Related papers: Tensor train based sampling algorithms for approxi…
In this paper, we focus on the fixed TT-rank and precision problems of finding an approximation of the tensor train (TT) decomposition of a tensor. Note that the TT-SVD and TT-cross are two well-known algorithms for these two problems.…
Estimation of probability density function from samples is one of the central problems in statistics and machine learning. Modern neural network-based models can learn high dimensional distributions but have problems with hyperparameter…
Thompson sampling (TS) is a class of algorithms for sequential decision-making, which requires maintaining a posterior distribution over a model. However, calculating exact posterior distributions is intractable for all but the simplest…
General multivariate distributions are notoriously expensive to sample from, particularly the high-dimensional posterior distributions in PDE-constrained inverse problems. This paper develops a sampler for arbitrary continuous multivariate…
Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the Streaming Tensor Train Approximation (STTA), a new class of algorithms for approximating a given tensor…
Generative Adversarial Networks (GANs) are one of the most practical methods for learning data distributions. A popular GAN formulation is based on the use of Wasserstein distance as a metric between probability distributions.…
Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
Most existing approximate Thompson Sampling (TS) algorithms for multi-armed bandits use Stochastic Gradient Langevin Dynamics (SGLD) or its variants in each round to sample from the posterior, relaxing the need for conjugacy assumptions…
Bayesian inference in high-dimensional discrete-input additive noise models is a fundamental challenge in communication systems, as the support of the required joint a posteriori probability (APP) mass function grows exponentially with the…
Sampling from probability densities is a common challenge in fields such as Uncertainty Quantification (UQ) and Generative Modelling (GM). In GM in particular, the use of reverse-time diffusion processes depending on the log-densities of…
In this work, we investigate the convergence properties of the backward regularized Wasserstein proximal (BRWP) method for sampling a target distribution. The BRWP approach can be shown as a semi-implicit time discretization for a…
Sampling from a target distribution is a fundamental problem. Traditional Markov chain Monte Carlo (MCMC) algorithms, such as the unadjusted Langevin algorithm (ULA), derived from the overdamped Langevin dynamics, have been extensively…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional function approximations arising from computational and data sciences. Various sequential and parallel TT decomposition algorithms have…
To address the scalability limitations of Gaussian process (GP) regression, several approximation techniques have been proposed. One such method is based on tensor networks, which utilizes an exponential number of basis functions without…
We consider sampling from a Gibbs distribution by evolving a finite number of particles using a particular score estimator rather than Brownian motion. To accelerate the particles, we consider a second-order score-based ODE, similar to…
This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem…
We propose a deep importance sampling method that is suitable for estimating rare event probabilities in high-dimensional problems. We approximate the optimal importance distribution in a general importance sampling problem as the…
Sampling with Markov chain Monte Carlo methods often amounts to discretizing some continuous-time dynamics with numerical integration. In this paper, we establish the convergence rate of sampling algorithms obtained by discretizing smooth…
Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important…