相关论文: Quantifying Gerrymandering in North Carolina

In recent years, many Machine Learning (ML) explanation techniques have been designed using ideas from cooperative game theory. These game-theoretic explainers suffer from high complexity, hindering their exact computation in practical…

The U.S. Supreme Court is currently deliberating over whether a proposed mathematical formula should be used to detect unconstitutional partisan gerrymandering. We show that in some cases, this formula will only flag bizarrely shaped…

Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…

Real-time dispatch practices for operating the electric grid in an economic and reliable manner are evolving to accommodate higher levels of renewable energy generation. In particular, stochastic optimization is receiving increased…

We study how the realignment criterion (also called computable cross-norm criterion) succeeds asymptotically in detecting whether random states are separable or entangled. We consider random states on $\C^d \otimes \C^d$ obtained by partial…

Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal…

Mapping political party systems to metric policy spaces is one of the major methodological problems in political science. At present, in most political science project this task is performed by domain experts relying on purely qualitative…

Researchers and legislators alike continue the search for methods of drawing fair districting plans. A districting plan is a partition of a state's subdivisions (e.g. counties, voting precincts, etc.). By modeling these districting plans as…

We describe a general strategy for sampling configurations from a given distribution, NOT based on the standard Metropolis (Markov chain) strategy. It uses the fact that nontrivial problems in statistical physics are high dimensional and…

We apply a Bayesian data analysis scheme known as the Markov Chain Monte Carlo (MCMC) to the tomographic reconstruction of quantum states. This method yields a vector, known as the Markov chain, which contains the full statistical…

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 present novel methods for predicting the outcome of large elections. Our first algorithm uses a diffusion process to model the time uncertainty inherent in polls taken with substantial calendar time left to the election. Our second model…

The map of elections framework is a methodology for visualizing and analyzing election datasets. So far, the framework was restricted to elections that have equal numbers of candidates, equal numbers of voters, and where all the (ordinal)…

We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate,…

High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…

We compare two methods for making predictions of the climatological distribution of the number of hurricanes making landfall along short sections of the North American coastline. The first method uses local data, and the second method uses…

Artificial Neural Networks were recently shown to be an efficient representation of highly-entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in Variational Monte Carlo, most…

Map makers have long searched for a way to construct cartograms -- maps in which the sizes of geographic regions such as countries or provinces appear in proportion to their population or some other analogous property. Such maps are…

Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue…

A novel variational inference based resampling framework is proposed to evaluate the robustness and generalization capability of deep learning models with respect to distribution shift. We use Auto Encoding Variational Bayes to find a…