We compute that the index set of PAC-learnable concept classes is m-complete Σ30\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^{0}_{3}}$$\end{document} within the set of indices for all concept classes of a reasonable form. All concept classes considered are computable enumerations of computable Π10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi^{0}_{1}}$$\end{document} classes, in a sense made precise here. This family of concept classes is sufficient to cover all standard examples, and also has the property that PAC learnability (...) is equivalent to finite VC dimension. (shrink)

Computer scientists have provided a distinct justification of Occam’s Razor. Using the probably approximately correct framework, they provide a theorem that they claim demonstrates that we should favor simpler hypotheses. The argument relies on a philosophical interpretation of the theorem. I argue that the standard interpretation of the result in the literature is misguided and that a better reading does not, in fact, support Occam’s Razor at all. To this end, I state and prove a very similar theorem that, if (...) interpreted the same way, would justify the contradictory Anti-Occam’s Razor—the principle that we should favor more complex hypotheses. (shrink)

The Probably Approximately Correct (PAC) learning is a machine learning model introduced by Leslie Valiant in 1984. The PACi reducibility refers to the PAC reducibility independent of size and computation time. This reducibility in PAC learning resembles the reducibility in Turing computability. The ordering of concept classes under PAC reducibility is nonlinear, even when restricted to particular concrete examples.Due to the resemblance to Turing Reducibility, we suspected that there could be incomparable PACi and PAC degrees for the (...) PACi and PAC reducibilities as in Turing incomparable degrees. In 1957 Friedberg and in 1956 Muchnik independently solved the Post problem by constructing computably enumerable sets A and B of incomparable degrees using the priority construction method. We adapt this idea to PACi and PAC reducibilities and construct two effective concept classes C and D such that C is not reducible to D and vice versa. When considering PAC reducibility it was necessary to work on the size of an effective concept class, thus we use Kolmogorov complexity to obtain the size. The non-learnability of concept classes in the PAC learning model is explained by the existence of PAC incomparable degrees.Analogous to the Turing jump, we give a jump operation on effective concept classes for the zero jump. To define the zero jump operator for PACi degrees the join of all the effective concept classes is constructed and proved that it is a greatest element. There are many properties proven for existing degrees. Thus we can explore proving those properties to PACi and PAC degrees. But if we prove an embedding from those degrees to PACi and PAC degrees then those properties will be true for PACi and PAC degrees without explicitly proving them.Abstract prepared by Dodamgodage Gihnee M. Senadheera and taken directly from the thesisE-mail: [email protected]: https://www.proquest.com/docview/2717762461/abstract/ACD19F29A8774AF6PQ/1?accountid=13864. (shrink)

About 25 years ago, it came to light that a single combinatorial property determines both an important dividing line in model theory and machine learning. The following years saw a fruitful exchange of ideas between PAC-learning and the model theory of NIP structures. In this article, we point out a new and similar connection between model theory and machine learning, this time developing a correspondence between stability and learnability in various settings of online learning. In particular, (...) this gives many new examples of mathematically interesting classes which are learnable in the online setting. (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.

Publication date: 22 December 2020 Source: International Letters of Social and Humanistic Sciences Vol. 89 Author: Oleg Tarnopolsky, Marina Kabanova The article analyzes using Content and Language Integrated Learning for teaching one of the optional humanities disciplines to Ukrainian university students of different majors. The discipline discussed in the article as an example of using CLIL methodology is “The Fundamentals of Psychology and Pedagogy” and it is in the list of optional humanities subjects for the first-year students of Alfred (...) Nobel University in Dnipro, Ukraine. However, unlike the other optional humanities disciplines, the methodology underlying this course is based on teaching the subject in English, instead of Ukrainian, following the CLIL approach widely used in the European education but still little known in Ukraine. The purpose of the paper is to expose and analyze the original methodology developed that conditioned the specific structure of the relevant course, and the specific learning activities used in it. The essence of the developed CLIL theory-based methodology and its practical application are manifested through learning activities that include students’ mini-lectures/workshop-type presentations, brainstorming, case-studies, discussions, and a learning project with its results summarized in students’ essays, abstracts, and summaries written in English. The students collect the information required for completing their tasks not only from the teacher’s lectures and the recommended literature but also by way of doing extensive Internet-search on psychological and pedagogical sites in English. All this makes CLIL in the case under discussion experiential-interactive, blended, autonomous, and cooperative. As the result, students mostly self-construct their knowledge of the discipline by way of using the target language as the tool for such self-construction. This makes the elaborated course a clear-cut case of constructivism in CLIL pedagogy. Subject Classification Numbers: PACS 01.40.-d. (shrink)

Recent years have yielded many discussions on how to endow autonomous agents with the ability to make ethical decisions, and the need for explicit ethical reasoning and transparency is a persistent theme in this literature. We present a modular and transparent approach to equip autonomous agents with the ability to comply with ethical prescriptions, while still enacting pre-learned optimal behaviour. Our approach relies on a normative supervisor module, that integrates a theorem prover for defeasible deontic logic within the control loop (...) of a reinforcement learning agent. The supervisor operates as both an event recorder and an on-the-fly compliance checker w.r.t. an external norm base. We successfully evaluated our approach with several tests using variations of the game Pac-Man, subject to a variety of “ethical” constraints. (shrink)

In this paper, we perform a worst-case analysis of rule discovery based on generality and accuracy. A rule is defined as a probabilistic constraint of true assignment to the class attribute for corresponding examples. In data mining, a rule can be considered as representing an important class of discovered patterns. We accomplish the aforementioned objective by extending a preliminary version of PAC learning, which represents a worst-case analysis for classification. Our analysis consists of two cases: the case in which (...) we try to avoid finding a bad rule, and the case in which we try to avoid overlooking a good rule. Discussions on related work are also provided for PAC learning, multiple comparison, analysis of association rule discovery, and simultaneous reliability evaluation of a discovered rule. (shrink)

We study computable PAC (CPAC) learning as introduced by Agarwal et al. (2020). First, we consider the main open question of finding characterizations of proper and improper CPAC learning. We give a characterization of a closely related notion of strong CPAC learning, and provide a negative answer to the COLT open problem posed by Agarwal et al. (2021) whether all decidably representable VC classes are improperly CPAC learnable. Second, we consider undecidability of (computable) PAC learnability. We give (...) a simple general argument to exhibit such ndecidability, and initiate a study of the arithmetical complexity of learnability. We briefly discuss the relation to the undecidability result of Ben-David et al. (2019), that motivated the work of Agarwal et al. (shrink)

Indirect negative evidence is clearly an important way for learners to constrain overgeneralisation, and yet a good learning theoretic analysis has yet to be provided for this, whether in a PAC or a probabilistic identification in the limit framework. In this paper we suggest a theoretical analysis of indirect negative evidence that allows the presence of ungrammatical strings in the input and also accounts for the relationship between grammaticality/acceptability and probability. Given independently justified assumptions about lower bounds on the (...) probabilities of grammatical strings, we establish that a limited number of membership queries of some strings can be probabilistically simulated. (shrink)

Humans' voice offers the widest variety of motor phenomena of any human activity. However, its clinical evaluation in people with movement disorders such as Parkinson's disease lags behind current knowledge on advanced analytical automatic speech processing methodology. Here, we use deep learning-based speech processing to differentially analyze voice recordings in 14 people with PD before and after dopaminergic medication using personalized Convolutional Recurrent Neural Networks and Phone Attribute Codebooks. p-CRNN yields an accuracy of 82.35% in the binary classification of (...) ON and OFF motor states at a sensitivity/specificity of 0.86/0.78. The PAC-based approach's accuracy was slightly lower with 73.08% at a sensitivity/specificity of 0.69/0.77, but this method offers easier interpretation and understanding of the computational biomarkers. Both p-CRNN and PAC provide a differentiated view and novel insights into the distinctive components of the speech of persons with PD. Both methods detect voice qualities that are amenable to dopaminergic treatment, including active phonetic and prosodic features. Our findings may pave the way for quantitative measurements of speech in persons with PD. (shrink)

En el presente escrito indagamos en representaciones de docentes en torno a la experiencia de llevar adelante propuestas de filosofía con niños. Para ello, proponemos, primero, precisar las implicancias de lo que denominamos escenas filosóficas, definimos a la enseñanza de la filosofía como un problema filosófico y caracterizamos, luego, la práctica a partir de una polémica sobre su denominación de filosofía para niños o filosofía con niños. Para relevar estas representaciones, realizamos seis entrevistas en profundidad a docentes que tienen amplia (...) experiencia en esta práctica, y, a partir de un análisis de las entrevistas, ponemos el énfasis en la potencia de la reflexión sobre la experiencia. Recuperamos, en las narraciones, la revisión de la propia formación, de la idea de planificación y del modo en el que irrumpen las infancias. Por último, subrayamos el reconocimiento del carácter transformador del hacer filosofía con niños que relatan los docentes. (shrink)

Discovering high-level causal relations from low-level data is an important and challenging problem that comes up frequently in the natural and social sciences. In a series of papers, Chalupka etal. (2015, 2016a, 2016b, 2017) develop a procedure forcausal feature learning (CFL) in an effortto automate this task. We argue that CFL does not recommend coarsening in cases where pragmatic considerations rule in favor of it, and recommends coarsening in cases where pragmatic considerations rule against it. We propose a new (...) technique, pragmatic causal feature learning (PCFL), which extends the original CFL algorithm in useful and intuitive ways. We show that PCFL has the same attractive measure-theoretic properties as the original CFL algorithm. We compare the performance of both methods through theoretical analysis and experiments. (shrink)

Research in sport pedagogy and its applied recommendations are still characterized by a contrast between the different learning theories from psychology. Traditional theories and their corresponding approaches to the specific case of teaching and learning “how to play [team sports like soccer]” are subject to compatibilities and incompatibilities. We discuss how behaviorism as an approach to teaching the game shows more incompatibilities with the nature of tactical actions when compared to constructivism. As coaches strive to teach the game (...) and make their players and team perform, we argue that teaching the game requires teaching approaches that will help develop their way to play without taking away their autonomy and adaptiveness. The teaching-learning-training process for playing the game should then be conducted to harmonize the characteristics of the contents, the context, and the individual at hand. We provide two illustrated examples and portray how the recommended approaches fit key contents of the game that are observed in the tactical behavior. We finally argue that the coherent design of games provides minimal conditions to teaching approaches, and that such a design should be a priority when elaborating the learning activities along the player development process. As a conclusion, the interactionist theory is the one that best serves the teaching of the game and the development of tactical behavior. We therefore defend that its principles can help coaches tailor their own strategy to teach the game with the many tools. (shrink)

Over the last decade, numerous interventions and techniques that aim to engender, strengthen, and expand compassion have been created, proliferating an evidence base for the benefits of compassion meditation training. However, to date, little research has been conducted to examine individual variation in the learning, beliefs, practices, and subjective experiences of compassion meditation. This mixed-method study examines changes in novice meditators’ knowledge and contemplative experiences before, during, and after taking an intensive course in CBCT®, a contemplative intervention that is (...) increasingly used for both inter- and intrapersonal flourishing. The participants in this study were Christian healthcare chaplains completing a 1-year residency in Clinical Pastoral Education who learned CBCT as part of their professional chaplaincy training curriculum. Prior to and upon completion of training, we surveyed participants to assess their beliefs about the malleability of compassion, types of engagement in compassion meditation, and perceptions of the impact of taking CBCT. We also conducted in-depth interviews with a subset of participants to gain a qualitative understanding of their subjective experiences of learning and practicing compassion meditation, a key component of CBCT. We found that participants reported increases in the extent to which they believed compassion to be malleable after studying CBCT. We also found high levels of variability of individual ways of practicing and considered the implications of this for the study of contemplative learning processes. This multi-methodological approach yielded novel insights into how compassion practice and compassion-related outcomes interrelate, insights that can inform the basic scientific understanding of the experience of learning and enacting compassion meditation as a means of strengthening compassion itself. (shrink)

Interpersonal physiological synchrony has been consistently found during collaborative tasks. However, few studies have applied synchrony to predict collaborative learning quality in real classroom. To explore the relationship between interpersonal physiological synchrony and collaborative learning activities, this study collected electrodermal activity and heart rate during naturalistic class sessions and compared the physiological synchrony between independent task and group discussion task. The students were recruited from a renowned university in China. Since each student learn differently and not everyone prefers (...) collaborative learning, participants were sorted into collaboration and independent dyads based on their collaborative behaviors before data analysis. The result showed that, during group discussions, high collaboration pairs produced significantly higher synchrony than low collaboration dyads. Given the equivalent engagement level during independent and collaborative tasks, the difference of physiological synchrony between high and low collaboration dyads was triggered by collaboration quality. Building upon this result, the classification analysis was conducted, indicating that EDA synchrony can identify different levels of collaboration quality. (shrink)

We investigate a simple stochastic model of social network formation by the process of reinforcement learning with discounting of the past. In the limit, for any value of the discounting parameter, small, stable cliques are formed. However, the time it takes to reach the limiting state in which cliques have formed is very sensitive to the discounting parameter. Depending on this value, the limiting result may or may not be a good predictor for realistic observation times.

On Jewish Learning collects essays, speeches, and letters that express Rosenzweig's desire to reconnect the profound truths of Judaism with the lives of ordinary people.

Infant language learners are faced with the difficult inductive problem of determining how new words map to novel or known objects in their environment. Bayesian inference models have been successful at using the sparse information available in natural child-directed speech to build candidate lexicons and infer speakers’ referential intentions. We begin by asking how a Bayesian model optimized for monolingual input generalizes to new monolingual or bilingual corpora and find that, especially in the case of the bilingual input, the model (...) shows a significant decrease in performance. In the next experiment, we propose the ME Model, a modified Bayesian model, which approximates infants’ mutual exclusivity bias to support the differential demands of monolingual and bilingual learning situations. The extended model is assessed using the same corpora of real child-directed speech, showing that its performance is more robust against varying input and less dependent than the Intentional Model on optimization of its parsimony parameter. We argue that both monolingual and bilingual demands on word learning are important considerations for a computational model, as they can yield significantly different results than when only one such context is considered. (shrink)

The distinction between students diagnosed with a learning disability and those considered merely slow learners is based on conceptually flawed assumptions that: 1) LD represents a brain dysfunction while SL does not; 2) LD is a well-defined disorder; 3) valid measurement instruments distinguish LD and SL; 4) special education for students with LD is fundamentally different from that for SL students. These erroneous beliefs are maintained because governmental legislation transformed a diagnosis of LD into an admission ticket to a (...) variety of government entitlements thereby subjecting it to political, legal, social and ideological forces. (shrink)

This paper introduces a hybrid model that unifies connectionist, symbolic, and reinforcement learning into an integrated architecture for bottom-up skill learning in reactive sequential decision tasks. The model is designed for an agent to learn continuously from on-going experience in the world, without the use of preconceived concepts and knowledge. Both procedural skills and high-level knowledge are acquired through an agent’s experience interacting with the world. Computational experiments with the model in two domains are reported.

Growing evidence in recent years has led to an agreement on the importance and benefits that inclusive education has for students with special educational needs (SEN). However, the extension and universalization of an inclusive approach will also be enhanced with more evidence on the benefits that inclusion has for all students, including those without SEN. Based on the existing knowledge that learning interactions among diverse students are a key component of educational inclusion, the aim of this study is to (...) identify the impact on students without SEN of being educated with students with SEN in shared, inclusive, interactive learning environments. Data were collected in three schools using a qualitative approach with a communicative orientation. Semistructured interviews were held with teachers as well as community volunteers participating in the schools. Further, focus groups were conducted with students and teachers. The results show that students without SEN benefit from participating in interactive learning activities with peers with SEN in different ways: (1) they learn to respect others, accept differences, and acknowledge different abilities, thereby creating opportunities for new friendships to develop; (2) they learn about abilities related to helping others participate and learn, to be patient and to gain the satisfaction in helping others learn and behave better; and (3) they benefit from the cognitive effort required to explain themselves and from the contributions of peers with SEN from which they can learn. (shrink)

ABSTRACT Disagreements about art are considered here for their potential to pose questions about reality beyond the artwork. The project of assessing artistic value is useful for bringing complex questions to light. The ambitiousness of the cognitive stock, in Richard Wollheim's term, that can be relevant to understanding an artwork may mean that confident evaluation will elude us. Thinking about artistic value judgment in this way shifts its centrality as the point of artistic interpretation and evaluation; the goal of judging (...) a work's meaning and value is a useful tool for prompting us to understand a work. But if we fail to reach that goal, that does not mean we have failed to engage with the work appropriately. The artistic value judgment, and achieving consensus on that value, can be secondary in importance to grasping the problems a work poses that are not immediately resolvable. Examples drawn from literary and philosophical imagining, in the work of Grace Paley and Mary Mothersill, and from Toni Morrison's literary criticism are used to illustrate and support the fruitfulness of this approach. (shrink)

This paper addresses weighting and partitioning in complex reinforcement learning tasks, with the aim of facilitating learning. The paper presents some ideas regarding weighting of multiple agents and extends them into partitioning an input/state space into multiple regions with di erential weighting in these regions, to exploit di erential characteristics of regions and di erential characteristics of agents to reduce the learning complexity of agents (and their function approximators) and thus to facilitate the learning overall. It (...) analyzes, in reinforcement learning tasks, di erent ways of partitioning a task and using agents selectively based on partitioning. Based on the analysis, some heuristic methods are described and experimentally tested. We nd that some o -line heuristic methods performed the best, signi cantly better than single-agent models. (shrink)

Despite the accumulation of substantial cognitive science research relevant to education, there remains confusion and controversy in the application of research to educational practice. In support of a more systematic approach, we describe the Knowledge-Learning-Instruction (KLI) framework. KLI promotes the emergence of instructional principles of high potential for generality, while explicitly identifying constraints of and opportunities for detailed analysis of the knowledge students may acquire in courses. Drawing on research across domains of science, math, and language learning, we (...) illustrate the analyses of knowledge, learning, and instructional events that the KLI framework affords. We present a set of three coordinated taxonomies of knowledge, learning, and instruction. For example, we identify three broad classes of learning events (LEs): (a) memory and fluency processes, (b) induction and refinement processes, and (c) understanding and sense-making processes, and we show how these can lead to different knowledge changes and constraints on optimal instructional choices. (shrink)

"Philosophy for Children" has preponderantly started from the assumption that there is no fundamental difference between the thinking of adults and the thinking of children: both make use of the same mental operations. Moreover, children seem to be interested in the same basic questions about life and its meaning as adults. So children and adults apparently perform the same activities when they join in philosophical discussions. It is also easily assumed that children are particularly apt to philosophical thinking, because they (...) are inquisitive, unconventional and - contrary to traditional educational opinion - rational, often even more so than adults. (shrink)