The goal of machine learning is to program computers to use example data or past experience to solve a given problem. Many successful applications of machine learning exist already, including systems that analyze past sales data to predict customer behavior, optimize robot behavior so that a task can be completed using minimum resources, and extract knowledge from bioinformatics data. Introduction to Machine Learning is a comprehensive textbook on the subject, covering a broad array of topics not usually included in introductory machine learning texts. In order to present a unified treatment of machine learning problems and solutions, it discusses many methods from different fields, including statistics, pattern recognition, neural networks, artificial intelligence, signal processing, control, and data mining. All learning algorithms are explained so that the student can easily move from the equations in the book to a computer program. The text covers such topics as supervised learning, Bayesian decision theory, parametric methods, multivariate methods, multilayer perceptrons, local models, hidden Markov models, assessing and comparing classification algorithms, and reinforcement learning. New to the second edition are chapters on kernel machines, graphical models, and Bayesian estimation; expanded coverage of statistical tests in a chapter on design and analysis of machine learning experiments; case studies available on the Web (with downloadable results for instructors); and many additional exercises. All chapters have been revised and updated. Introduction to Machine Learning can be used by advanced undergraduates and graduate students who have completed courses in computer programming, probability, calculus, and linear algebra. It will also be of interest to engineers in the field who are concerned with the application of machine learning methods. Adaptive Computation and Machine Learning series

Introduction to Machine Learning

In the data stream scenario, input arrives very rapidly and there is limited memory to store the input. Algorithms have to work with one or few passes over the data, space less than linear in the input size or time significantly less than the input size. In the past few years, a new theory has emerged for reasoning about algorithms that work within these constraints on space, time, and number of passes. Some of the methods rely on metric embeddings, pseudo-random computations, sparse approximation theory and communication complexity. The applications for this scenario include IP network traffic analysis, mining text message streams and processing massive data sets in general. Researchers in Theoretical Computer Science, Databases, IP Networking and Computer Systems are working on the data stream challenges. This article is an overview and survey of data stream algorithmics and is an updated version of [1].

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Data streams: algorithms and applications

1 Introduction 2 Map 3 The Data Stream Phenomenon 4 Data Streaming: Formal Aspects 5 Foundations: Basic Mathematical Ideas 6 Foundations: Basic Algorithmic Techniques 7 Foundations: Summary 8 Streaming Systems 9 New Directions 10 Historic Notes 11 Concluding Remarks Acknowledgements References

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Data Streams: Algorithms and Applications

In this paper, we are concerned with the finite-length analysis of low-density parity-check (LDPC) codes when used over the binary erasure channel (BEC). The main result is an expression for the exact average bit and block erasure probability for a given regular ensemble of LDPC codes when decoded iteratively. We also give expressions for upper bounds on the average bit and block erasure probability for regular LDPC ensembles and the standard random ensemble under maximum-likelihood (ML) decoding. Finally, we present what we consider to be the most important open problems in this area.

/pdf/finite-length-analysis-of-low-density-parity-check-codes-on-4jld71f17q.pdf

Finite-length analysis of low-density parity-check codes on the binary erasure channel

The three-dimensional dose, volume, and outcome data for lung are reviewed in detail. The rate of symptomatic pneumonitis is related to many dosimetric parameters, and there are no evident threshold "tolerance dose-volume" levels. There are strong volume and fractionation effects.

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Radiation dose-volume effects in the lung.

Stopping sets determine the performance of low-density parity-check (LDPC) codes under iterative decoding over erasure channels. We derive several results on the asymptotic behavior of stopping sets in Tanner-graph ensembles, including the following. An expression for the normalized average stopping set distribution, yielding, in particular, a critical fraction of the block length above which codes have exponentially many stopping sets of that size. A relation between the degree distribution and the likely size of the smallest nonempty stopping set, showing that for a /spl radic/1-/spl lambda/'(0)/spl rho/'(1) fraction of codes with /spl lambda/'(0)/spl rho/'(1) 2, the smallest nonempty stopping set is linear in the block length. Bounds on the average block error probability as a function of the erasure probability /spl epsi/, showing in particular that for codes with lowest variable degree 2, if /spl epsi/ is below a certain threshold, the asymptotic average block error probability is 1-/spl radic/1-/spl lambda/'(0)/spl rho/'(1)/spl epsi/.

http://fleece.ucsd.edu/~alon/papers/stp_set_dst.pdf

Stopping set distribution of LDPC code ensembles

It has long been known that the compression redundancy of independent and identically distributed (i.i.d.) strings increases to infinity as the alphabet size grows. It is also apparent that any string can be described by separately conveying its symbols, and its pattern-the order in which the symbols appear. Concentrating on the latter, we show that the patterns of i.i.d. strings over all, including infinite and even unknown, alphabets, can be compressed with diminishing redundancy, both in block and sequentially, and that the compression can be performed in linear time. To establish these results, we show that the number of patterns is the Bell number, that the number of patterns with a given number of symbols is the Stirling number of the second kind, and that the redundancy of patterns can be bounded using results of Hardy and Ramanujan on the number of integer partitions. The results also imply an asymptotically optimal solution for the Good-Turing probability-estimation problem.

Universal compression of memoryless sources over unknown alphabets

While deciphering the German Enigma code during World War II, I.J. Good and A.M. Turing considered the problem of estimating a probability distribution from a sample of data. They derived a surprising and unintuitive formula that has since been used in a variety of applications and studied by a number of researchers. Borrowing an information-theoretic and machine-learning framework, we define the attenuation of a probability estimator as the largest possible ratio between the per-symbol probability assigned to an arbitrarily-long sequence by any distribution, and the corresponding probability assigned by the estimator. We show that some common estimators have infinite attenuation and that the attenuation of the Good-Turing estimator is low, yet larger than one. We then derive an estimator whose attenuation is one, namely, as the length of any sequence increases, the per-symbol probability assigned by the estimator is at least the highest possible. Interestingly, some of the proofs use celebrated results by Hardy and Ramanujan on the number of partitions of an integer. To better understand the behavior of the estimator, we study the probability it assigns to several simple sequences. We show that some sequences this probability agrees with our intuition, while for others it is rather unexpected.

Always Good Turing: asymptotically optimal probability estimation

While deciphering the Enigma code, Good and Turing derived an unintuitive, yet effective, formula for estimating a probability distribution from a sample of data. We define the attenuation of a probability estimator as the largest possible ratio between the per-symbol probability assigned to an arbitrarily long sequence by any distribution, and the corresponding probability assigned by the estimator. We show that some common estimators have infinite attenuation and that the attenuation of the Good-Turing estimator is low, yet greater than 1. We then derive an estimator whose attenuation is 1; that is, asymptotically it does not underestimate the probability of any sequence.

https://science.sciencemag.org/content/sci/302/5644/427.full.pdf

Always Good Turing: asymptotically optimal probability estimation.

Recent work has related the error probability of iterative decoding over erasure channels to the presence of stopping sets in the Tanner graph of the code used. In particular, it was shown that the smallest number of uncorrected erasures is the size of the graph's smallest stopping set. Relating stopping sets and girths, we consider the size /spl sigma/(d,g) of the smallest stopping set in any bipartite graph of girth g and left degree d. For g/spl les/8 and any d, we determine /spl sigma/(d,g) exactly. For larger gs we bound /spl sigma/(d,g) in terms of d, showing that for fixed d, /spl sigma/(d,g) grows exponentially with g. Since constructions of high-girth graphs are known, one can therefore design codes with good erasure-correction guarantees under iterative decoding.

Junan Zhang

Papers

Stopping set distribution of LDPC code ensembles

Universal compression of memoryless sources over unknown alphabets

Always Good Turing: asymptotically optimal probability estimation

Always Good Turing: asymptotically optimal probability estimation.

Stopping sets and the girth of Tanner graphs