Related papers: An Exact Algorithm for the Stratification Problem …
This paper considers the problem of design-based inference for the average treatment effect in finely stratified experiments. Here, by "design-based'' we mean that the only source of uncertainty stems from the randomness in treatment…
In this article, we propose several quantization-based stratified sampling methods to reduce the variance of a Monte Carlo simulation. Theoretical aspects of stratification lead to a strong link between optimal quadratic quantization and…
We consider the problem of online stratified sampling for Monte Carlo integration of a function given a finite budget of $n$ noisy evaluations to the function. More precisely we focus on the problem of choosing the number of strata $K$ as a…
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…
A quick count seeks to estimate the voting trends of an election and communicate them to the population on the evening of the same day of the election. In quick counts, the sampling is based on a stratified design of polling stations.…
Optimizing the allocation of units into treatment groups can help researchers improve the precision of causal estimators and decrease costs when running factorial experiments. However, existing optimal allocation results typically assume a…
This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…
In this paper, we consider distributed optimization design for resource allocation problems over weight-balanced graphs. With the help of singular perturbation analysis, we propose a simple sub-optimal continuous-time optimization…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
This paper presents a practical method for finding the globally optimal solution to the sum-of-ratios problem arising in image processing, engineering and management. Unlike traditional methods which may get trapped in local minima due to…
The Graphical House Allocation problem asks: how can $n$ houses (each with a fixed non-negative value) be assigned to the vertices of an undirected graph $G$, so as to minimize the "aggregate local envy", i.e., the sum of absolute…
In this article we propose an optimal method referred to as SPlit for splitting a dataset into training and testing sets. SPlit is based on the method of Support Points (SP), which was initially developed for finding the optimal…
We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…
Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…
We consider the selective graph coloring problem, which is a generalization of the classical graph coloring problem. Given a graph together with a partition of its vertex set into clusters, we want to choose exactly one vertex per cluster…
We introduce a graph partitioning problem motivated by computational topology and propose two algorithms that produce approximate solutions. Specifically, given a weighted, undirected graph $G$ and a positive integer $k$, we desire to find…
This paper proposes an optimal allocation problem with ramified transport technology in a spatial economy. Ramified transportation is used to model the transport economy of scale in group transportation observed widely in both nature and…
In this paper, we determine which non-random sampling of fixed size gives the best linear predictor of the sum of a finite spatial population. We employ different multiscale superpopulation models and use the minimum mean-squared error as…
The Steiner tree problem aims to determine a minimum edge-weighted tree that spans a given set of terminal vertices from a given graph. In the past decade, a considerable number of algorithms have been developed to solve this…
We consider the problem of learning over non-stationary ranking streams. The rankings can be interpreted as the preferences of a population and the non-stationarity means that the distribution of preferences changes over time. Our goal is…