An information theory for preferences

Recent literature in the last Maximum Entropy workshop introduced an analogy between cumulative probability distributions and normalized utility functions. Based on this analogy, a utility density function can de defined as the derivative of a normalized utility function. A utility density function is non-negative and integrates to unity. These two properties form the basis of a correspondence between utility and probability. A natural application of this analogy is a maximum entropy principle to assign maximum entropy utility values. Maximum entropy utility interprets many of the common utility functions based on the preference information needed for their assignment, and helps assign utility values based on partial preference information. This paper reviews maximum entropy utility and introduces further results that stem from the duality between probability and utility

Improving Classification When a Class Hierarchy is Available Using a Hierarchy-Based Prior

We introduce a new method for building classification models when we have prior knowledge of how the classes can be arranged in a hierarchy, based on how easily they can be distinguished. The new method uses a Bayesian form of the multinomial logit (MNL, a.k.a. ``softmax'') model, with a prior that introduces correlations between the parameters for classes that are nearby in the tree. We compare the performance on simulated data of the new method, the ordinary MNL model, and a model that uses the hierarchy in different way. We also test the new method on a document labelling problem, and find that it performs better than the other methods, particularly when the amount of training data is small

Beyond the Spectral Theorem: Spectrally Decomposing Arbitrary Functions of Nondiagonalizable Operators

Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, often the linear operator techniques that one would then use simply fail since the operators cannot be diagonalized. This curse is well known. It also occurs for finite-dimensional linear operators. We circumvent it by developing a meromorphic functional calculus that can decompose arbitrary functions of nondiagonalizable linear operators in terms of their eigenvalues and projection operators. It extends the spectral theorem of normal operators to a much wider class, including circumstances in which poles and zeros of the function coincide with the operator spectrum. By allowing the direct manipulation of individual eigenspaces of nonnormal and nondiagonalizable operators, the new theory avoids spurious divergences. As such, it yields novel insights and closed-form expressions across several areas of physics in which nondiagonalizable dynamics are relevant, including memoryful stochastic processes, open non unitary quantum systems, and far-from-equilibrium thermodynamics. The technical contributions include the first full treatment of arbitrary powers of an operator. In particular, we show that the Drazin inverse, previously only defined axiomatically, can be derived as the negative-one power of singular operators within the meromorphic functional calculus and we give a general method to construct it. We provide new formulae for constructing projection operators and delineate the relations between projection operators, eigenvectors, and generalized eigenvectors. By way of illustrating its application, we explore several, rather distinct examples.Comment: 29 pages, 4 figures, expanded historical citations; http://csc.ucdavis.edu/~cmg/compmech/pubs/bst.ht

A Double-Hurdle Approach to Modelling Tobacco Consumption in Italy

This paper analyses the determinants of tobacco expenditures for a sample of Italian households. A Box- Cox double-hurdle model adjusted for heteroscedasticity is estimated to account for separate individual decisions concerning smoking participation and tobacco consumption and to correct for non-normality in the bivariate distribution of the error terms. Nested univariate and bivariate models are found to be excessively restrictive, supporting the adequacy of a generalized specification. Estimation results show that consumption decisions are significantly affected by income and demographic characteristics. In particular, income positively impacts tobacco expenditure, while participation probability substantially declines as age increases. The existence of significant gender differences in both smoking participation and tobacco consumption patterns is found, while high education and white collar occupation reduce the likelihood to smoke and tobacco expenditure levels. Single adult households have a lower probability of smoking initiation even if, conditional on smoking, they consume more. Finally, complementarity between tobacco and alcohol beverages suggests the necessity of joint public health strategies.tobacco consumption, double-hurdle models, limited dependent variables, Box-Cox transformation

Identification and Estimation of Partial Effects with Proxy Variables

I develop a new identification approach for partial effects in nonseparable models with endogeneity. I use a proxy variable for the unobserved heterogeneity correlated with the endogenous variable to construct a valid control function, where the definition of a proxy variable is the same as in the measurement error literature. The identifying assumptions are distinct from existing methods, in particular instrumental variables and selection on observables approaches, and I provide an alternative identification strategy in settings where existing approaches are not applicable. Building on the identification result, I consider three estimation approaches, ranging from nonparametric to flexible parametric methods, and characterize asymptotic properties of the proposed estimators.Comment: 48 pages with the appendi

Household production, time allocation, and welfare in Peru

This paper uses the Peruvian Living Standard Survey (PLSS) data to analyze: (a) inequality in the distribution of income; (b) labor market participation of men and women and the variations in hours of work; and (c) the relationship between variations in labor supply and income inequality. It uses a decomposing method to analyze income inequality and utilizes a structural neo-classical model to analyze household production, consumption, time allocation and welfare. The purpose is to study the effect on production, consumption, and time allocation of changes in education and wage rates. Most of the available information on economic inequality in developing countries refers to the distribution of income among earners. Although this information constitutes an important element for understanding the labor market and the related distribution of income, it is less helpful in the analysis of inequality as a welfare issue. A more relevant indicator of welfare is per capita household income or consumption. This paper uses this indicator in an analysis of economic inequality. The methodological approach is based on a summary measure of inequality which is closely related to the Gini coefficient. The essential difference is that the proposed measure of inequality gives more weight than the Gini coefficient to transfers related to the very poor.Economic Theory&Research,Inequality,Environmental Economics&Policies,Work&Working Conditions,Consumption

Empirical Applications of Multidimensional Inequality Analysis

This paper explores the empirical application of theoretical multidimensional inequality analysis using real household welfare distributions. The paper operationalises recent conceptual developments in multidimensional inequality theory and assesses their usefulness for measurement and policy analysis. Despite the existence of a thriving theoretical literature on multidimensional inequality, empirical applications, particularly at the individual and household levels, are few and far between. This paper compares and contrasts different methodologies for the analysis of multidimensional welfare, including multidimensional inequality indices and stochastic dominance techniques. The results strongly highlight the importance of bringing non-monetary aspects of household welfare into the forefront of inequality analysis since measurements based solely on the distribution of income variables may misrepresent the degree of overall inequality in society. Agreement over the various approaches to the measurement of multidimensional inequality entails, however, non-trivial decisions that may limit the practical usefulness of these measures. We suggest that the use of multidimensional inequality ranges and restrictive dominance criteria may open significant scope for further developments in the empirical analysis of multidimensional inequality.Multidimensional inequality; inequality indices; income inequality; education inequality; health inequality; stochastic dominance

Measuring multivariate redundant information with pointwise common change in surprisal

The problem of how to properly quantify redundant information is an open question that has been the subject of much recent research. Redundant information refers to information about a target variable S that is common to two or more predictor variables Xi . It can be thought of as quantifying overlapping information content or similarities in the representation of S between the Xi . We present a new measure of redundancy which measures the common change in surprisal shared between variables at the local or pointwise level. We provide a game-theoretic operational definition of unique information, and use this to derive constraints which are used to obtain a maximum entropy distribution. Redundancy is then calculated from this maximum entropy distribution by counting only those local co-information terms which admit an unambiguous interpretation as redundant information. We show how this redundancy measure can be used within the framework of the Partial Information Decomposition (PID) to give an intuitive decomposition of the multivariate mutual information into redundant, unique and synergistic contributions. We compare our new measure to existing approaches over a range of example systems, including continuous Gaussian variables. Matlab code for the measure is provided, including all considered examples