 1) and by asking participants to make legal moves as in problem-solving tasks (Experiment 2). Our hypothesis was that having a specific goal state to reach has a (...) dual effect on rule discovery. The first effect is positive and related to feedback from moves done in order to attain the goal: generalising the results of action and associating them to the conditions in which they were obtained allows discovery of the rule and learning it. The second effect is negative. In attempting to reach a specific goal, participants first tend to reduce the distance that separates the current state from the goal state (hill climbing) and so neglect the kind of exploration that facilitates rule and procedure discovery because this would seem to be a detour from the goal. Results show that having to plan actions improved performance in implicit learning tasks (Experiment 1), yet it impaired performance in problem-solving tasks (Experiment 2). Although implicit learning and problem solving are based on rule discovery, and entail noticing regularities in the material, in both cases, rule discovery processes appear to be task-dependent. (shrink)

In _Reliable Reasoning_, Gilbert Harman and Sanjeev Kulkarni -- a philosopher and an engineer -- argue that philosophy and cognitive science can benefit from statistical learning theory, the theory that lies behind recent advances in machine learning. The philosophical problem of induction, for example, is in part about the reliability of inductive reasoning, where the reliability of a method is measured by its statistically expected percentage of errors -- a central topic in SLT. After discussing philosophical attempts (...) to evade the problem of induction, Harman and Kulkarni provide an admirably clear account of the basic framework of SLT and its implications for inductive reasoning. They explain the Vapnik-Chervonenkis dimension of a set of hypotheses and distinguish two kinds of inductive reasoning. The authors discuss various topics in machine learning, including nearest-neighbor methods, neural networks, and support vector machines. Finally, they describe transductive reasoning and suggest possible new models of human reasoning suggested by developments in SLT. (shrink)

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)

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are (...) re-examined within the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A.. Giving the boot to the bootstrap: How not to learn the natural numbers. Cognition, 101, B51–B60.] argue that such an inductive inference is consistent with a representational system that (...) clearly does not express the natural numbers and that possession of the natural numbers requires further principles that make the inductive inference superfluous. We argue that their critique is unsuccessful. Provided that children have access to a suitable initial system of representation, the sort of inductive inference that Rips et al. call into question can in fact facilitate the acquisition of larger integer concepts without the addition of any further principles. (shrink)

Almost all words are the names of categories. We can learn most of our words (and hence our categories) from dictionary definitions, but not all of them. Some have to be learned from direct experience. To understand a word from its definition we need to already understand the words used in the definition. This is the “Symbol Grounding Problem” [1]. How many words (and which ones) do we need to ground directly in sensorimotor experience in order to be able to (...) learn all other words via definition alone? The answer may shed some light both on the developmental origin of word meanings and on the evolutionary origin and adaptive value of language. We used an algorithm to reduce each of our dictionaries (Longmans LDOCE, Cambridge CIDE and WordNet) to its “grounding kernel” (“Kernel”) (which turned out to be about 10% of the dictionary) by systematically eliminating.. (shrink)

I examine the construction and evaluation of machine learning binary classification models. These models are increasingly used for societal applications such as classifying patients into two categories according to the presence or absence of a certain disease like cancer and heart disease. I argue that the construction of ML classification models involves an optimisation process aiming at the minimization of the inductive risk associated with the intended uses of these models. I also argue that the construction of these (...) models is underdetermined by the available data, and that this makes it necessary for ML modellers to make social value judgments in determining the error costs used in ML optimization. I thus suggest that the assessment of the inductive risk with respect to the social values of the intended users is an integral part of the construction and evaluation of ML classification models. I also discuss the implications of this conclusion for the philosophical debate concerning inductive risk. (shrink)

In reinforcement learning, a decision maker searching for the most rewarding option is often faced with the question: What is the value of an option that has never been tried before? One way to frame this question is as an inductive problem: How can I generalize my previous experience with one set of options to a novel option? We show how hierarchical Bayesian inference can be used to solve this problem, and we describe an equivalence between the Bayesian (...) model and temporal difference learning algorithms that have been proposed as models of RL in humans and animals. According to our view, the search for the best option is guided by abstract knowledge about the relationships between different options in an environment, resulting in greater search efficiency compared to traditional RL algorithms previously applied to human cognition. In two behavioral experiments, we test several predictions of our model, providing evidence that humans learn and exploit structured inductive knowledge to make predictions about novel options. In light of this model, we suggest a new interpretation of dopaminergic responses to novelty. (shrink)