Related papers: Stochastic dominance for linear combinations of in…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
Building on recent developments in models focused on the shape properties of odds ratios, this paper introduces two new models that expand the class of available distributions while preserving specific shape characteristics of an underlying…
We study p-adic counterparts of stable distributions, that is limit distributions for sequences of normalized sums of independent identically distributed p-adic-valued random variables. In contrast to the classical case, non-degenerate…
For sample covariance matrices with iid entries with sub-Gaussian tails, when both the number of samples and the number of variables become large and the ratio approaches to one, it is a well-known result of A. Soshnikov that the limiting…
Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…
The well-known "Janson's inequality" gives Poisson-like upper bounds for the lower tail probability \Pr(X \le (1-\eps)\E X) when X is the sum of dependent indicator random variables of a special form. We show that, for large deviations,…
For several pairs $(P,Q)$ of classical distributions on $\N_0$, we show that their stochastic ordering $P\leq_{st} Q$ can be characterized by their extreme tail ordering equivalent to $ P(\{k_\ast \})/Q(\{k_\ast\}) \le 1 \le \lim_{k\to…
We consider the following recurrence relation with random i.i.d. coefficients $(a_n,b_n)$: $$ x_{n+1}=a_{n+1} x_n+b_{n+1} $$ where $a_n\in GL(d,\mathbb{R}),b_n\in \mathbb{R}^d$. Under natural conditions on $(a_n,b_n)$ this equation has a…
For a stochastic difference equation $D_n=A_nD_{n-1}+B_n$ which stabilises upon time we study tail distribution asymptotics of $D_n$ under the assumption that the distribution of $\log(1+|A_1|+|B_1|)$ is heavy-tailed, that is, all its…
We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models,…
We characterise the learning of a mixture of two clouds of data points with generic centroids via empirical risk minimisation in the high dimensional regime, under the assumptions of generic convex loss and convex regularisation. Each cloud…
Hadar and Russell (1974) and Levy and Paroush (1974) presented sufficient conditions for multivariate stochastic dominance when the distributions involved are continuous with compact support. Further generalizations involved either…
In this paper, we obtain some results on precise large deviations for non-random and random sums of widely dependent random variables with common dominatedly varying tail distribution or consistently varying tail distribution on…
Stochastic iterative methods are useful in a variety of large-scale numerical linear algebraic, machine learning, and statistical problems, in part due to their low-memory footprint. They are frequently used in a variety of applications,…
The asymptotic tail behaviour of sums of independent subexponential random variables is well understood, one of the main characteristics being the principle of the single big jump. We study the case of dependent subexponential random…
The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a…
In this paper we find and develop a stochastic integral representation for the class of strictly stable distributions. We establish an explicit relationship between stochastic integral and shot-noise series representations of strictly…
We define a notion of stochastic domination between trees, where one tree dominates another if when the vertices of each are labeled with independent, identically distributed random variables, one tree is always more likely to contain a…
In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of…
With latent variables, stochastic recurrent models have achieved state-of-the-art performance in modeling sound-wave sequence. However, opposite results are also observed in other domains, where standard recurrent networks often outperform…