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We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting…
Many practical samplers rely on time-dependent drifts -- often induced by annealing or tempering schedules -- to improve exploration and stability. This motivates a unified non-asymptotic analysis of the corresponding Langevin diffusions…
For temporal regularly spaced datasets, a lot of methods are available and the properties of these methods are extensively investigated. Less research has been performed on irregular temporal datasets subject to measurement error with…
We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…
There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable…
In this paper, we introduce a Matlab program method to compute Carleman estimate for the fourth order partial differential operator $\gamma\partial_t+\partial_x^4\ (\gamma\in\mathbb{R})$. We obtain two kinds of Carleman estimates with…
We expect the generalization error to improve with more samples from a similar task, and to deteriorate with more samples from an out-of-distribution (OOD) task. In this work, we show a counter-intuitive phenomenon: the generalization error…
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…
In this paper, we analyze the drift-implicit (or backward) Euler numerical scheme for a class of stochastic differential equations with unbounded drift driven by an arbitrary $\lambda$-H\"older continuous process, $\lambda\in(0,1)$. We…
Deep generative models aim to learn the underlying distribution of data and generate new ones. Despite the diversity of generative models and their high-quality generation performance in practice, most of them lack rigorous theoretical…
We present a unified technique for sequential estimation of convex divergences between distributions, including integral probability metrics like the kernel maximum mean discrepancy, $\varphi$-divergences like the Kullback-Leibler…
Predictive models often degrade in performance due to evolving data distributions, a phenomenon known as data drift. Among its forms, concept drift, where the relationship between explanatory variables and the response variable changes, is…
In this work we develop an effective Monte Carlo method for estimating sensitivities, or gradients of expectations of sufficiently smooth functionals, of a reflected diffusion in a convex polyhedral domain with respect to its defining…
Distribution shifts on graphs -- the discrepancies in data distribution between training and employing a graph machine learning model -- are ubiquitous and often unavoidable in real-world scenarios. These shifts may severely deteriorate…
We study supervised multiclass classification for diffusion processes, where each class is characterized by a distinct drift function and trajectories are observed at discrete times. We first derive a multidimensional Bayes rule and then…
Deep learning has gained great popularity due to its widespread success on many inference problems. We consider the application of deep learning to the sparse linear inverse problem encountered in compressive sensing, where one seeks to…
We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…
Diffusion probabilistic models (DPMs) represent a class of powerful generative models. Despite their success, the inference of DPMs is expensive since it generally needs to iterate over thousands of timesteps. A key problem in the inference…
In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of independent random variables, each with support on the whole real…
Distribution learning finds probability density functions from a set of data samples, whereas clustering aims to group similar data points to form clusters. Although there are deep clustering methods that employ distribution learning…