Probably Approximately Correct

Probably Approximately Correct Author : Leslie Valiant
Release : 2013-06-04
Publisher : Hachette UK
ISBN : 0465037909
File Size : 42.74 MB
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From a leading computer scientist, a unifying theory that will revolutionize our understanding of how life evolves and learns. How does life prosper in a complex and erratic world? While we know that nature follows patterns -- such as the law of gravity -- our everyday lives are beyond what known science can predict. We nevertheless muddle through even in the absence of theories of how to act. But how do we do it? In Probably Approximately Correct, computer scientist Leslie Valiant presents a masterful synthesis of learning and evolution to show how both individually and collectively we not only survive, but prosper in a world as complex as our own. The key is "probably approximately correct" algorithms, a concept Valiant developed to explain how effective behavior can be learned. The model shows that pragmatically coping with a problem can provide a satisfactory solution in the absence of any theory of the problem. After all, finding a mate does not require a theory of mating. Valiant's theory reveals the shared computational nature of evolution and learning, and sheds light on perennial questions such as nature versus nurture and the limits of artificial intelligence. Offering a powerful and elegant model that encompasses life's complexity, Probably Approximately Correct has profound implications for how we think about behavior, cognition, biological evolution, and the possibilities and limits of human and machine intelligence.

Probably Approximately Correct Learning

Probably Approximately Correct Learning Author : David Haussler
Release : 1990
Publisher :
ISBN :
File Size : 66.51 MB
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Abstract: "This paper surveys some recent theoretical results on the efficiency of machine learning algorithms. The main tool described is the notion of Probably Approximately Correct (PAC) learning, introduced by Valiant. We define this learning model and then look at some of the results obtained in it. We then consider some criticisms of the PAC model and the extensions proposed to address these criticisms. Finally, we look briefly at other models recently proposed in computational learning theory."

Probably Approximately Correct Learnable Fuzzy System

Probably Approximately Correct Learnable Fuzzy System Author : Yan Wang
Release : 2019
Publisher :
ISBN :
File Size : 59.86 MB
Format : PDF, ePub
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This dissertation develops the probably approximately correct (PAC) learnable fuzzy system to predict clinical outcomes from a small number of survey questions (short form). There are five layers in the system: input, fuzzification, inference, defuzzification, and production. The major product in this dissertation is to derive the PAC learnable knowledge-driven machine learning algorithm by growing sample using Bootstrap samples with Gaussian distributed noise. The input layer is the procedure for preparing data input. In the fuzzification layer, sample size is significantly increased using bootstrap re-sampling with replacement. The fuzzy set with proposed membership function is generated by introducing Gaussian distributed noise to survey responses of the bootstrap samples to reflect uncertainty. This is a natural language extension from the point option in survey questions to region input with probabilities from survey design space. The inference layer includes both classification and prediction. Here we use machine learning techniques to derive the algorithms in this layer, e.g. Naive Bayesian method and eXtreme Gradient Boosting (XGBoost). The final predicted values require a defuzzification process in the next layer to remove noise in prediction. There are four types of input after fuzzification, original input, fuzzy input, input required interpolation and input required extrapolation. The defuzzification process is based on weighted means of related information. The last step of the system is the output layer with algorithms, final prediction and validation internally and externally. Lastly, we apply this fuzzy system to derive PAC learnable algorithms to predict oral health clinical outcomes. The input predictors include short forms and demographic information. The short forms, developed from Graded Response Models in Item Response Theory, have two versions (children and their parents). The clinical outcomes are referral for treatment needs (categorical) and children's oral health status index score (continuous). The prediction is evaluated internally and externally by sensitivity and specificity of a binary variable, correlation (between original value and predicted value) and root mean square error (RMSE) of a continuous variable. Both internal and external validation show the improvement of prediction when new information is added and generalizability as well as the stability of the algorithm. The best prediction (high sensitivity and relatively high specificity for categorical variables, low RMSE and high correlation) is reached when using child's self-reported short form, plus parent's proxy-reported short form, and demographic characteristics.

Probably Approximately Correct (PAC) Exploration in Reinforcement Learning

Probably Approximately Correct (PAC) Exploration in Reinforcement Learning Author :
Release : 2007
Publisher :
ISBN :
File Size : 36.15 MB
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Reinforcement Learning (RL) in finite state and action Markov Decision Processes is studied with an emphasis on the well-studied exploration problem. We provide a general RL framework that applies to all results in this thesis and to other results in RL that generalize the finite MDP assumption. We present two new versions of the Model-Based Interval Estimation (MBIE) algorithm and prove that they are both PAC-MDP. These algorithms are provably more efficient any than previously studied RL algorithms. We prove that many model-based algorithms (including R-MAX and MBIE) can be modified so that their worst-case per-step computational complexity is vastly improved without sacrificing their attractive theoretical guarantees. We show that it is possible to obtain PAC-MDP bounds with a model-free algorithm called Delayed Q-learning.

Existence of PAC Concept Classes of Incomparable Degrees

Existence of PAC Concept Classes of Incomparable Degrees Author : D. Gihanee M. Senadheera
Release : 2019
Publisher :
ISBN :
File Size : 58.64 MB
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Probably Approximately Correct (PAC) Learning is one of the models used in machine learning. This model was proposed by Valiant in 1984. The work related to this abstract was inspired by the Post's problem. Post classified computably enumerable (c.e.) sets and their degrees and was interested in finding more than two c.e. degrees. This was known as the Post's problem. In 1957 Friedberg and Muchnik independently showed this is possible. In PAC learning model, there are concept classes which are learnable also there are concept classes which are hard to learn. Later mathematicians were able to postulate the notion of PAC reducibility. That is, if a concept class C0 is PAC learnable through an algorithm then the concept class C1 reduces to the concept class C0 means C1 can be learned through the existing algorithm for C0. The term PAC degree means degree of unsolvability of a PAC concept class. It is natural to ask the question whether there are incomparable PAC degrees. In order to prove that there are incomparable PAC degrees we use the method known as priority construction, which is used by Freidbuerg and Muchnik in their work. We construct two concept classes C0 and C1 such that C0 is not reducible to C1 and C1 is not reducible to C0.

An Introduction to Computational Learning Theory

An Introduction to Computational Learning Theory Author : Michael J. Kearns
Release : 1994
Publisher : MIT Press
ISBN : 9780262111935
File Size : 84.7 MB
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Emphasizing issues of computational efficiency, Michael Kearns and Umesh Vazirani introduce a number of central topics in computational learning theory for researchers and students in artificial intelligence, neural networks, theoretical computer science, and statistics. Emphasizing issues of computational efficiency, Michael Kearns and Umesh Vazirani introduce a number of central topics in computational learning theory for researchers and students in artificial intelligence, neural networks, theoretical computer science, and statistics. Computational learning theory is a new and rapidly expanding area of research that examines formal models of induction with the goals of discovering the common methods underlying efficient learning algorithms and identifying the computational impediments to learning. Each topic in the book has been chosen to elucidate a general principle, which is explored in a precise formal setting. Intuition has been emphasized in the presentation to make the material accessible to the nontheoretician while still providing precise arguments for the specialist. This balance is the result of new proofs of established theorems, and new presentations of the standard proofs. The topics covered include the motivation, definitions, and fundamental results, both positive and negative, for the widely studied L. G. Valiant model of Probably Approximately Correct Learning; Occam's Razor, which formalizes a relationship between learning and data compression; the Vapnik-Chervonenkis dimension; the equivalence of weak and strong learning; efficient learning in the presence of noise by the method of statistical queries; relationships between learning and cryptography, and the resulting computational limitations on efficient learning; reducibility between learning problems; and algorithms for learning finite automata from active experimentation.

Formal Concept Analysis

Formal Concept Analysis Author : Karell Bertet
Release : 2017-06-02
Publisher : Springer
ISBN : 3319592718
File Size : 63.29 MB
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This book constitutes the proceedings of the 14th International Conference on Formal Concept Analysis, ICFCA 2017, held in Rennes, France, in June 2017. The 13 full papers presented in this volume were carefully reviewed and selected from 37 submissions. The book also contains an invited contribution and a historical paper translated from German and originally published in “Die Klassifkation und ihr Umfeld”, edited by P. O. Degens, H. J. Hermes, and O. Opitz, Indeks-Verlag, Frankfurt, 1986. The field of Formal Concept Analysis (FCA) originated in the 1980s in Darmstadt as a subfield of mathematical order theory, with prior developments in other research groups. Its original motivation was to consider complete lattices as lattices of concepts, drawing motivation from philosophy and mathematics alike. FCA has since then developed into a wide research area with applications much beyond its original motivation, for example in logic, data mining, learning, and psychology.

An Introduction to Computational Learning Theory

An Introduction to Computational Learning Theory Author : Michael J. Kearns
Release : 1994
Publisher : MIT Press
ISBN : 0262111934
File Size : 37.50 MB
Format : PDF
Download : 763
Read : 1186

Emphasizing issues of computational efficiency, Michael Kearns and Umesh Vazirani introduce a number of central topics in computational learning theory for researchers and students in artificial intelligence, neural networks, theoretical computer science, and statistics. Emphasizing issues of computational efficiency, Michael Kearns and Umesh Vazirani introduce a number of central topics in computational learning theory for researchers and students in artificial intelligence, neural networks, theoretical computer science, and statistics. Computational learning theory is a new and rapidly expanding area of research that examines formal models of induction with the goals of discovering the common methods underlying efficient learning algorithms and identifying the computational impediments to learning. Each topic in the book has been chosen to elucidate a general principle, which is explored in a precise formal setting. Intuition has been emphasized in the presentation to make the material accessible to the nontheoretician while still providing precise arguments for the specialist. This balance is the result of new proofs of established theorems, and new presentations of the standard proofs. The topics covered include the motivation, definitions, and fundamental results, both positive and negative, for the widely studied L. G. Valiant model of Probably Approximately Correct Learning; Occam's Razor, which formalizes a relationship between learning and data compression; the Vapnik-Chervonenkis dimension; the equivalence of weak and strong learning; efficient learning in the presence of noise by the method of statistical queries; relationships between learning and cryptography, and the resulting computational limitations on efficient learning; reducibility between learning problems; and algorithms for learning finite automata from active experimentation.

Design and Analysis of Efficient Reinforcement Learning Algorithms

Design and Analysis of Efficient Reinforcement Learning Algorithms Author : Claude-Nicolas Fiechter
Release : 1997
Publisher :
ISBN :
File Size : 54.4 MB
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Reinforcement learning considers the problem of learning a task or behavior by interacting with one's environment. The learning agent is not explicitly told how the task is to be achieved and has to learn by trial-and-error, using only the rewards and punishments that it receives in response to the actions it takes. In the last ten years there has been a rapidly growing interest in reinforcement learning techniques as a base for intelligent control architectures. Many methods have been proposed and a number of very successful applications have been developed. This dissertation contributes to a theoretical foundation for the study of reinforcement learning by applying some of the methods and tools of computational learning theory to the problem. We propose a formal model of efficient reinforcement learning based on Valiant's Probably Approximately Correct (PAC) learning framework, and use it to design reinforcement learning algorithms and to analyze their performance. We describe the first polynomial-time PAC algorithm for the general finite-state reinforcement learning problem and show that an active and directed exploration of its environment by the learning agent is necessary and sufficient to obtain efficient learning for that problem. We consider the trade-off between exploration and exploitation in reinforcement learning algorithms and show how in general an off-line PAC algorithm can be converted into an on-line algorithm that efficiently balances exploration and exploitation. We also consider the problem of generalization in reinforcement learning and show how in some cases the underlying structure of the environment can be exploited to achieve faster learning. We describe a PAC algorithm for the associative reinforcement learning problem that uses a form of decision lists to represent the policies in a compact way and generalize across different inputs. In addition, we describe a PAC algorithm for a special case of reinforcement learning where the environment can be modeled by a linear system. This particular reinforcement learning problem corresponds to the so-called linear quadratic regulator which is extensively studied and used in automatic and adaptive control.

Relational Knowledge Discovery

Relational Knowledge Discovery Author : M. E. Müller
Release : 2012-06-21
Publisher : Cambridge University Press
ISBN : 0521190215
File Size : 73.88 MB
Format : PDF
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Introductory textbook presenting relational methods in machine learning.

Encyclopedia of Computer Science and Technology

Encyclopedia of Computer Science and Technology Author : Allen Kent
Release : 2021-07-29
Publisher : CRC Press
ISBN : 1000444260
File Size : 82.18 MB
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"This comprehensive reference work provides immediate, fingertip access to state-of-the-art technology in nearly 700 self-contained articles written by over 900 international authorities. Each article in the Encyclopedia features current developments and trends in computers, software, vendors, and applications...extensive bibliographies of leading figures in the field, such as Samuel Alexander, John von Neumann, and Norbert Wiener...and in-depth analysis of future directions."

A Unifying Framework for Computational Reinforcement Learning Theory

A Unifying Framework for Computational Reinforcement Learning Theory Author : Lihong Li
Release : 2009
Publisher :
ISBN :
File Size : 84.45 MB
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Computational learning theory studies mathematical models that allow one to formally analyze and compare the performance of supervised-learning algorithms such as their sample complexity. While existing models such as PAC (Probably Approximately Correct) have played an influential role in understanding the nature of supervised learning, they have not been as successful in reinforcement learning (RL). Here, the fundamental barrier is the need for active exploration in sequential decision problems. An RL agent tries to maximize long-term utility by exploiting its knowledge about the problem, but this knowledge has to be acquired by the agent itself through exploring the problem that may reduce short-term utility. The need for active exploration is common in many problems in daily life, engineering, and sciences. For example, a Backgammon program strives to take good moves to maximize the probability of winning a game, but sometimes it may try novel and possibly harmful moves to discover how the opponent reacts in the hope of discovering a better game-playing strategy. It has been known since the early days of RL that a good tradeoff between exploration and exploitation is critical for the agent to learn fast (i.e., to reach near-optimal strategies with a small sample complexity), but a general theoretical analysis of this tradeoff remained open until recently. In this dissertation, we introduce a novel computational learning model called KWIK (Knows What It Knows) that is designed particularly for its utility in analyzing learning problems like RL where active exploration can impact the training data the learner is exposed to. My thesis is that the KWIK learning model provides a flexible, modularized, and unifying way for creating and analyzing reinforcement-learning algorithms with provably efficient exploration. In particular, we show how the KWIK perspective can be used to unify the analysis of existing RL algorithms with polynomial sample complexity. It also facilitates the development of new algorithms with smaller sample complexity, which have demonstrated empirically faster learning speed in real-world problems. Furthermore, we provide an improved, matching sample complexity lower bound, which suggests the optimality (in a sense) of one of the KWIK-based algorithms known as delayed Q-learning.

Introduction to Machine Learning, fourth edition

Introduction to Machine Learning, fourth edition Author : Ethem Alpaydin
Release : 2020-03-24
Publisher : MIT Press
ISBN : 0262358069
File Size : 45.80 MB
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A substantially revised fourth edition of a comprehensive textbook, including new coverage of recent advances in deep learning and neural networks. The goal of machine learning is to program computers to use example data or past experience to solve a given problem. Machine learning underlies such exciting new technologies as self-driving cars, speech recognition, and translation applications. This substantially revised fourth edition of a comprehensive, widely used machine learning textbook offers new coverage of recent advances in the field in both theory and practice, including developments in deep learning and neural networks. The book covers a broad array of topics not usually included in introductory machine learning texts, including supervised learning, Bayesian decision theory, parametric methods, semiparametric methods, nonparametric methods, multivariate analysis, hidden Markov models, reinforcement learning, kernel machines, graphical models, Bayesian estimation, and statistical testing. The fourth edition offers a new chapter on deep learning that discusses training, regularizing, and structuring deep neural networks such as convolutional and generative adversarial networks; new material in the chapter on reinforcement learning that covers the use of deep networks, the policy gradient methods, and deep reinforcement learning; new material in the chapter on multilayer perceptrons on autoencoders and the word2vec network; and discussion of a popular method of dimensionality reduction, t-SNE. New appendixes offer background material on linear algebra and optimization. End-of-chapter exercises help readers to apply concepts learned. Introduction to Machine Learning can be used in courses for advanced undergraduate and graduate students and as a reference for professionals.

Efficiency and Computational Limitations of Learning Algorithms

Efficiency and Computational Limitations of Learning Algorithms Author : Vitaly Feldman
Release : 2007
Publisher :
ISBN : 9781109894431
File Size : 65.94 MB
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This thesis presents new positive and negative results concerning the learnability of several well-studied function classes in the Probably Approximately Correct (PAC) model of learning.

The Harmonic Sieve: a Novel Application of Fourier Analysis of Machine Learning Theory and Practice

The Harmonic Sieve: a Novel Application of Fourier Analysis of Machine Learning Theory and Practice Author : Carnegie-Mellon University. Computer Science Department
Release : 1995
Publisher :
ISBN :
File Size : 51.7 MB
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Abstract: "This thesis presents new positive results -- both theoretical and empirical -- in machine learning. The primary learning- theoretic contribution is the Harmonic Sieve, the first efficient algorithm for learning the well-studied class of Disjunctive Normal Form (DNF) expressions (learning is accomplished within the Probably Approximately Correct model with respect to the uniform distribution using membership queries). Of particular interest is the novel use of Fourier methods within the algorithm. Specifically, all prior Fourier-based learning algorithms focused on finding large Fourier coefficients of the function to be learned (the target). The Harmonic Sieve departs from this paradigm; it instead learns by finding large coefficients of certain functions other than the target. The robustness of this new Fourier technique is illustrated by applying it to prove learnability of noisy DNF expressions, of a circuit class that is even more expressive than DNF, and of an interesting class of geometric concepts. Empirically, the thesis demonstrates the significant particular potential of a classification- learning algorithm closely related to the Harmonic Sieve. The Boosting- based Perceptron (BBP) learning algorithm produces classifiers that are nonlinear perceptrons (weighted thresholds over higher-order features). On several previously-studied machine learning benchmarks, the BBP algorithm produces classifiers that achieve accuracies essentially equivalent to or even better than the best previously-reported classifiers. Additionally, the perceptrons produced by the BBP algorithm tend to be relatively intelligible, an important feature in many machine learning applications. In a related vein, BBP and the Harmonic Sieve are applied successfully to the problem of rule extraction, that is, the problem of approximating an unintelligible classifier by a more intelligible function."

Intelligent Computing Theories and Applications

Intelligent Computing Theories and Applications Author : De-Shuang Huang
Release : 2012-07-09
Publisher : Springer
ISBN : 3642315763
File Size : 42.90 MB
Format : PDF, Kindle
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This book constitutes the refereed proceedings of the 8th International Conference on Intelligent Computing, ICIC 2012, held in Huangshan, China, in July 2012. The 85 revised full papers presented were carefully reviewed and selected from 753 submissions. The papers are organized in topical sections on neural networks, evolutionar learning and genetic algorithms, granular computing and rough sets, biology inspired computing and optimization, nature inspired computing and optimization, cognitive science and computational neuroscience, knowledge discovery and data mining, quantum computing, machine learning theory and methods, healthcare informatics theory and methods, biomedical informatics theory and methods, complex systems theory and methods, intelligent computing in signal processing, intelligent computing in image processing, intelligent computing in robotics, intelligent computing in computer vision, intelligent agent and web applications, special session on advances in information security 2012.

Understanding Machine Learning

Understanding Machine Learning Author : Shai Shalev-Shwartz
Release : 2014-05-19
Publisher : Cambridge University Press
ISBN : 1107057132
File Size : 71.89 MB
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Introduces machine learning and its algorithmic paradigms, explaining the principles behind automated learning approaches and the considerations underlying their usage.