Related papers: Optimal Representative Sample Weighting
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…
In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…
Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realise the position suggested by the optimal portfolios, he/she needs to estimate the unknown…
In clinical settings, we often face the challenge of building prediction models based on small observational data sets. For example, such a data set might be from a medical center in a multi-center study. Differences between centers might…
Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…
Many data-fitting applications require the solution of an optimization problem involving a sum of large number of functions of high dimensional parameter. Here, we consider the problem of minimizing a sum of $n$ functions over a convex…
Given a large set $U$ where each item $a\in U$ has weight $w(a)$, we want to estimate the total weight $W=\sum_{a\in U} w(a)$ to within factor of $1\pm\varepsilon$ with some constant probability $>1/2$. Since $n=|U|$ is large, we want to do…
The concept of probabilistic values, such as Beta Shapley values and weighted Banzhaf values, has gained recent attention in applications like feature attribution and data valuation. However, exact computation of these values is often…
We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…
The large-scale multiple testing inherent to high throughput biological data necessitates very high statistical stringency and thus true effects in data are difficult to detect unless they have high effect sizes. One promising approach for…
The paper analyzes theoretically and empirically the performance of likelihood weighting (LW) on a subset of nodes in Bayesian networks. The proposed scheme requires fewer samples to converge due to reduction in sampling variance. The…
Sampling is a fundamental problem in computer science and statistics. However, for a given task and stream, it is often not possible to choose good sampling probabilities in advance. We derive a general framework for adaptively changing the…
In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We…
Probability proportional to size (PPS) sampling schemes with a target sample size aim to produce a sample comprising a specified number $n$ of items while ensuring that each item in the population appears in the sample with a probability…
Optimization software enables the solution of problems with millions of variables and associated parameters. These parameters are, however, often uncertain and represented with an analytical description of the parameter's distribution or…
Motivation: Gene selection has become a common task in most gene expression studies. The objective of such research is often to identify the smallest possible set of genes that can still achieve good predictive performance. The problem of…
In this paper, we focus on the model specification problem in multivariate spatial econometric models when a candidate set for the spatial weights matrix is available. We propose a model selection method for the multivariate spatial…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
Given a random sample of points from some unknown distribution, we propose a new data-driven method for estimating its probability support $S$. Under the mild assumption that $S$ is $r$-convex, the smallest $r$-convex set which contains the…