Related papers: Complementary First and Second Derivative Methods …

We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of…

Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be cheaper than orthogonal projection or linear optimization…

While first-order optimization methods are usually designed to efficiently reduce the function value $f(x)$, there has been recent interest in methods efficiently reducing the magnitude of $\nabla f(x)$, and the findings show that the two…

We study several aspects of the recently introduced fixed-phase spin-orbit diffusion Monte Carlo (FPSODMC) method, in particular, its relation to the fixed-node method and its potential use as a general approach for electronic structure…

In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…

Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…

Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…

We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…

We present a variational function that targets excited states directly based on their position in the energy spectrum, along with a Monte Carlo method for its evaluation and minimization whose cost scales polynomially for a wide class of…

Particle filters provide Monte Carlo approximations of intractable quantities such as point-wise evaluations of the likelihood in state space models. In many scenarios, the interest lies in the comparison of these quantities as some…

Monte Carlo methods represent a cornerstone of computer science. They allow to sample high dimensional distribution functions in an efficient way. In this paper we consider the extension of Automatic Differentiation (AD) techniques to Monte…

We propose sequential Monte Carlo (SMC) methods for sampling the posterior distribution of state-space models under highly informative observation regimes, a situation in which standard SMC methods can perform poorly. A special case is…

Recent progress in deep latent variable models has largely been driven by the development of flexible and scalable variational inference methods. Variational training of this type involves maximizing a lower bound on the log-likelihood,…

Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the…

Bayesian analyses combine information represented by different terms in a joint Bayesian model. When one or more of the terms is misspecified, it can be helpful to restrict the use of information from suspect model components to modify…

In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlations detection - classical and modified rescaled range analyses. A focus is put on an effect of different distributional…

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…

First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov…

This paper investigates a novel a-posteriori variance reduction approach in Monte Carlo image synthesis. Unlike most established methods based on lateral filtering in the image space, our proposition is to produce the best possible estimate…

We show that the equivalent linearization technique, when used properly, enables us to calculate frequency corrections of weakly nonlinear oscillators beyond the first order in nonlinearity. We illustrate the method by applying it to the…