TMD Discussion Papers contain preliminary material and research results, and are circulated prior to a full peer review in order to stimulate discussion and critical comment. It is expected that most Discussion Papers will eventually be published in some other form, and that their content may also be revised. This paper is available at

TMD Discussion Papers contain preliminary material and research results, and are circulated prior to a full peer review in order to stimulate discussion and critical comment. It is expected that most Discussion Papers will eventually be published in some other form, and that their content may also be revised.

We present an extension to Jaynes' maximum entropy principle that handles latent variables. The principle of latent maximum entropy we propose is di#erent from both Jaynes' maximum entropy principle and maximum likelihood estimation, but often yields better estimates in the presence of hidden variables and limited training data. We first show that solving for a latent maximum entropy model poses a hard nonlinear constrained optimization problem in general. However, we then show that feasible solutions to this problem can be obtained e#ciently for the special case of log-linear models---which forms the basis for an e#cient approximation to the latent maximum entropy principle. We derive an algorithm that combines expectation-maximization with iterative scaling to produce feasible log-linear solutions. This algorithm can be interpreted as an alternating minimization algorithm in the information divergence, and reveals an intimate connection between the latent maximum entropy and maximum likelihood principles.

of 15 agricultural research centers that receive principal funding from governments, private foundations, and international and regional organizations, most of which are members of the

The Principle of Maximum Entropy is discussed and two classic probabilistic models of information retrieval, the Binary Independence Model of Robertson and Sparck Jones and the Combination Match Model of Croft and Harper are derived using the maximum entropy approach. The assumptions on which the classical models are based are not made. In their place, the probability distribution of maximum entropy consistent with a set of constraints is determined. It is argued that this subjectivist approach is more philosophically coherent than the frequentist conceptualization of probability that is often assumed as the basis of probabilistic modeling and that this philosophical stance has important practical consequences with respect to the realization of information retrieval research.

This paper develops a simulation method for pricing path-dependent American options, and American options on a large number of underlying assets, such as basket options. Standard numerical procedures (lattice methods and nite difference methods) are generally inapplicable to such high-dimensional problems, and this has motivated research into simulation-based methods. The optimal stopping problem embedded in the pricing of American options makes this a nonstandard problem for simulation. This paper extends the stochastic mesh introduced in Broadie and Glasserman [5]. In its original form, the stochastic mesh method required knowledge of the transition density of the underlying process of asset prices and other state variables. This paper extends the method to settings in which the transition density is either unknown or fails to exist. We avoid the need for a transition density by choosing mesh weights through a constrained optimization problem. If the weights are constrained to correctly price su ciently many simple instruments, they can be expected to work well in pricing a more complex American option. We investigate two criteria for use in the optimization | maximum entropy and least squares. The methods are illustrated through numerical examples. 32 1

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Within the task of collaborative filtering two challenges for computing conditional probabilities exist. First, the amount of training data available is typically sparse with respect to the size of the domain. Thus, support for higher-order interactions is generally not present. Second, the variables that we are conditioning upon vary for each query. That is, users label different variables during each query. For this reason, there is no consistent input to output mapping. To address these problems we purpose a maximum entropy approach using a non-standard measure of entropy. This approach can be simplified to solving a set of linear equations that can be efficiently solved. 1

There is a continuing need to use recent and consistent multisectoral economic data to support policy analysis and the development of economywide models. Updating and estimating input-output tables and Social Accounting Matrices (SAMs) for a recent year is a difficult and a challenging problem. Typically, input-output data are collected at long intervals (usually five years or more), while national income and product data are available annually, but with a lag. Supporting data also come from a variety of sources; e.g., censuses of manufacturing, labor surveys, agricultural data, government accounts, international trade accounts, and household surveys. The problem in estimating a SAM for a recent year is to find an efficient (and cost-effective) way to incorporate and reconcile information from a variety of sources, including data from prior years. The traditional RAS approach requires that we start with a consistent SAM for a particular period and “update ” it for a later period given new information on row and column sums. This paper extends the RAS method by proposing a flexible entropy difference approach to estimating a consistent SAM starting from inconsistent data estimated with error, a common experience in many countries. The method is flexible and powerful when dealing with

Newey and Smith (2001) have recently shown that Empirical Likelihood (EL) exhibits desirable higher-order asymptotic properties, namely, that its O ¡ n −1 ¢ bias is particularly small and that biascorrected EL is higher-order efficient. Although EL possesses these properties when the model is correctly specified, this paper shows that the asymptotic variance of EL in the presence of model misspecification may become undefined when the functions defining the moment conditions are unbounded. In contrast, the Exponential Tilting (ET) estimator avoids this problem under mild regularity conditions. Since ET does not share the higher-order asymptotic properties of EL, there is a need for an estimator that combines the qualities of both estimators. This paper introduces a new estimator called Exponentially Tilted Empirical Likelihood (ETEL) that is shown to have the same O ¡ n −1 ¢ bias and the same O ¡ n −2¢ variance as EL, while maintaining a well-defined asymptotic variance under model misspecification.