Information is digital, it is the same as transmiting 0s1s with no reference to what they represent. Strong dataprocessing inequalities for channels and bayesian. I then add noise to this signal, that happens to be somewhere below 300 hz. These are my personal notes from an information theory course taught by prof. 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 adam kelleher medium.
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. Oct 10, 20 34 entropy, relative entropy, and mutual information 2. It is highly recommended for students planning to delve into the fields of communications, data compression, and statistical signal processing. This can be expressed concisely as post processing cannot increase information. Employing a new informationtheoretic systems theory, the book analyzes various systems in the signal processing engineers toolbox. 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. Product filter button description contents resources courses about the authors this book is a mathematically accessible and uptodate introduction to the tools needed to address modern inference problems in engineering and data science, ideal for graduate students taking courses on statistical inference and detection and estimation, and an invaluable reference for researchers and. Today, i want to talk about how it was so successful partially from an information theoretic perspective and some lessons that we all. The intimate relationship between fisher information and entropy is explored, culminating in a common proof of the entropy power inequality and the brunn. This is based on the book of thomas cover elements of information theory 2ed 2006 in information theory there are two key concepts.
Four variable data processing inequality stack exchange. 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. 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. 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. In information theory, the data processing inequality states. When the smooth minentropy is used as the relevant information measure, then the dpi follows immediately from the definition of the entropy. Jensens inequality, data processing theorem, fanoss inequality. Given an information source, can additional processing gain more amount of information about that source. We are hence required to consider a pair of random variables not just a single random variable. Lecture notes on information theory statistics, yale university. Mutual information is a measure of how much two random variables carry information about each other. This note will explore the basic concepts of information theory. We will use the dataprocessing property of mutual information to be proved.
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. Mutual information between continuous and discrete variables from numerical data. This sounded great to me, as im just not comfortable. However, a fundamental theorem in information theorydata processing inequalitystates that deterministic processing always involves information loss. And selection unlike mutation is not a local operation on the dna strands as required by the data processing inequality. Applications to mcmc and graphical models duration. Two proofs of the fisher information inequality via data. Minimal su cient statistic is a function of all other su cient statistic maximally compresses information about in the sample dr. This book is devoted to the theory of probabilistic information measures and. Strong dataprocessing inequalities for channels and bayesian networks yury polyanskiy and yihong wu abstract the dataprocessing inequality, that is, iu. Veeravalli is the henry magnuski professor in the ece department at the university of illinois, urbanachampaign. Data processing inequality and unsurprising implications.
This chapter summarizes and reorganizes the inequalities found throughout this book. 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. Control functions have their root in the dataprocessing inequality cover and thomas, 2012, which states that. 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. This can be expressed concisely as postprocessing cannot increase information. The notion of entropy, which is fundamental to the whole topic of this book. Does evolution violate the data processing inequality. However, very few, if any, of these books have been able to cover the fundamentals of the theory without losing the reader in. The authors have applied their experience in teaching information theory and data compression to the careful preparation and unique organization of this oneofakind text.
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. Automating inequality how hightech tools profile, police, and punish the poor by virginia eubanks 260 pp. 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. Y, has been the method of choice for proving impossibility converse results. Information theory, mutual information, data processing inequality, chain rule. The number of books on the market dealing with information theory and coding has been on the rise over the past. Introduction to information theory and data compression.
The chapters contain treatments of entropy, mutual information, lossless. Y, has been the method of choice for proving impossibility converse results in information theory and many other disciplines. This book introduces readers to essential tools for the measurement and analysis of information loss in signal processing systems. The data processing inequality and bounded rationality. An intuitive proof of the data processing inequality. Elements of information theory 2nd edition wiley series in telecommunications and signal processing thomas m. Selection tosses out some individuals carrying certain strands in relation to others carrying different strands. How does information theory relate to image processing. Entropy and information theory first edition, corrected robert m. How big data is automating inequality the new york times. By data processing inequality, by processing we are losing. Check out raymond yeungs book on information theory and network coding to convert the above problem.
Information is uncertainty and is modeled as random variables. In a communication system, these are the transmitter sender and receiver. Dataprocessing, fano dataprocessing inequality su cient statistics fanos inequality dr. It discusses the information associated to a certain source and.
The book presents the historical evolution of information theory, along with the basic concepts linked to information. A number of new inequalities on the entropy rates of subsets and the relationship of entropy and p norms are also developed. When the smooth minentropy is used as the relevant information measure. 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. Yao xie, ece587, information theory, duke university. Jul 04, 2011 the data processing inequality dpi is a fundamental feature of information theory. Statistical inference engineers and data scientists. 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. Strong dataprocessing inequalities for channels and. Champaign information theory, learning and big data. Signal or data processing operates on the physical representation of information so that users can easily access and extract that information. 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.
Fundamentals of information theory and coding design. 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. 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. It is useful in compression analysis, autoadjustment control for example, autofocus and thres. But the data processing inequality doesnt say the inclusion of r1 cant increase is, r2, it only says is,r1 is,r2. 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. Thomas the latest edition of this classic is updated with new problem sets and materialthe second edition of this fundamental textbook maintains the book s tradition of clear, thoughtprovoking instruction. 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. 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. Sending such a telegram costs only twenty ve cents. Chapter 2 looks at ways of encoding source symbols such that any errors.
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. Lecture notes information theory electrical engineering. Question feed subscribe to rss question feed to subscribe to this rss feed, copy and paste this url into your rss reader. Is there an analog of the data processing inequality for. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory. The notion of entropy, which is fundamental to the whole topic of this book, is introduced here. This section provides the schedule of lecture topics for the course along with the lecture notes for each session. 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. The data processing inequality dpi is a fundamental feature of information theory. Information source state of nature true amount of information in source observed process. 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. Information loss in deterministic signal processing systems. 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. 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.
On the inequalities in information theory 5 in most systems that deals with information theory, at least two entities are relevant. Informally it states that you cannot increase the information content of a quantum system by acting on it with a local physical operation. Apply dataprocessing inequality twice to the map x, y y, x to get dpxy pxpy dpy x py px. However, a fundamental theorem in information theory. Strong data processing inequalities for channels and bayesian networks yury polyanskiy and yihong wu abstract the data processing inequality, that is, iu. 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. A great many important inequalities in information theory are actually lower bounds for the kullbackleibler divergence. Elements of information theory edition 2 by thomas m. All the essential topics in information theory are covered in detail, including.
Elements of information theory 2nd edition wiley series. 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. Information loss in deterministic signal processing. 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.
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