Related papers: Scalable Sampling of Truncated Multivariate Normal…
In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…
Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model,…
We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate,…
Multivariate normal (MVN) probabilities arise in myriad applications, but they are analytically intractable and need to be evaluated via Monte-Carlo-based numerical integration. For the state-of-the-art minimax exponential tilting (MET)…
A non trivial problem that arises in several applications is the estimation of the mean of a truncated normal distribution. In this paper, an iterative deterministic scheme for approximating this mean is proposed. It has been inspired from…
Sampling from high-dimensional distributions is a fundamental problem in statistical research and practice. However, great challenges emerge when the target density function is unnormalized and contains isolated modes. We tackle this…
In this paper, we propose new randomization based algorithms for large scale linear discrete ill-posed problems with general-form regularization: ${\min} \|Lx\|$ subject to ${\min} \|Ax - b\|$, where $L$ is a regularization matrix. Our…
When data are collected subject to a detection limit, observations below the detection limit may be considered censored. In addition, the domain of such observations may be restricted; for example, values may be required to be non-negative.…
We provide an efficient algorithm for the classical problem, going back to Galton, Pearson, and Fisher, of estimating, with arbitrary accuracy the parameters of a multivariate normal distribution from truncated samples. Truncated samples…
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…
This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…
We develop a modular approach to Markov chain Monte Carlo (MCMC) sampling for unnormalized target densities. In this approach, Markov chains are constructed in parallel, each constrained to a subset of the target space. The Monte Carlo…
We show a statistical version of Taylor's theorem and apply this result to non-parametric density estimation from truncated samples, which is a classical challenge in Statistics \cite{woodroofe1985estimating, stute1993almost}. The…
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…
We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…
The Transductive Confidence Machine Nearest Neighbours (TCMNN) algorithm and a supporting, simple user interface was developed. Different settings of the TCMNN algorithms' parameters were tested on medical data sets, in addition to the use…
Completely random measures provide a principled approach to creating flexible unsupervised models, where the number of latent features is infinite and the number of features that influence the data grows with the size of the data set. Due…
Reducing acquisition time is of fundamental importance in various imaging modalities. The concept of variable density sampling provides a nice framework to achieve this. It was justified recently from a theoretical point of view in the…
We suggest a robust nearest-neighbor approach to classifying high-dimensional data. The method enhances sensitivity by employing a threshold and truncates to a sequence of zeros and ones in order to reduce the deleterious impact of…
We consider the problem of approximating an unknown function $u\in L^2(D,\rho)$ from its evaluations at given sampling points $x^1,\dots,x^n\in D$, where $D\subset \mathbb{R}^d$ is a general domain and $\rho$ is a probability measure. The…