Related papers: States of Disarray: Cleaning Data for Gerrymanderi…

We examine the extent of gerrymandering for the 2010 General Assembly district map of Wisconsin. We find that there is substantial variability in the election outcome depending on what maps are used. We also found robust evidence that the…

In recent years, methods for Bayesian inference have been widely used in many different problems in physics where detection and characterization are necessary. Data analysis in gravitational-wave astronomy is a prime example of such a case.…

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…

The problem of representative selection amounts to sampling few informative exemplars from large datasets. This paper presents MOSAIC, a novel representative selection approach from high-dimensional data that may exhibit non-linear…

We introduce a Markov Chain Monte Carlo (MCMC) method that is designed to sample from target distributions with irregular geometry using an adaptive scheme. In cases where targets exhibit non-Gaussian behaviour, we propose that adaption…

With the rapid development of large language models (LLMs), the quality of training data has become crucial. Among the various types of training data, mathematical data plays a key role in enabling LLMs to acquire strong reasoning…

In this article we consider computing expectations w.r.t.~probability laws associated to a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation, but…

Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…

The quality of datasets plays a crucial role in the successful training and deployment of deep learning models. Especially in the medical field, where system performance may impact the health of patients, clean datasets are a safety…

Dirichlet Process Mixture Models (DPMMs) are widely used to address clustering problems. Their main advantage lies in their ability to automatically estimate the number of clusters during the inference process through the Bayesian…

We propose an approach to lossy source coding, utilizing ideas from Gibbs sampling, simulated annealing, and Markov Chain Monte Carlo (MCMC). The idea is to sample a reconstruction sequence from a Boltzmann distribution associated with an…

The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms…

In this paper, we study the problem of estimating the state of a dynamic state-space system where the output is subject to quantization. We compare some classical approaches and a new development in the literature to obtain the filtering…

Gerrymandering is a long-standing issue within the U.S. political system, and it has received scrutiny recently by the U.S. Supreme Court. In this note, we prove that deciding whether there exists a fair redistricting among legal maps is…

Congressional district lines in many U.S. states are drawn by partisan actors, raising concerns about gerrymandering. To separate the partisan effects of redistricting from the effects of other factors including geography and redistricting…

When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by…

The examination of uncertainty in the predictions of machine learning (ML) models is receiving increasing attention. One uncertainty modeling technique used for this purpose is Monte-Carlo (MC)-Dropout, where repeated predictions are…

We study the classic $k$-means/median clustering, which are fundamental problems in unsupervised learning, in the setting where data are partitioned across multiple sites, and where we are allowed to discard a small portion of the data by…

Clustering, or unsupervised classification, is a task often plagued by outliers. Yet there is a paucity of work on handling outliers in clustering. Outlier identification algorithms tend to fall into three broad categories: outlier…

Assuming that partisan fairness and responsiveness are important aspects of redistricting, it is important to measure them. Many measures of partisan bias are satisfactory for states that are balanced with roughly equal proportions of…