Related papers: Oracle Lower Bounds for Stochastic Gradient Sampli…

Variance-reduced stochastic gradient methods have gained popularity in recent times. Several variants exist with different strategies for the storing and sampling of gradients and this work concerns the interactions between these two…

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…

In this paper, we revisit the recently established theoretical guarantees for the convergence of the Langevin Monte Carlo algorithm of sampling from a smooth and (strongly) log-concave density. We improve the existing results when the…

We study the problem of sampling from a probability distribution $\pi$ on $\rset^d$ which has a density \wrt\ the Lebesgue measure known up to a normalization factor $x \mapsto \rme^{-U(x)} / \int_{\rset^d} \rme^{-U(y)} \rmd y$. We analyze…

We focus on analyzing the classical stochastic projected gradient methods under a general dependent data sampling scheme for constrained smooth nonconvex optimization. We show the worst-case rate of convergence $\tilde{O}(t^{-1/4})$ and…

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…

We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, let $k$ be the number of groups, $d$ be the average degree, the probability of edges between vertices…

We propose a method for estimating a log-concave density on $\mathbb R^d$ from samples, under the assumption that there exists an orthogonal transformation that makes the components of the random vector independent. While log-concave…

We consider stochastic optimization over $\ell_p$ spaces using access to a first-order oracle. We ask: {What is the minimum precision required for oracle outputs to retain the unrestricted convergence rates?} We characterize this precision…

Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…

ADAGB2, a generalization of the Adagrad algorithm for stochastic optimization is introduced, which is also applicable to bound-constrained problems and capable of using second-order information when available. It is shown that, given…

In large-data applications, such as the inference process of diffusion models, it is desirable to design sampling algorithms with a high degree of parallelization. In this work, we study the adaptive complexity of sampling, which is the…

We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model…

For the task of sampling from a density $\pi \propto \exp(-V)$ on $\mathbb{R}^d$, where $V$ is possibly non-convex but $L$-gradient Lipschitz, we prove that averaged Langevin Monte Carlo outputs a sample with $\varepsilon$-relative Fisher…

Risk minimization for nonsmooth nonconvex problems naturally leads to first-order sampling or, by an abuse of terminology, to stochastic subgradient descent. We establish the convergence of this method in the path-differentiable case and…

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…

Given a convex function $f\colon\mathbb{R}^{d}\to\mathbb{R}$, the problem of sampling from a distribution $\propto e^{-f(x)}$ is called log-concave sampling. This task has wide applications in machine learning, physics, statistics, etc. In…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

Motivated by applications to deep learning which often fail standard Lipschitz smoothness requirements, we examine the problem of sampling from distributions that are not log-concave and are only weakly dissipative, with log-gradients…

We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, consider the symmetric stochastic block model with $q$ groups, average degree $d$, and connection…