Strong data processing inequalities for channels and bayesian networks yury polyanskiy and yihong wu abstract the data processing inequality, that is, iu. Given an information source, can additional processing gain more amount of information about that source. Lecture notes on information theory preface \there is a whole book of readymade, long and convincing, lavishly composed telegrams for all occasions. This is based on the book of thomas cover elements of information theory 2ed 2006 in information theory there are two key concepts. All the essential topics in information theory are covered in detail, including. Oct 10, 20 34 entropy, relative entropy, and mutual information 2. Y, has been the method of choice for proving impossibility converse results in information theory and many other disciplines. Even the shannontype inequalities can be considered part of this category, since the bivariate mutual information can be expressed as the kullbackleibler divergence of the joint distribution with respect to the product. These are my personal notes from an information theory course taught by prof.
Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory. Minimal su cient statistic is a function of all other su cient statistic maximally compresses information about in the sample dr. Does evolution violate the data processing inequality. Cover is a past president of the ieee information theory society, a fellow of the ieee and the institute of mathematical statistics, and a member of the national academy of engineering and the american academy of arts and. Korner, information theory, cambridge university press 2011 r. Check out raymond yeungs book on information theory and network coding to convert the above problem to that of set theoretic and measure theoretic manipulation. In a communication system, these are the transmitter sender and receiver. This book introduces readers to essential tools for the measurement and analysis of information loss in signal processing systems.
Fundamentals of information theory and coding design. However, very few, if any, of these books have been able to cover the fundamentals of the theory without losing the reader in. The data processing inequality dpi is a fundamental feature of information theory. Lecture notes on information theory statistics, yale university. Cover, phd, is professor in the departments of electrical engineering and statistics, stanford university.
Yao xie, ece587, information theory, duke university. Strong dataprocessing inequalities for channels and. Introduction to information theory and data compression. How big data is automating inequality the new york times. Elements of information theory 2nd edition wiley series. Elements of information theory 2nd edition wiley series in telecommunications and signal processing thomas m.
Information is uncertainty and is modeled as random variables. How does information theory relate to image processing. Two proofs of the fisher information inequality via data. Strong dataprocessing inequalities for channels and bayesian networks yury polyanskiy and yihong wu abstract the dataprocessing inequality, that is, iu. A great many important inequalities in information theory are actually lower bounds for the kullbackleibler divergence. This book is very specifically targeted to problems in communications and compression by providing the fundamental principles and results in information theory and rate distortion theory for these applications and presenting methods that have proved and will prove useful in analyzing and designing real systems.
An intuitive proof of the data processing inequality. The data processing inequality is an information theoretic concept which states that the information content of a signal cannot be increased via a local physical operation. Jensens inequality, data processing theorem, fanoss inequality. Consider a channel that produces y given xbased on the law p yjx shown. It is useful in compression analysis, autoadjustment control for example, autofocus and thres.
Informally it states that you cannot increase the information content of a quantum system by acting on it with. Lecture notes for statistics 311electrical engineering 377. By increased the mutual information i assume you mean, increased the mutual information between the signal and the output of the highpass filter, by adding the noise. I then add noise to this signal, that happens to be somewhere below 300 hz. It discusses the information associated to a certain source and. Jul 04, 2011 the data processing inequality dpi is a fundamental feature of information theory. This note will explore the basic concepts of information theory. Dataprocessing, fano dataprocessing inequality su cient statistics fanos inequality dr. However, a fundamental theorem in information theorydata processing inequalitystates that deterministic processing always involves information loss. The ratedistortion theory founded by shannon 10 is a cornerstone of information theory and, in particular, the processing, compression, and storage of continuous data see 11, chapter 10 for. Informally it states that you cannot increase the information content of a quantum system by acting on it with a local physical operation. Strong dataprocessing inequalities for channels and bayesian. The intimate relationship between fisher information and entropy is explored, culminating in a common proof of the entropy power inequality and the brunn. An effective blend of carefully explained theory and practicalapplications, this book has been written to offer access to the basics of information theory and data compression.
Lecture notes on information theory by yury polyanskiy mit and yihong wu yale other useful books recommended, will not be used in an essential way. Automating inequality how hightech tools profile, police, and punish the poor by virginia eubanks 260 pp. And selection unlike mutation is not a local operation on the dna strands as required by the data processing inequality. If ix,y is the information in common between x and y, then you can write the data processing inequality as from elements of information theory, a great book. Gallager, information theory and reliable communication, wiley 1969. Mutual information between continuous and discrete variables from numerical data. Data processing inequality and unsurprising implications. Control functions have their root in the dataprocessing inequality cover and thomas, 2012, which states that. Data processing is a general principle in information theory, in that any quantity under the name information should obey some sort of data processing inequality. Is there an analog of the data processing inequality for. Introduction to information theory, a simple data compression problem, transmission of two messages over a noisy channel, measures of information and their properties, source and channel coding, data compression, transmission over noisy channels, differential entropy, ratedistortion theory. The number of books on the market dealing with information theory and coding has been on the rise over the past. This book is devoted to the theory of probabilistic information measures and.
Is it possible to obtain more information about a source given additional further. But the data processing inequality doesnt say the inclusion of r1 cant increase is, r2, it only says is,r1 is,r2. Information is digital, it is the same as transmiting 0s1s with no reference to what they represent. Question feed subscribe to rss question feed to subscribe to this rss feed, copy and paste this url into your rss reader.
Information source state of nature true amount of information in source observed process. If the probability of any sequence event is unchanged by shifting the event, that is, by shifting all of the sequences in the event, then the. The premise is learn bayesian statistics using python, explains the math notation in terms of python code not the other way around. The data processing inequality dpi states that for three random variables, x, y, and z, arranged in markov chain such that, then, where here stands for mutual information. However, a fundamental theorem in information theory. Check out raymond yeungs book on information theory and network coding to convert the above problem. The data processing inequality adam kelleher medium. This sounded great to me, as im just not comfortable. His research interests include statistical inference and machine learning, detection and estimation theory, and information theory, with applications to data science, wireless communications and sensor networks. In this sense, zamirs data processing inequality for fisher information merely pointed out the fact that fisher information bears the real meaning as an information quantity. Lecture notes information theory electrical engineering. Apply dataprocessing inequality twice to the map x, y y, x to get dpxy pxpy dpy x py px.
Champaign information theory, learning and big data. The notion of entropy, which is fundamental to the whole topic of this book, is introduced here. Four variable data processing inequality stack exchange. Information inequality presents a telling account of the current shift in the information landscape from a model of social accountability to a more privatized corporate model.
Signal or data processing operates on the physical representation of information so that users can easily access and extract that information. Information loss in deterministic signal processing systems. In summary, chapter 1 gives an overview of this book, including the system model, some basic operations of information processing, and illustrations of how an information source is encoded. Today, i want to talk about how it was so successful partially from an information theoretic perspective and some lessons that we all. On the inequalities in information theory 5 in most systems that deals with information theory, at least two entities are relevant. The notion of entropy, which is fundamental to the whole topic of this book. The data processing inequality is an information theoretic concept which states that the information content of a signal cannot be increased via a local physical. This is must reading for information professionals who maintain some sort of professional literacy. This can be expressed concisely as post processing cannot increase information. This can be expressed concisely as postprocessing cannot increase information. By data processing inequality, by processing we are losing.
You see, what gets transmitted over the telegraph is not the text of the telegram, but simply the number under which it is listed in the book. A number of new inequalities on the entropy rates of subsets and the relationship of entropy and p norms are also developed. Information is uncertainty and is modeled as random variables information is digital, it is the same as transmiting 0s1s with no reference to what they represent. Entropy and information theory first edition, corrected robert m. Employing a new informationtheoretic systems theory, the book analyzes various systems in the signal processing engineers toolbox. Applications to mcmc and graphical models duration. It is highly recommended for students planning to delve into the fields of communications, data compression, and statistical signal processing. This is based on the book of thomas cover elements of information theory. Y, has been the method of choice for proving impossibility converse results. In information theory, the data processing inequality states. Information loss in deterministic signal processing. When the smooth minentropy is used as the relevant information measure, then the dpi follows immediately from the definition of the entropy.
The latest edition of this classic is updated with new problem sets and material the second edition of this fundamental textbook maintains the books tradition of clear, thoughtprovoking instruction. Jun 07, 2009 lets suppose i have a speech signal with frequency content 300 hz. It discusses the information associated to a certain source and the usual types of source codes, the information transmission, joint information, conditional entropy, mutual information, and channel capacity. We are hence required to consider a pair of random variables not just a single random variable. This chapter summarizes and reorganizes the inequalities found throughout this book. May 04, 2018 while technology is often touted by researchers and policymakers as a way to deliver services to the poor more efficiently, eubanks shows that more often, it worsens inequality. Chapter 2 looks at ways of encoding source symbols such that any errors. The authors have applied their experience in teaching information theory and data compression to the careful preparation and unique organization of this oneofakind text.
Sending such a telegram costs only twenty ve cents. Veeravalli is the henry magnuski professor in the ece department at the university of illinois, urbanachampaign. The chapters contain treatments of entropy, mutual information, lossless. Statistical inference engineers and data scientists. The data processing inequality and bounded rationality.
Data processing inequality and unsurprising implications we have heard enough about the great success of neural networks and how they are used in real problems. When the smooth minentropy is used as the relevant information measure. The book presents the historical evolution of information theory, along with the basic concepts linked to information. Selection tosses out some individuals carrying certain strands in relation to others carrying different strands.
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