Related papers: Discussion: The Dantzig selector: Statistical esti…

Let $d\ge 3$ be a fixed integer, $p\in (0,1)$, and let $n\geq 1$ be a positive integer such that $dn$ is even. Let $\mathbb{G}(n, d, p)$ be a (random) graph on $n$ vertices obtained by drawing uniformly at random a $d$-regular (simple)…

What is the largest number accessible to the human imagination? The question is neither entirely mathematical nor entirely philosophical. Mathematical formulations of the problem fall into two classes: those that fail to fully capture the…

Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is…

Identification of multinomial choice models is often established by using special covariates that have full support. This paper shows how these identification results can be extended to a large class of multinomial choice models when all…

We wish to contribute to the discussion of "Comparing Consensus Monte Carlo Strategies for Distributed Bayesian Computation" by offering our views on the current best methods for Bayesian computation, both at big-data scale and with smaller…

We consider the problem of selecting a small subset of representative variables from a large dataset. In the computer science literature, this dimensionality reduction problem is typically formalized as Column Subset Selection (CSS).…

This paper compares two different ways of estimating statistical language models. Many statistical NLP tagging and parsing models are estimated by maximizing the (joint) likelihood of the fully-observed training data. However, since these…

We complete a proof of a theorem that was inspired by an Indian Olympiad problem, which gives an interesting characterization of a prime number $p$ with respect to the binomial coefficients ${n\choose p}$. We also derive a related result…

Estimating the parameters from $k$ independent Bin$(n,p)$ random variables, when both parameters $n$ and $p$ are unknown, is relevant to a variety of applications. It is particularly difficult if $n$ is large and $p$ is small. Over the past…

This article is the rejoinder for the paper "Probabilistic Integration: A Role in Statistical Computation?" to appear in Statistical Science with discussion. We would first like to thank the reviewers and many of our colleagues who helped…

In this note, we revisit a classical problem related to the density of nonlinear statistics. We obtain a new representation of densities and, for the first time, a necessary and sufficient condition for the existence of densities is…

The Possible-Winner problem asks, given an election where the voters' preferences over the set of candidates is partially specified, whether a distinguished candidate can become a winner. In this work, we consider the computational…

In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…

In many problems involving generalized linear models, the covariates are subject to measurement error. When the number of covariates p exceeds the sample size n, regularized methods like the lasso or Dantzig selector are required. Several…

New cases of the multiplicity conjecture are considered.

A novel powerful mathematical method is presented, which allows us to find an analytical solution of a simplified version of the statistical multifragmentation model with the restriction that the largest fragment size cannot exceed the…

This is a comment on arXiv:2202.01553. In regression Gaussian covariate p-values (Davies and D{\"u}mbgen, arXiv:2202.01553) are used to control greedy forward subset selection by accounting for choosing the best when fitting many variables.…

For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probabilistic perspective. We assume that data points (possibly…

We consider the sparse regression model where the number of parameters $p$ is larger than the sample size $n$. The difficulty when considering high-dimensional problems is to propose estimators achieving a good compromise between…

There are two distinct definitions of 'P-value' for evaluating a proposed hypothesis or model for the process generating an observed dataset. The original definition starts with a measure of the divergence of the dataset from what was…