One of the limiting factors of using support vector machines (SVMs) in large scale applications are their super-linear computational requirements in terms of the number of training samples. To address this issue, several approaches that train SVMs on many small chunks separately have been proposed in the literature. With the exception of random chunks, which is also known as divide-and-conquer ...

It is shown that the minmax principle of Ky Fan leads to a quick simple derivation of a recent inequality of V. S. Sunder giving a lower bound for the spectral distance between two Hermitian matrices. This brings out a striking parallel between this result and an earlier known upper bound for the spectral distance due to L. Mirsky. Let A be a Hermitian matrix of order n and let A ¿(A) denote th...

The goal of many randomized experiments and quasi-experimental studies in economics is to inform policies that aim to raise incomes and reduce economic inequality. A policy maximizing the sum of individual incomes may not be desirable if it magnifies economic inequality and post-treatment redistribution of income is infeasible. This paper develops a method to estimate the optimal treatment assi...

The matrix completion problem consists in reconstructing a matrix from a sample of entries, possibly observed with noise. A popular class of estimator, known as nuclear norm penalized estimators, are based on minimizing the sum of a data fitting term and a nuclear norm penalization. Here, we investigate the case where the noise distribution belongs to the exponential family and is subexponentia...

This paper considers the performance of a compensation mechanism that has received increasing attention in recent experimental literature. Our purpose is two-fold: (i) to characterize endogenous payments that can induce (mutual) cooperation in prisoner’s dilemma in the absence of social preferences; (ii) using models of quasi-maximin and inequality-aversion preferences to evaluate the possibili...

This paper reports results of a ’probabilistic dictator game’ experiment in which subjects had to allocate chances to win a prize between themselves and a dummy player. We have manipulated (within subjects) two aspects of the game: the relative values of the prizes (being equal for the two players, higher for the dictator or higher for the dummy) and the nature of the lottery determining the ea...

In [14], a new local minimax method that characterizes a saddle point as a solution to a local minimax problem is established. Based on the local characterization, a numerical minimax algorithm is designed for finding multiple saddle points. Numerical computations of many examples in semilinear elliptic PDE have been successfully carried out to solve for multiple solutions. One of the important...

This paper addresses the control design problem for discrete-time, nite-state Markov Decision Processes (MDPs), when both risk-neutral and minimax objectives are of interest. We introduce the mixed risk-neutral/minimax objective, and utilize results from risk-neutral and minimax control to derive an information state process and dynamic programming equations for the value function. We synthesiz...

We study minimax rates of convergence for nonparametric regression and prediction under a random design with dependent errors. It is shown that dependence among errors in general does not hurt a prediction of the next response. For estimating the regression function, however, dependence may damage the minimax rate of convergence. Under the assumption that the errors are independent of the expla...