Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

Deep Learning

Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives when interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the key ideas and algorithms of reinforcement learning. Their discussion ranges from the history of the field's intellectual foundations to the most recent developments and applications. The only necessary mathematical background is familiarity with elementary concepts of probability. The book is divided into three parts. Part I defines the reinforcement learning problem in terms of Markov decision processes. Part II provides basic solution methods: dynamic programming, Monte Carlo methods, and temporal-difference learning. Part III presents a unified view of the solution methods and incorporates artificial neural networks, eligibility traces, and planning; the two final chapters present case studies and consider the future of reinforcement learning.

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Reinforcement Learning: An Introduction

In the first part of the paper we consider the problem of dynamically apportioning resources among a set of options in a worst-case on-line framework. The model we study can be interpreted as a broad, abstract extension of the well-studied on-line prediction model to a general decision-theoretic setting. We show that the multiplicative weight-update Littlestone?Warmuth rule can be adapted to this model, yielding bounds that are slightly weaker in some cases, but applicable to a considerably more general class of learning problems. We show how the resulting learning algorithm can be applied to a variety of problems, including gambling, multiple-outcome prediction, repeated games, and prediction of points in Rn. In the second part of the paper we apply the multiplicative weight-update technique to derive a new boosting algorithm. This boosting algorithm does not require any prior knowledge about the performance of the weak learning algorithm. We also study generalizations of the new boosting algorithm to the problem of learning functions whose range, rather than being binary, is an arbitrary finite set or a bounded segment of the real line.

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A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting

https://www2.econ.iastate.edu/tesfatsi/DeepLearningInNeuralNetworksOverview.JSchmidhuber2015.pdf

Deep learning in neural networks

The game of Go has long been viewed as the most challenging of classic games for artificial intelligence owing to its enormous search space and the difficulty of evaluating board positions and moves. Here we introduce a new approach to computer Go that uses ‘value networks’ to evaluate board positions and ‘policy networks’ to select moves. These deep neural networks are trained by a novel combination of supervised learning from human expert games, and reinforcement learning from games of self-play. Without any lookahead search, the neural networks play Go at the level of stateof-the-art Monte Carlo tree search programs that simulate thousands of random games of self-play. We also introduce a new search algorithm that combines Monte Carlo simulation with value and policy networks. Using this search algorithm, our program AlphaGo achieved a 99.8% winning rate against other Go programs, and defeated the human European Go champion by 5 games to 0. This is the first time that a computer program has defeated a human professional player in the full-sized game of Go, a feat previously thought to be at least a decade away.

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Mastering the game of Go with deep neural networks and tree search

This work gives a polynomial time algorithm for learning decision trees with respect to the uniform distribution. (This algorithm uses membership queries.) The decision tree model that is considered is an extension of the traditional boolean decision tree model that allows linear operations in each node (i.e., summation of a subset of the input variables over $GF(2)$).This paper shows how to learn in polynomial time any function that can be approximated (in norm $L_2 $) by a polynomially sparse function (i.e., a function with only polynomially many nonzero Fourier coefficients). The authors demonstrate that any function f whose $L_1 $-norm (i.e., the sum of absolute value of the Fourier coefficients) is polynomial can be approximated by a polynomially sparse function, and prove that boolean decision trees with linear operations are a subset of this class of functions. Moreover, it is shown that the functions with polynomial $L_1 $-norm can be learned deterministically.The algorithm can also exactly identi...

Learning decision trees using the Fourier spectrum

Boolean functions in AC/sup O/ are studied using the harmonic analysis of the cube. The main result is that an AC/sup O/ Boolean function has almost all of its power spectrum on the low-order coefficients. This result implies the following properties of functions in AC/sup O/: functions in AC/sup O/ have low average sensitivity; they can be approximated well be a real polynomial of low degree; they cannot be pseudorandom function generators and their correlation with any polylog-wide independent probability distribution is small. An O(n/sup polylog(/ /sup sup)/ /sup (n)/)-time algorithm for learning functions in AC/sup O/ is obtained. The algorithm observed the behavior of an AC/sup O/ function on O(n/sup polylog/ /sup (n)/) randomly chosen inputs and derives a good approximation for the Fourier transform of the function. This allows it to predict with high probability the value of the function on other randomly chosen inputs. >

Constant depth circuits, Fourier transform, and learnability

This work gives apolynomial time algorithm for learning decision trees with respect to the uniform distribution (This algorithm uses membership queries) The decision tree model that is considered is an extension of the traditional boolean decision tree model that allows linear operations in each node (ie, summation of a subset of the input variables over GF(2)) This paper shows how to learn in polynomial time any function that can be approximated (in norm L2) by a polynomially sparse function (ie, a function with only polynomially many nonzero Fourier coefficients) The authors demonstrate that any functionf whose L -norm (ie, the sum of absolute value of the Fourier coefficients) is polynomial can be approximated by a polynomially sparse function, and prove that boolean decision trees with linear operations are a subset of this class of functions Moreover, it is shown that the functions with polynomial L -norm can be learned deterministically The algorithm can also exactly identify a decision tree of depth d in time polynomial in 2 a and n This result implies that trees of logarithmic depth can be identified in polynomial time

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We introduce and investigate a new model of learning probability distributions from independent draws. Our model is inspired by the popular Probably Approximately Correct (PAC) model for learning boolean functions from labeled examples [24], in the sense that we emphasize efficient and approximate learning, and we study the learnability of restricted classes of target distributions. The dist ribut ion classes we examine are often defined by some simple computational mechanism for transforming a truly random string of input bits (which is not visible to the learning algorithm) into the stochastic observation (output) seen by the learning algorithm. In this paper, we concentrate on discrete distributions over {O, I}n. The problem of inferring an approximation to an unknown probability distribution on the basis of independent draws has a long and complex history in the pattern recognition and statistics literature. For instance, the problem of estimating the parameters of a Gaussian density in highdimensional space is one of the most studied statistical problems. Distribution learning problems have often been investigated in the context of unsupervised learning, in which a linear mixture of two or more distributions is generating the observations, and the final goal is not to model the distributions themselves, but to predict from which distribution each observation was drawn. Data clustering methods are a common tool here. There is also a large literature on nonpararnetric density estimation, in which no assumptions are made on the unknown target density. Nearest-neighbor approaches to the unsupervised learning problem often arise in the nonparametric setting. While we obviously cannot do justice to these areas here, the books of Duda and Hart [9] and Vapnik [25] provide excellent overviews and introductions to the pattern recognition work, as well as many pointers for further reading. See also Izenman’s recent survey article [16]. Roughly speaking, our work departs from the traditional statistical and pattern recognition approaches in two ways. First, we place explicit emphasis on the comput ationrd complexity of distribution learning. It seems fair to say that while previous research has provided an excellent understanding of the information-theoretic issues involved in dis-

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On the learnability of discrete distributions

We present a new construction of a pseudorandom generator based on a simple combination of two LFSRs. The construction has attractive properties as simplicity (conceptual and implementation-wise), scalability (hardware and security), proven minimal security conditions (exponential period, exponential linear complexity, good statistical properties), and resistance to known attacks. The construction is suitable for practical implementation of efficient stream cipher cryptosystems.

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Yishay Mansour

Papers

Learning decision trees using the Fourier spectrum

Constant depth circuits, Fourier transform, and learnability

Learning decision trees using the Fourier spectrum

On the learnability of discrete distributions

The shrinking generator