Related papers: An Efficient Sampling Algorithm for Non-smooth Com…

In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques…

We propose a new stochastic proximal quasi-Newton method for minimizing the sum of two convex functions in the particular context that one of the functions is the average of a large number of smooth functions and the other one is nonsmooth.…

This paper concerns the minimization of the sum of a twice continuously differentiable function $f$ and a nonsmooth convex function $g$ without closed-form proximal mapping. For this class of nonconvex and nonsmooth problems, we propose a…

This paper develops and analyzes an accelerated proximal descent method for finding stationary points of nonconvex composite optimization problems. The objective function is of the form $f+h$ where $h$ is a proper closed convex function,…

We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…

Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distributions. For models that…

We analyze the convergence of compressive sensing based sampling techniques for the efficient evaluation of functionals of solutions for a class of high-dimensional, affine-parametric, linear operator equations which depend on possibly…

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 show that the gradient norm $\|\nabla f(x)\|$ for $x \sim \exp(-f(x))$, where $f$ is strongly convex and smooth, concentrates tightly around its mean. This removes a barrier in the prior state-of-the-art analysis for the well-studied…

This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…

This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and…

We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward…

The supervised learning problem to determine a neural network approximation $\mathbb{R}^d\ni x\mapsto\sum_{k=1}^K\hat\beta_k e^{{\mathrm{i}}\omega_k\cdot x}$ with one hidden layer is studied as a random Fourier features algorithm. The…

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived…

Recent works propose using the discriminator of a GAN to filter out unrealistic samples of the generator. We generalize these ideas by introducing the implicit Metropolis-Hastings algorithm. For any implicit probabilistic model and a target…

For a $d$-dimensional log-concave distribution $\pi(\theta) \propto e^{-f(\theta)}$ constrained to a convex body $K$, the problem of outputting samples from a distribution $\nu$ which is $\varepsilon$-close in infinity-distance…

We study the mixing time of Metropolis-Adjusted Langevin algorithm (MALA) for sampling a target density on $\mathbb{R}^d$. We assume that the target density satisfies $\psi_\mu$-isoperimetry and that the operator norm and trace of its…

We investigate the use of the Metropolis-Hastings algorithm to sample posterior distribution in a Bayesian inverse problem, where the likelihood function is random. Concretely, we consider the case where one has full field observations of a…

We consider the problem of sampling from a strongly log-concave density in $\mathbb{R}^d$, and prove a non-asymptotic upper bound on the mixing time of the Metropolis-adjusted Langevin algorithm (MALA). The method draws samples by…