Set Of Marginal Distributions Research Articles

Decomposed adversarial domain generalization

We tackle the problem of generalizing a predictor trained on a set of source domains to an unseen target domain, where the source and target domains are different but related to one another, i.e., the domain generalization problem. Prior adversarial methods rely on solving the minimax problems to align in the neural network embedding space the components of the domains (i.e., a set of marginal distributions, a set of marginal distributions and multiple sets of class-conditional distributions). However, these methods introduce additional parameters (for each set of distributions) to the network predictor and are difficult to train. In this work, we propose to directly align the domains themselves via solving a minimax problem that can be decomposed and converted into a min one. Particularly, we analytically solve the max problem with respect to (w.r.t.) the domain discriminators, and convert the minimax problem into a min one w.r.t. the embedding function. This is more advantageous since in the end our approach introduces no additional network parameters and simplifies the training procedure. We evaluate our approach on several multi-domain datasets and testify its superiority over the relevant methods. The source code is available at https://github.com/sentaochen/Decomposed-Adversarial-Domain-Generalization.

Enhanced independent spectral histogram representations in face recognition

A spectral histogram descriptor computes a set of marginal distributions based on the filter bank’s responses, and further encodes them into the images. The encoding process for local image structure takes place during the filtering stage, whereas the encoding process of global image feature is conducted during the histogram stage. One drawback of spectral histogram descriptors is their performances will be greatly deteriorated when the filter bank’s responses are not stochastically independent. To tackle this problem, a computational technique named Enhanced Independent Spectral Histogram Feature (EISHF) is proposed. EISHF is composed of four working modules: (1) unsupervised independent filter bank responses computation, (2) binary hashing, (3) XOR bitwise operation and feature encoding, and lastly, (4) block-wise histogramming. To ensure the performance of ordinary spectral histogram descriptors, an XOR operation has been delicately adopted to increase the independency of the filter responses. Tested on three public face databases, the experimental results have substantiated the performance of EISHF in handling different kinds of facial expressions, illuminations, time spans as well as facial makeup effects.

Conditional Forecasting with DSGE Models - A Conditional Copula Approach

DSGE models may be misspecified in many dimensions, which can affect their forecasting performance. To correct for these misspecifications we can apply conditional information from other models or judgment. Conditional information is not accurate, and can be provided as a probability distribution over different outcomes. These probability distributions are often provided by a set of marginal distributions. To be able to condition on this information in a structural model we must construct the multivariate distribution of the conditional information, i.e. we need to draw multivariate paths from this distribution. One way to do this is to draw from the marginal distributions given a correlation structure between the different marginal distributions. In this paper we use the theoretical correlation structure of the model and a copula to solve this problem. The copula approach makes it possible to take into account more flexible assumption on the conditional information, such as skewness and/or fat tails in the marginal density functions. This method may not only improve density forecasts from the DSGE model, but can also be used to interpret the conditional information in terms of structural shocks/innovations.

The Effect of the Raters' Marginal Distributions on Their Matched Agreement: A Rescaling Framework for Interpreting Kappa

Cohen's κ measures the improvement in classification above chance level and it is the most popular measure of interjudge agreement. Yet, there is considerable confusion about its interpretation. Specifically, researchers often ignore the fact that the observed level of matched agreement is bounded from above and below and the bounds are a function of the particular marginal distributions of the table. We propose that these bounds should be used to rescale the components of κ (observed and expected agreement). Rescaling κ in this manner results in κ′, a measure that was originally proposed by Cohen (1960) and was largely ignored in both research and practice. This measure provides a common scale for agreement measures of tables with different marginal distributions. It reaches the maximal value of 1 when the judges show the highest level of agreement possible, given their marginal disagreements. We conclude that κ′ should be used to measure the level of matched agreement contingent on a particular set of marginal distributions. The article provides a framework and a set of guidelines that facilitate comparisons between various types of agreement tables. We illustrate our points with simulations and real data from two studies—one involving judges' ratings of baseball players and one involving ratings of essays in high-stakes tests.

De Finetti-type theorems for random selection processes. Necessary and sufficient conditions

This paper is concerned with random selection processes for which, in the previous literature, several sufficient conditions for a De Finetti-type theorem (granting the conditional independence of a family of random variables) have been proposed. In this paper, we prove that these conditions are also necessary. In this sense, we identify the extremes of the convex set of marginal distributions of a random selection process, and then we give a thorough description and classification of such processes.

Properties of Certain Class of Mixture Distributions

In this study, by considering special class of mixture distributions, the conditional distribution (called accelerated model) of a random vector (called failure-time X) given an uncontrolled variable (called stress level θ) is obtained. Various approaches for obtaining multivariate conditional probability distributions that would admit a given set of marginal distributions have been proposed. Marshal and Olkin (1988) showed that some multivariate families can be derived by a unified model. By using Mellin transform, a similar conclusion is obtained in accelerated models. It is showed that the positive dependency of association is sometimes exposed.

Chessboard Distributions and Random Vectors with Specified Marginals and Covariance Matrix

There is a growing need for the ability to specify and generate correlated random variables as primitive inputs to stochastic models.Moti vated by this need, several authors have explored the generation of random vectors with specified marginals, together with a specified covariance matrix, through the use of a transformation of a multivariate normal random vector (the NORTA method). A covariance matrix is said to be feasible for a given set of marginal distributions if a random vector exists with these characteristics. We develop a computational approach for establishing whether a given covariance matrix is feasible for a given set of marginals. The approach is used to rigorously establish that there are sets of marginals with feasible covariance matrix that the NORTA method cannot match. In such cases, we show how to modify the initialization phase of NORTA so that it will exactly match the marginals, and approximately match the desired covariance matrix. An important feature of our analysis is that we show that for almost any covariance matrix (in a certain precise sense), our computational procedure either explicitly provides a construction of a random vector with the required properties, or establishes that no such random vector exists.

Asymptotic Lower Bounds for Risk in Robust Estimation

Robustness and efficiency of a parameter estimate $T$ can be assessed by comparing the fitted parametric distribution $P_T$ with the actual distribution, which is assumed to lie near the parametric family $\{P_\theta:\theta\in\Theta\}$. Asymptotic lower bounds are established for the minimax risk over distributions near the parametric model, taking as loss function a monotone increasing function of the Hellinger distance between the actual distribution of the sample and the fitted distribution determined by $T$. The set of marginal distributions considered in the minimax calculation is a subset of the Hellinger ball of radius $O(n^{-1/2})$ centered at $P_\theta, n$ being the sample size. When the loss function is bounded, the lower bound on maximum risk can be attained asymptotically. However, an estimator of $\theta$ which is asymptotically minimax for bounded loss functions may be far from optimal when the loss function is unbounded. Such divergent behavior is exhibited, for instance, by the sample mean in nearly normal models.