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The main focus of this article is to provide a mathematical study of the algorithm proposed in \cite{boyaval2010variance} where the authors proposed a variance reduction technique for the computation of parameter-dependent expectations…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
Uncertain information on input parameters of reliability models is usually modeled by considering these parameters as random, and described by marginal distributions and a dependence structure of these variables. In numerous real-world…
Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…
We consider the vacant set of random interlacements on Z^d, with d bigger or equal to 3, in the percolative regime. Motivated by the large deviation principles obtained in our recent work arXiv:1304.7477, we investigate the asymptotic…
With the violation of the assumption of homoskedasticity, least squares estimators of the variance become inefficient and statistical inference conducted with invalid standard errors leads to misleading rejection rates. Despite a vast…
Many strongly correlated systems exhibit strange metallic behavior in certain parameter regimes characterized by anomalous transport properties that are irreconcilable with a Fermi-liquid-like description in terms of quasiparticles. The…
Regression models for limited continuous dependent variables having a non-negligible probability of attaining exactly their limits are presented. The models differ in the number of parameters and in their flexibility. Fractional data being…
In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically…
A prominent technique for self-supervised representation learning has been to contrast semantically similar and dissimilar pairs of samples. Without access to labels, dissimilar (negative) points are typically taken to be randomly sampled…
When learning from positive and unlabelled data, it is a strong assumption that the positive observations are randomly sampled from the distribution of $X$ conditional on $Y = 1$, where X stands for the feature and Y the label. Most…
We consider the random point processes on a measure space X defined by the Gibbs measures associated to a given sequence of N-particle Hamiltonians H^{(N)}. Inspired by the method of Messer-Spohn for proving concentration properties for the…
The ability of Variational Autoencoders to learn disentangled representations has made them appealing for practical applications. However, their mean representations, which are generally used for downstream tasks, have recently been shown…
Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…
This paper develops Kolmogorov-type maximal inequalities for sums of Negative Binomial random variables under both independence and dependence structures. For independent heterogeneous Negative Binomial variables we derive sharp Markov-type…
In this paper, we propose a novel Euclidean-distance-based coefficient, named differential distance correlation, to measure the strength of dependence between a random variable $ Y \in \mathbb{R} $ and a random vector $ \boldsymbol{X} \in…
Random features provide a practical framework for large-scale kernel approximation and supervised learning. It has been shown that data-dependent sampling of random features using leverage scores can significantly reduce the number of…
In this paper, we establish the convergence rate in central limit theorem (CLT) for linearly extended negative quadrant dependent (LENQD) random variables (rv's). Under some weak conditions, the rate of normal approximation is shown as…
In this article we study weighted sums of $n$ i.i.d. Gamma($\alpha$) random variables with nonnegative weights. We show that for $n \geq 1/\alpha$ the sum with equal coefficients maximizes differential entropy when variance is fixed. As a…
We consider the extreme value statistics of correlated random variables that arise from a Langevin equation. Recently, it was shown that the extreme values of the Ornstein-Uhlenbeck process follow a different distribution than those…