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Variational autoencoders were proven successful in domains such as computer vision and speech processing. Their adoption for modeling user preferences is still unexplored, although recently it is starting to gain attention in the current…
The variational autoencoder (VAE) is a popular model for density estimation and representation learning. Canonically, the variational principle suggests to prefer an expressive inference model so that the variational approximation is…
We consider delay differential equations (DDE) that are on the verge of an instability, i.e. the characteristic equation for the linearized equation has one root as zero and all other roots have negative real parts. In presence of small…
The estimate of coefficients of the Convection-Diffusion Equation (CDE) from experimental measurements belongs in the category of inverse problems, which are known to come with issues of ill-conditioning or singularity. Here we concentrate…
Stochastic linear combinations of some random vectors are studied where the distribution of the random vectors and the joint distribution of their coefficients are Dirichlet. A method is provided for calculating the distribution of these…
We introduce and analyze a new class of monotone stochastic recursions in a regenerative environment which is essentially broader than that of Markov chains. We prove stability theorems and apply our results {to three canonical models in…
Consider a reflecting diffusion in a domain in $R^d$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the…
We analyze the diffusion processes associated to equations of Wright-Fisher type in one spatial dimension. These are defined by a degenerate second order operator on the interval [0, 1], where the coefficient of the second order term…
Recent successes in image generation, model-based reinforcement learning, and text-to-image generation have demonstrated the empirical advantages of discrete latent representations, although the reasons behind their benefits remain unclear.…
Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…
We consider a variant of Dickson lemma, where each entry of a vector can be reseted or incremented by 1 in respect to the previous one. We give an example of non dominating sequence of length $2^{2^{\theta (n)}}$. It perfectly match the…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise…
We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are…
This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…
Second order recurrence of a $d$-dimensional diffusion with an additive Wiener process, with switching, and with one recurrent and one transient regime and constant switching intensities is established under suitable conditions. The…
This paper is concerned with the existence of invariant measure for 3D stochastic primitive equations driven by linear multiplicative noise under non-periodic boundary conditions. The common method is to apply Sobolev imbedding theorem to…
We consider stochastic processes indexed by the vertices of an infinite binary tree having a simple recursive structure. The value at any vertex is some fixed function of the values at the two daughter vertices together with some…
In this paper, we aim to study solutions of reflected generalized BSDEs, involving the integral with respect to a continuous process, which is the local time of the diffusion on the boundary. We consider both a finite random terminal and a…
In this article we prove the bivariate uniqueness property for a particular ``max-type'' recursive distributional equation (RDE). Using the general theory developed by Aldous and Bandyopadhyay (2005) we then show that the corresponding…
The dispersion of inertial particles continuously emitted from a point source is analytically investigated in the limit of small inertia. Our focus is on the evolution equation of the particle joint probability density function p(x,v,t), x…