Related papers: Data-driven Error Estimation: Excess Risk Bounds w…
Diffusion models have demonstrated state-of-the-art performance across vision, language, and scientific domains. Despite their empirical success, prior theoretical analyses of the sample complexity suffer from poor scaling with input data…
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…
We study the excess risk evaluation of classical penalized empirical risk minimization (ERM) with Bregman losses. We show that by leveraging the idea of wild refitting, one can efficiently upper bound the excess risk through the so-called…
Minimizing the empirical risk is a popular training strategy, but for learning tasks where the data may be noisy or heavy-tailed, one may require many observations in order to generalize well. To achieve better performance under less…
This paper presents a unified approach based on Wasserstein distance to derive concentration bounds for empirical estimates for two broad classes of risk measures defined in the paper. The classes of risk measures introduced include as…
Cross-validation techniques for risk estimation and model selection are widely used in statistics and machine learning. However, the understanding of the theoretical properties of learning via model selection with cross-validation risk…
This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms…
In this paper, we address learning problems for high dimensional data. Previously, oblivious random projection based approaches that project high dimensional features onto a random subspace have been used in practice for tackling…
Today, data analysts largely rely on intuition to determine whether missing or withheld rows of a dataset significantly affect their analyses. We propose a framework that can produce automatic contingency analysis, i.e., the range of values…
This paper extends standard results from learning theory with independent data to sequences of dependent data. Contrary to most of the literature, we do not rely on mixing arguments or sequential measures of complexity and derive uniform…
Generalization error bounds are critical to understanding the performance of machine learning models. In this work, building upon a new bound of the expected value of an arbitrary function of the population and empirical risk of a learning…
In this paper, we consider a best action identification problem in the stochastic linear bandit setup with a fixed confident constraint. In the considered best action identification problem, instead of minimizing the accumulative regret as…
A fundamental challenge in interactive learning and decision making, ranging from bandit problems to reinforcement learning, is to provide sample-efficient, adaptive learning algorithms that achieve near-optimal regret. This question is…
Although a majority of the theoretical literature in high-dimensional statistics has focused on settings which involve fully-observed data, settings with missing values and corruptions are common in practice. We consider the problems of…
This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…
Data-driven and adaptive control approaches face the problem of introducing sudden distributional shifts beyond the distribution of data encountered during learning. Therefore, they are prone to invalidating the very assumptions used in…
We design a general framework for answering adaptive statistical queries that focuses on providing explicit confidence intervals along with point estimates. Prior work in this area has either focused on providing tight confidence intervals…
Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…
Optimum parameter estimation methods require knowledge of a parametric probability density that statistically describes the available observations. In this work we examine Bayesian and non-Bayesian parameter estimation problems under a…
We develop a formalism for constructing stochastic upper bounds on the expected full sample risk for supervised classification tasks via the Hilbert coresets approach within a transductive framework. We explicitly compute tight and…