Y, has been the method of choice for proving impossibility converse results. This criterion arises naturally as a weakened form of the wellknown data processing inequality dpi. Hawaii has very few black residents and a relatively low gini coefficient for withinblack inequality. While focusing primarily on social class, it also deals broadly with other forms of social inequality, including racialethnic, gender, and political. The global economic crisis of 20082009 seemed a crisis of the systems underlying political ideology and economic theory. According to this theory, the explanation for higher wage inequality in the us is higher skill inequality.
On hypercontractivity and a data processing inequality. Recently interesting applications of information inequalities beyond information theory were found 10,12,14. I rarely purchase books but this one is definitely a keeper. The ratio of labor wages w to the rent of capital r serves as a plausible measure of equality that has been used empirically to good effect in recent economic history. The same ideas were introduced independently by ziv and zakai 14, with the primary moti vation of using it to obtain sharper distortion bounds for classes of simple codes for joint source. In particular, if xk has probability density function pdf p, then hxk elog 1 pxk. If you are interested in finding out more about inequality we suggest reading the following books.
The poor suffer because they dont have enough, not because others have more, and some have far too much. Intergenerational wealth transmission and the dynamics of inequality in smallscale societies. Yet few would argue that inequality is a greater evil than poverty. Informally it states that you cannot increase the information content of a quantum system by acting on it with a local physical operation. For further information on strong data processing inequalities, the. Cover and thomas wrote a book on information theory 49 ten years ago which covers most of the. Artificial intelligence blog data processing inequality. Specifically, this hypothesis is the view that a burst of new technologies led to an increased demand by. Information inequality presents a crisp and farreaching indictment of the data deprivation that corporate interests are inflicting on the social fabric.
This paper describes the correlations between inequality and the growth rates in crosscountry data. We establish a connection between this bound and the fact that correlations between two systems cannot increase under local operations, a property known as the data processing inequality. Macrae, inequality and institutions 18 august 2004 apsa 6 a exogenous changes in inequality. Jul 04, 2011 the data processing inequality dpi is a fundamental feature of information theory. Information theory and the stock market university of belgrade. Even for x with pdf h x can be positive, negative, take values of. Using nonparametric methods, we show that the growth rate is an inverted ushaped function of net changes in inequality. On the inequalities in information theory 5 in most systems that deals with information theory, at least two entities are relevant. In a communication system, these are the transmitter sender and receiver. In particular, we shall find the competitively optimal and growth rate optimal portfolio strategies. Her deep dive into how britain discarded women technologists and lost its edge in computing, the subtitle, is a sobering tale of the real consequences of gender biasa problem that persists in many technical fields today. This paper describes a new dataset, in which measures of educational level and inequality were collected for 48 countries over 5year birth cohorts.
Strong dataprocessing inequalities for channels and. Information theory, in the technical sense, as it is used today goes back to the work. Patterns and processes introduces key concepts, theories, research findings, and trends associated with the major forms of social inequality. Pdf dataprocessing inequalities based on a certain. Dataprocessing inequality clari es an important idea in statistics su cient statistics given a family of distributions ff xg indexed by let x be sample from f, tx be any statistics, then. Strong dataprocessing inequalities for channels and bayesian networks yury polyanskiy and yihong wu abstract the dataprocessing inequality, that is, iu. These are my personal notes from an information theory course taught by prof. Information theoretic proofs of entropy power inequalities. Inequality has profound consequences for how we think, how we respond to stress, how our immune systems function, and even how we view justice, fairness, and other moral concepts.
We know a random variable y and we want to guess the valus of a correlated r. Lecture notes on information theory department of statistics, yale. When opening a textbook on linear 1 or nonlinear 2 deterministic signal processing. Forthcoming in the handbook of economic growth philippe aghion and steven durlauf, eds. Want to delve deeper into the issues inequality raises. We offer this survey of important reads both classic and contemporary.
Yao xie, ece587, information theory, duke university 12. Data processing inequality clari es an important idea in statistics su cient statistics given a family of distributions ff xg indexed by let x be sample from f, tx be any statistics, then. Drawing on four representative international surveys ess, eusilc, ials and issp, we collected measures of individual educational attainment and aggregated them to generate synthetic indices of educational level and dispersion by countries. There are 2 n subsets, for which joint entropies can be computed. At the same time, there seems to be little consensus on the causes of spatial inequality and on a list. We only need to prove the ag inequality because the hg inequality follows from the ag inequality and properties of the means ha 1 a 1 a. Asec and provide information for calendar years 2000, 2001, and 2002, respectively. In the labor economics literature this consensus view has become known as the skillbiased technological change sbtc hypothesis. A rapid history of cultural and informational institutions in the u. X gy,hxjy 0 fanos inequality is a quantitative version of the above. This can be expressed concisely as post processing cannot increase information. Spatial inequality is an important feature of many developing countries that seems to increase with economic growth and development. Inequality, technology, and the social contract roland benabou1 first draft. On inequality download pdf 96de5 economic inequality is one of the most divisive issues of our time.
C q that stems from the data processing inequality of i q. The estimated relationship is robust to variations in control variables and. This can be expressed concisely as postprocessing cannot increase information. Appendix c provides summary statistics for the data used. Tsirelsons bound from a generalised data processing. Information inequalities are widely used for proving converse coding theorems in information theory. If x is a function of y, then the degree of surprise in x given y is 0 and vice versa. Information theory will help us identify these fundamental limits of data compression, tranmission and inference. At the same time, there seems to be little consensus on the causes of spatial inequality and on a list of effective policy instruments that. Fanoss inequality, information theory,electrical engineering and computer science, engineering, massachusetts institute of. So investigation of the class of all valid information inequalities is an interesting problem. Data processing inequality 20612 leave a comment printable version project feature extraction, a b.
Technology, institutions and wealth inequality in the very long run lectures 4 and 5 are alternative final topics, one or the other, but not both will be presented. Thanks for contributing an answer to mathematics stack exchange. According to recent pisa report, inequality in educational achivement among 15yrold math tests is as large in france as in the us but it is possible that inequality in access to higher. The strength of quantum correlations is bounded from above by tsirelsons bound. The data processing inequality dpi is a fundamental feature of information theory. Mutual information staying constant under composition of channels. Tsirelsons bound from a generalised data processing inequality.
This inequality will seem obvious to those who know information theory, but i still think its cute. These notes have not been subjected to the usual scrutiny reserved for formal publications. But avoid asking for help, clarification, or responding to other answers. Countries included in each group are listed in appendix a, and the definitions of variables are listed in appendix b. Information theory and the stock market the duality between the growth rate of wealth in the stock market and the entropy rate of the market is striking. Kate pickett and richard wilkinsons the spirit level not only changed the way we understand and view inequality, it inspired the creation of the equality trust and our work. Inequality has profound consequences for how we think, how we respond to stress, how. They may be distributed outside this class only with the permission of the instructor. We do not know how people who reported more than one race in 2002.
Foremost among these is mutual information, a quantity of central importance in information theory 5, 6. All dpisatisfying dependence measures are thus proved to satisfy selfequitability. Epi is one of the deepest inequalities in information theory, and has a. The most influential and talkedabout book on society in the last decade. We will prove later in the paper that the inequality is strict in general by providing an explicit example. Suppose x,y, z are random variables and z is independent of x given y, then.
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. The data processing inequality is a nice, intuitive inequality about mutual information. When the smooth minentropy is used as the relevant information measure, then the dpi follows immediately from the definition of the entropy. Strong dataprocessing inequalities for channels and bayesian.
An introduction to information theory and applications. 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. Download pdf social inequality patterns and processes. As observed by gottschalk 1997, income inequality in oecd countries has increased over. Keith payne penguin random house, 2017 the disparity between rich and poor has ramifications that extend far beyond mere financial means. There are a number of different contexts in which these inequalities appear. Data processing theorems and the second law of thermodynamics. Wiley also publishes its books in a variety of electronic formats. The notion of entropy, which is fundamental to the whole topic of this book, is introduced here. Generalizations of some inequalities from information theory are obtained, including a generalized information inequality and a generalized log sum inequality, which states for a,b. Because the majority of oecd countries are at the later stages of development, kuznets hypothesis would lead us to anticipate falling income inequality in these countries. For the first time in 2003, cps respondents were asked to identify themselves in one or more racial groups.
May 2003 this version october 2004 1princeton university, nber, cepr, irp and bread. The issue at stake is an economically and politically charged one, with questions as to how the government can best redistribute income from those with greater income. Download pdf social inequality patterns and processes free. Students will gain a keen awareness of the subtle and often unseen ways in which inequality is structured, and how it impinges on virtually all facets of individual and group life. Its a dense book, full of rich information, but is not. Information processing and learning spring 2012 lecture 2. Strong data processing inequalities for channels and bayesian networks yury polyanskiy and yihong wu abstract the data processing inequality, that is, iu.
Suppose x,y, z are random variables and z is independent of x given y, then mix,z data processing inequality. Economic growth is also closely aligned to factors such as income inequality and income distribution. Find materials for this course in the pages linked along the left. Inequalities are very important in the study of information theory.
Consider a channel that produces y given xbased on the law p yjx shown. The term is synonymous today with income inequality in the current climate. Y, has been the method of choice for proving impossibility converse results in information theory and many other disciplines. An intuitive proof of the data processing inequality. Indeed from theorem 2 and remark 1 it is immediate that m x. List of books and articles about income inequality.
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