Related papers: Projective Averages for Summarizing Redistricting …

When auditing a redistricting plan, a persuasive method is to compare the plan with an ensemble of neutrally drawn redistricting plans. Ensembles are generated via algorithms that sample distributions on balanced graph partitions. To audit…

Ensemble analysis has become an important tool for quantifying gerrymandering; the main idea is to generate a large, random sample of districting plans (an "ensemble") to which any proposed plan may be compared. If a proposed plan is an…

The process of drawing electoral district boundaries is known as political redistricting. Within this context, gerrymandering is the practice of drawing these boundaries such that they unfairly favor a particular political party, often…

We introduce a very general method for high-dimensional classification, based on careful combination of the results of applying an arbitrary base classifier to random projections of the feature vectors into a lower-dimensional space. In one…

We introduce a new framework for dimension reduction in the context of high-dimensional regression. Our proposal is to aggregate an ensemble of random projections, which have been carefully chosen based on the empirical regression…

Calculating averages with respect to probability measures on submanifolds is often necessary in various application areas such as molecular dynamics, computational statistical mechanics and Bayesian statistics. In recent years, various…

The importance of accurately quantifying forecast uncertainty has motivated much recent research on probabilistic forecasting. In particular, a variety of deep learning approaches has been proposed, with forecast distributions obtained as…

In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov…

This article introduces the 50stateSimulations, a collection of simulated congressional districting plans and underlying code developed by the Algorithm-Assisted Redistricting Methodology (ALARM) Project. The 50stateSimulations allow for…

With appropriately chosen sampling probabilities, sampling-based random projection can be used to implement large-scale statistical methods, substantially reducing computational cost while maintaining low statistical error. However,…

In distributional or average-case analysis, the goal is to design an algorithm with good-on-average performance with respect to a specific probability distribution. Distributional analysis can be useful for the study of general-purpose…

In contrast to classical reinforcement learning (RL), distributional RL algorithms aim to learn the distribution of returns rather than their expected value. Since the nature of the return distribution is generally unknown a priori or…

Sample surveys are widely used to obtain information about totals, means, medians, and other parameters of finite populations. In many applications, similar information is desired for subpopulations such as individuals in specific…

Density aggregation is a central problem in machine learning, for instance when combining predictions from a Deep Ensemble. The choice of aggregation remains an open question with two commonly proposed approaches being linear pooling…

An ensemble method is introduced that utilizes randomization and loss function gradients to compute a prediction. Multiple weakly-correlated estimators approximate the gradient at randomly sampled points on the error surface and are…

In this paper, we consider the parameter estimation problem over sensor networks in the presence of quantized data and directed communication links. We propose a two-stage algorithm aiming at achieving the centralized sample mean estimate…

Distributed averaging, or distributed average consensus, is a common method for computing the sample mean of the data dispersed among the nodes of a network in a decentralized manner. By iteratively exchanging messages with neighbors, the…

We study the problem of resilient average consensus in multi-agent systems where some of the agents are subject to failures or attacks. The objective of resilient average consensus is for non-faulty/normal agents to converge to the average…

Subdivision is a well-known and established method for generating smooth curves and surfaces from discrete data by repeated refinements. The typical input for such a process is a mesh of vertices. In this work we propose to refine 2D data…

Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods are fast and scalable, but can have instability when used to approximate…