Multilayer neural networks trained with the back-propagation algorithm constitute the best example of a successful gradient based learning technique. Given an appropriate network architecture, gradient-based learning algorithms can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters, with minimal preprocessing. This paper reviews various methods applied to handwritten character recognition and compares them on a standard handwritten digit recognition task. Convolutional neural networks, which are specifically designed to deal with the variability of 2D shapes, are shown to outperform all other techniques. Real-life document recognition systems are composed of multiple modules including field extraction, segmentation recognition, and language modeling. A new learning paradigm, called graph transformer networks (GTN), allows such multimodule systems to be trained globally using gradient-based methods so as to minimize an overall performance measure. Two systems for online handwriting recognition are described. Experiments demonstrate the advantage of global training, and the flexibility of graph transformer networks. A graph transformer network for reading a bank cheque is also described. It uses convolutional neural network character recognizers combined with global training techniques to provide record accuracy on business and personal cheques. It is deployed commercially and reads several million cheques per day.

Gradient-based learning applied to document recognition

LIBSVM is a library for Support Vector Machines (SVMs). We have been actively developing this package since the year 2000. The goal is to help users to easily apply SVM to their applications. LIBSVM has gained wide popularity in machine learning and many other areas. In this article, we present all implementation details of LIBSVM. Issues such as solving SVM optimization problems theoretical convergence multiclass classification probability estimates and parameter selection are discussed in detail.

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LIBSVM: A library for support vector machines

Setting of the learning problem consistency of learning processes bounds on the rate of convergence of learning processes controlling the generalization ability of learning processes constructing learning algorithms what is important in learning theory?.

The Nature of Statistical Learning Theory

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

Disclosed is an improved technique for training a support vector machine using a distributed architecture. A training data set is divided into subsets, and the subsets are optimized in a first level of optimizations, with each optimization generating a support vector set. The support vector sets output from the first level optimizations are then combined and used as input to a second level of optimizations. This hierarchical processing continues for multiple levels, with the output of each prior level being fed into the next level of optimizations. In order to guarantee a global optimal solution, a final set of support vectors from a final level of optimization processing may be fed back into the first level of the optimization cascade so that the results may be processed along with each of the training data subsets. This feedback may continue in multiple iterations until the same final support vector set is generated during two sequential iterations through the cascade, thereby guaranteeing that the solution has converged to the global optimal solution. In various embodiments, various combinations of inputs may be used by the various optimizations. The individual optimizations may be processed in parallel.

Parallel support vector method and apparatus

To implement the SRM inductive principle in learning algorithms one has to minimize the risk in a given set of functions by controlling two factors: the value of the empirical risk and the value of the confidence interval.

Constructing Learning Algorithms

Learning using hidden information: Master-class learning

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.

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Falsificationism and Statistical Learning Theory: Comparing the Popper and Vapnik-Chervonenkis Dimensions

We examine the so-called rigorous support vector machine (RSVM) approach proposed by Vapnik (1998). The formulation of RSVM is derived by explicitly implementing the structural risk minimization principle with a parameter H used to directly control the VC dimension of the set of separating hyperplanes. By optimizing the dual problem, RSVM finds the optimal separating hyperplane from a set of functions with VC dimension approximate to H 2+1. RSVM produces classifiers equivalent to those obtained by classic SVMs for appropriate parameter choices, but the use of the parameter H facilitates model selection, thus minimizing VC bounds on the generalization risk more effectively. In our empirical studies, good models are achieved for an appropriate H 2 ∈ [5% l, 30% l] where l is the size of training data.

Vladimir Vapnik

Papers

Parallel support vector method and apparatus

Constructing Learning Algorithms

Learning using hidden information: Master-class learning

Falsificationism and Statistical Learning Theory: Comparing the Popper and Vapnik-Chervonenkis Dimensions

Learning with Rigorous Support Vector Machines