Related papers: Sampling approach to sparse approximation problem:…
This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction…
Simultaneous sparse approximation (SSA) seeks to represent a set of dependent signals using sparse vectors with identical supports. The SSA model has been used in various signal and image processing applications involving multiple…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…
A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…
This paper concerns the use of sequential Monte Carlo methods (SMC) for smoothing in general state space models. A well-known problem when applying the standard SMC technique in the smoothing mode is that the resampling mechanism introduces…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
In a random ray method of neutral particle transport simulation, each iteration begins by sampling a set of rays before proceeding to solve the characteristic transport equation along the linear paths the rays follow. Historically,…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…
In this paper, we present the Monte-Carlo Compressive Optimization algorithm, a new method to solve a combinatorial optimization problem that is assumed compressible. The method relies on random queries to the objective function in order to…
Given a real symmetric positive semi-definite matrix E, and an approximation S that is a sum of n independent matrix-valued random variables, we present bounds on the relative error in S due to randomization. The bounds do not depend on the…
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…
Stochastic Approximation (SA) is a popular approach for solving fixed-point equations where the information is corrupted by noise. In this paper, we consider an SA involving a contraction mapping with respect to an arbitrary norm, and show…
We analyze and compare the computational complexity of different simulation strategies for Monte Carlo in the setting of classically scaled population processes. This allows a range of widely used competing strategies to be judged…
We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding $L^2$ inner products instead of the…
Most solved dynamic structural macrofinance models are non-linear and/or non-Gaussian state-space models with high-dimensional and complex structures. We propose an annealed controlled sequential Monte Carlo method that delivers numerically…
Equality-constrained models naturally arise in problems in which measurements are taken at different levels of resolution. The challenge in this setting is that the models usually induce a joint distribution which is intractable. Resorting…
We proposed a probabilistic algorithm to solve the Multiple Sequence Alignment problem. The algorithm is a Simulated Annealing (SA) that exploits the representation of the Multiple Alignment between $D$ sequences as a directed polymer in…
We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…
The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks. A large number of solutions have been proposed to…