Related papers: Compact Redistricting Plans Have Many Spanning Tre…
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…
This paper brings explicit considerations of distributed computing architectures and data structures into the rigorous design of Sequential Monte Carlo (SMC) methods. A theoretical result established recently by the authors shows that…
We consider MAP estimators for structured prediction with exponential family models. In particular, we concentrate on the case that efficient algorithms for uniform sampling from the output space exist. We show that under this assumption…
Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the…
We consider local Markov chain Monte-Carlo algorithms for sampling from the weighted distribution of independent sets with activity $\l$, where the weight of an independent set $I$ is $\l^{|I|}$. A recent result has established that Gibbs…
In the computational study of political redistricting, feasibility necessitates the use of a discretization of regions such as states, counties, and towns. In nearly all cases, researchers use a dual graph, whose vertices represent small…
Simulation methods have become important tools for quantifying partisan and racial bias in redistricting plans. We generalize the Sequential Monte Carlo (SMC) algorithm of McCartan and Imai (2023), one of the commonly used approaches.…
Markov chains based on spanning trees have been hugely influential in algorithms for assessing fairness in political redistricting. The input graph represents the geographic building blocks of a jurisdiction. The goal is to output a large…
Redistricting is the problem of partitioning a set of geographical units into a fixed number of districts, subject to a list of often-vague rules and priorities. In recent years, the use of randomized methods to sample from the vast space…
We present new MCMC algorithms for computing the posterior distributions and expectations of the unknown variables in undirected graphical models with regular structure. For demonstration purposes, we focus on Markov Random Fields (MRFs).…
We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for…
Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…
Among subgraphs with a fixed number of vertices of the regular square lattice, we prove inequalities that essentially say that those with smaller boundaries have larger numbers of spanning trees and vice-versa. As an application, we relate…
In the United States, regions are frequently divided into districts for the purpose of electing representatives. How the districts are drawn can affect who's elected, and drawing districts to give an advantage to a certain group is known as…
Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
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…
Using an ensemble of redistricting plans, we evaluate whether a given political districting faithfully represents the geo-political landscape. Redistricting plans are sampled by a Monte Carlo algorithm from a probability distribution that…