Related papers: Sample complexity of Schr\"odinger potential estim…
Biological systems use energy to maintain non-equilibrium distributions for long times, e.g. of chemical concentrations or protein conformations. What are the fundamental limits of the power used to "hold" a stochastic system in a desired…
We consider the problem where an agent aims to combine the views and insights of different experts' models. Specifically, each expert proposes a diffusion process over a finite time horizon. The agent then combines the experts' models by…
Generative models have achieved remarkable success across a range of applications, yet their evaluation still lacks principled uncertainty quantification. In this paper, we develop a method for comparing how close different generative…
Let $V_* : \mathbb{R}^d \to \mathbb{R}$ be some (possibly non-convex) potential function, and consider the probability measure $\pi \propto e^{-V_*}$. When $\pi$ exhibits multiple modes, it is known that sampling techniques based on…
Recently, continual learning has received a lot of attention. One of the significant problems is the occurrence of \emph{concept drift}, which consists of changing probabilistic characteristics of the incoming data. In the case of the…
We study the reducibility of a Linear Schr\"odinger equation subject to a small unbounded almost-periodic perturbation which is analytic in time and space. Under appropriate assumptions on the smallness, analiticity and on the frequency of…
Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based…
In many applications in biology, engineering and economics, identifying similarities and differences between distributions of data from complex processes requires comparing finite categorical samples of discrete counts. Statistical…
The Schrodinger Bridge and Bass (SBB) formulation, which jointly controls drift and volatility, is an established extension of the classical Schrodinger Bridge (SB). Building on this framework, we introduce LightSBB-M, an algorithm that…
The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence…
We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…
Probabilistic modelling of power systems operation and planning processes depends on data-driven methods, which require sufficiently large datasets. When historical data lacks this, it is desired to model the underlying data generation…
We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify…
A well-known technique in estimating probabilities of rare events in general and in information theory in particular (used, e.g., in the sphere-packing bound), is that of finding a reference probability measure under which the event of…
We develop a fully non-parametric, easy-to-use, and powerful test for the missing completely at random (MCAR) assumption on the missingness mechanism of a dataset. The test compares distributions of different missing patterns on random…
This paper presents an improved exponential tail bound for Beta distributions, refining a result in [15]. This improvement is achieved by interpreting their bound as a regular Kullback-Leibler (KL) divergence one, while introducing a…
Conditional generative models represent a significant advancement in the field of machine learning, allowing for the controlled synthesis of data by incorporating additional information into the generation process. In this work we introduce…
A Schr\"odinger bridge is the most probable time-dependent probability distribution that connects an initial probability distribution $w_{i}$ to a final one $w_{f}$. The problem has been solved and widely used for the case of simple…
This letter provides an adaptive resampling method. It determines the number of particles to resample so that the Kullback-Leibler distance (KLD) between distribution of particles before resampling and after resampling does not exceed a…
We analyse a class of time discretizations for solving the nonlinear Schr\"odinger equation with non-smooth potential and at low-regularity on an arbitrary Lipschitz domain $\Omega \subset \mathbb{R}^d$, $d \le 3$. We show that these…