Related papers: Efficient Robust Proper Learning of Log-concave Di…

We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing…

We study the approximation of arbitrary distributions $P$ on $d$-dimensional space by distributions with log-concave density. Approximation means minimizing a Kullback--Leibler-type functional. We show that such an approximation exists if…

Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning. We study the distributions of the form $p^{*}\propto\exp(-f(x))$, where…

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…

Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost…

Few-shot learning is a rapidly evolving area of research in machine learning where the goal is to classify unlabeled data with only one or "a few" labeled exemplary samples. Neural networks are typically trained to minimize a distance…

We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the…

Distributionally robust policy learning aims to find a policy that performs well under the worst-case distributional shift, and yet most existing methods for robust policy learning consider the worst-case joint distribution of the covariate…

We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…

We investigate the problem of learning Bayesian networks in a robust model where an $\epsilon$-fraction of the samples are adversarially corrupted. In this work, we study the fully observable discrete case where the structure of the network…

We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve…

We present a new adaptive algorithm for learning discrete distributions under distribution drift. In this setting, we observe a sequence of independent samples from a discrete distribution that is changing over time, and the goal is to…

We construct algorithms with optimal error for learning with adversarial noise. The overarching theme of this work is that the use of \textsl{randomized} hypotheses can substantially improve upon the best error rates achievable with…

Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. While efficient algorithms are known for log-concave densities, the worst-case…

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…

This work develops a distributed optimization strategy with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown in Part II to have a wider stability range…

We study the problem of learning-to-learn: inferring a learning algorithm that works well on tasks sampled from an unknown distribution. As class of algorithms we consider Stochastic Gradient Descent on the true risk regularized by the…

We provide full theoretical guarantees for the convergence behaviour of diffusion-based generative models under the assumption of strongly log-concave data distributions while our approximating class of functions used for score estimation…

Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…

We consider learning in an adversarial environment, where an $\varepsilon$-fraction of samples from a distribution $P$ are arbitrarily modified (global corruptions) and the remaining perturbations have average magnitude bounded by $\rho$…