Related papers: Randomized Empirical Processes and Confidence Band…
We consider three problems in high-dimensional Gaussian linear mixed models. Without any assumptions on the design for the fixed effects, we construct an asymptotic $F$-statistic for testing whether a collection of random effects is zero,…
Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…
The properties of the generalized Waring distribution defined on the non negative integers are reviewed. Formulas for its moments and its mode are given. A construction as a mixture of negative binomial distributions is also presented. Then…
Let $X_1, X_2,\dots$ be a short-memory linear process of random variables. For $1\leq q<2$, let $\cF$ be a bounded set of real-valued functions on $[0,1]$ with finite $q$-variation. It is proved that…
We consider the problem of random sampling for band-limited functions. When can a band-limited function $f$ be recovered from randomly chosen samples $f(x_j), j\in \mathbb{N}$? We estimate the probability that a sampling inequality of the…
First passage distributions of semi-Markov processes are of interest in fields such as reliability, survival analysis, and many others. The problem of finding or computing first passage distributions is, in general, quite challenging. We…
In many applications, different populations are compared using data that are sampled in a biased manner. Under sampling biases, standard methods that estimate the difference between the population means yield unreliable inferences. Here we…
In this paper, we study the classification problem by estimating the conditional probability function of the given data. Different from the traditional expected risk estimation theory on empirical data, we calculate the probability via…
Randomized benchmarking (RB) is an efficient and robust method to characterize gate errors in quantum circuits. Averaging over random sequences of gates leads to estimates of gate errors in terms of the average fidelity. These estimates are…
In this paper, we study random subsampling of Gaussian process regression, one of the simplest approximation baselines, from a theoretical perspective. Although subsampling discards a large part of training data, we show provable guarantees…
We develop inference procedures robust to general forms of weak dependence. The procedures utilize test statistics constructed by resampling in a manner that does not depend on the unknown correlation structure of the data. We prove that…
Resampling techniques are widely used in statistical inference and ensemble learning, in which estimators' statistical properties are essential. However, existing methods are computationally demanding, because repetitions of…
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression…
Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…
We develop new methods to integrate experimental and observational data in causal inference. While randomized controlled trials offer strong internal validity, they are often costly and therefore limited in sample size. Observational data,…
We consider the problem of estimating the joint distribution of $n$ independent random variables. Our approach is based on a family of candidate probabilities that we shall call a model and which is chosen to either contain the true…
Divide-and-conquer methods use large-sample approximations to provide frequentist guarantees when each block of data is both small enough to facilitate efficient computation and large enough to support approximately valid inferences. When…
The average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we…
In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of independent random variables, each with support on the whole real…
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…