Efficient Sampling Methods for Discrete Distributions

Sampling from Discrete Distributions:

At the 2001 FCSM Research Conference, Greene et al. introduced a problem in editing and imputation based on fire data. The editing problem consists of imputing values to cells in a 2x2 contingency table subject to extensive item and unit nonresponse. Mathematically, the nonresponse creates an incomplete 2-way table with partial counts for individual cells and marginal totals. Statistically, the...

Preconditioned Methods for Sampling Multivariate Gaussian Distributions

A common problem in statistics is to compute sample vectors from a multivariate Gaussian distribution with zero mean and a given covariance matrix A. A canonical approach to the problem is to compute vectors of the form y = Sz, where S is the Cholesky factor or square root of A, and z is a standard normal vector. When A is large, such an approach becomes computationally expensive. This paper co...

Sampling Distributions Sampling Distributions

Efficient Sampling Methods for Truncated Multivariate Normal and Student-t Distributions Subject to Linear Inequality Constraints

Sampling from a truncated multivariate normal distribution subject to multiple linear inequality constraints is a recurring problem in many areas in statistics and econometrics, such as the order restricted regressions, censored data models, and shape-restricted nonparametric regressions. However, the sampling problem still appears non-trivial due to the existence of the analytically intractabl...

Communication-Efficient Distributed Learning of Discrete Distributions

We initiate a systematic investigation of distribution learning (density estimation) when the data is distributed across multiple servers. The servers must communicate with a referee and the goal is to estimate the underlying distribution with as few bits of communication as possible. We focus on non-parametric density estimation of discrete distributions with respect to the `1 and `2 norms. We...