Related papers: Averaged deviations of Orlicz processes and majori…
Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly…
Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this…
Building on Talagrand's proof of the Hoffmann-J{\o}rgensen inequality for $L_p$ spaces and its version for the exponential Orlicz spaces we provide a full characterization of Orlicz functions $\Psi$ for which an analogous inequality holds…
The state of a stochastic process evolving over a time $t$ is typically assumed to lie on a normal distribution whose width scales like $t^{1/2}$. However, processes where the probability distribution is not normal and the scaling exponent…
We address the expected supremum of a linear combination of shifts of the sinc kernel with random coefficients. When the coefficients are Gaussian, the expected supremum is of order \sqrt{\log n}, where n is the number of shifts. When the…
In this paper, we study the asymptotic distribution of the maxima of suprema of dependent Gaussian processes with trend. For different scales of the time horizon we obtain different normalizing functions for the convergence of the maxima.…
We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium…
We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…
Suppose we observe an invertible linear process with independent mean-zero innovations and with coefficients depending on a finite-dimensional parameter, and we want to estimate the expectation of some function under the stationary…
Let $\{{\bf \mathcal{Z}}_n:n\geq 1\}$ be a sequence of i.i.d. random probability measures. Independently, for each $n\geq 1$, let $(X_{n1},\ldots, X_{nn})$ be a random vector of positive random variables that add up to one. This paper…
We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…
We consider probability measures on $A^N$, the set of sequences of symbols on a finite alphabet $A$ of length $N$, that give a weight to each sequence in terms of a collection of matrices with non-negative entries and having rows and…
In the article, Besov-Orlicz regularity of sample paths of stochastic processes that are represented by multiple integrals of order $n\in\mathbb{N}$ is treated. We give sufficient conditions for the considered processes to have paths in the…
We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle…
The OSSS inequality [O'Donnell, Saks, Schramm and Servedio, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05), Pittsburgh (2005)] gives an upper bound for the variance of a function f of independent 0-1 valued random…
We develop a general mathematical framework for variational problems where the unknown function assumes values in the space of probability measures on some metric space. We study weak and strong topologies and define a total variation…
Covariate shift, a widely used assumption in tackling {\it distributional shift} (when training and test distributions differ), focuses on scenarios where the distribution of the labels conditioned on the feature vector is the same, but the…
In this paper we show that, using combinatorial inequalities and Matrix-Averages, we can generate Musielak-Orlicz spaces, i.e., we prove that $1/\pi \sum_{\pi} \max\limits_{1 \leq i \leq n} \abs{x_i y_{i\pi(i)}} \sim \norm{x}_{\Sigma M_i}$,…
We consider the problem of deriving uniform confidence bands for the mean of a monotonic stochastic process, such as the cumulative distribution function (CDF) of a random variable, based on a sequence of i.i.d.~observations. Our approach…
The paper addresses a problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under a standard assumption formulated in terms of…