Related papers: Markov Chain Concentration with an Application in …

In empirical risk optimization, it has been observed that stochastic gradient implementations that rely on random reshuffling of the data achieve better performance than implementations that rely on sampling the data uniformly. Recent works…

A major limitation of machine learning (ML) prediction models is that they recover associational, rather than causal, predictive relationships between variables. In high-stakes automation applications of ML this is problematic, as the model…

Influence functions provide a principled method to assess the contribution of individual training samples to a specific target. Yet, their high computational costs limit their applications on large-scale models and datasets. Existing…

One popular method for dealing with large-scale data sets is sampling. For example, by using the empirical statistical leverage scores as an importance sampling distribution, the method of algorithmic leveraging samples and rescales…

Triplet Markov chains are general generative models for sequential data which take into account three kinds of random variables: (noisy) observations, their associated discrete labels and latent variables which aim at strengthening the…

For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…

We revisit random search for stochastic optimization, where only noisy function evaluations are available. We show that the method works under weaker smoothness assumptions than previously considered, and that stronger assumptions enable…

Let $(Y,X_1,...,X_m)$ be a random vector. It is desired to predict $Y$ based on $(X_1,...,X_m)$. Examples of prediction methods are regression, classification using logistic regression or separating hyperplanes, and so on. We consider the…

Motivated by broad applications in reinforcement learning and federated learning, we study local stochastic approximation over a network of agents, where their goal is to find the root of an operator composed of the local operators at the…

This paper provides a variational analysis of the unconstrained formulation of the LASSO problem, ubiquitous in statistical learning, signal processing, and inverse problems. In particular, we establish smoothness results for the optimal…

We prove that probability laws of certain multidimensional semimartingales which includes time-inhomogenous diffusions, under suitable assumptions, satisfy Quadratic Transportation Cost Inequality under the uniform metric. From this we…

We propose a reinforcement learning (RL) approach to compute the expression of quasi-stationary distribution. Based on the fixed-point formulation of quasi-stationary distribution, we minimize the KL-divergence of two Markovian path…

We use a new eigenvalue concentration bound for the fluctuation of the sample mean of the random extternal potential in the multi-particle Anderson model and prove the spectral exponential and the strong dynamical localization. The results…

We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…

Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…

Strassen's classical martingale coupling theorem states that two real-valued random variables are ordered in the convex (resp.\ increasing convex) stochastic order if and only if they admit a martingale (resp.\ submartingale) coupling. By…

We derive two upper bounds for the probability of deviation of a vector-valued Lipschitz function of a collection of random variables from its expected value. The resulting upper bounds can be tighter than bounds obtained by a direct…

Lecture notes for the Yale Computer Science course CPSC 4690/5690 Randomized Algorithms. Suitable for use as a supplementary text for an introductory graduate or advanced undergraduate course on randomized algorithms. Discusses tools from…

We introduce a method for proving almost sure termination in the context of lambda calculus with continuous random sampling and explicit recursion, based on ranking supermartingales. This result is extended in three ways. Antitone ranking…

Reinforcement learning algorithms are commonly analyzed (and designed) under the Markov assumption. This is unrealistic, as most environments encountered in practice are either partially observable, or require function approximation that…