Related papers: A Probabilistic Subspace Bound with Application to…
We study the problem of approximating the eigenspectrum of a symmetric matrix $\mathbf A \in \mathbb{R}^{n \times n}$ with bounded entries (i.e., $\|\mathbf A\|_{\infty} \leq 1$). We present a simple sublinear time algorithm that…
We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…
In a recent paper Beskos et al (2011), the Sequential Monte Carlo (SMC) sampler introduced in Del Moral et al (2006), Neal (2001) has been shown to be asymptotically stable in the dimension of the state space d at a cost that is only…
Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…
The sample average approximation (SAA) approach is applied to risk-neutral optimization problems governed by semilinear elliptic partial differential equations with random inputs. After constructing a compact set that contains the SAA…
In this paper, we consider convex stochastic optimization problems arising in machine learning applications (e.g., risk minimization) and mathematical statistics (e.g., maximum likelihood estimation). There are two main approaches to solve…
We introduce a general form of sequential Monte Carlo algorithm defined in terms of a parameterized resampling mechanism. We find that a suitably generalized notion of the Effective Sample Size (ESS), widely used to monitor algorithm…
In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted…
The effective sample size (ESS) is widely used in sample-based simulation methods for assessing the quality of a Monte Carlo approximation of a given distribution and of related integrals. In this paper, we revisit the approximation of the…
The likelihood-informed subspace (LIS) method offers a viable route to reducing the dimensionality of high-dimensional probability distributions arising in Bayesian inference. LIS identifies an intrinsic low-dimensional linear subspace…
This paper introduces an open-ended sequential algorithm for computing the p-value of a test using Monte Carlo simulation. It guarantees that the resampling risk, the probability of a different decision than the one based on the theoretical…
Psychiatric neuroscience is increasingly aware of the need to define psychopathology in terms of abnormal neural computation. The central tool in this endeavour is the fitting of computational models to behavioural data. The most prominent…
We consider the numerical approximation of $\mathbb{P}[G\in \Omega]$ where the $d$-dimensional random variable $G$ cannot be sampled directly, but there is a hierarchy of increasingly accurate approximations $\{G_\ell\}_{\ell\in\mathbb{N}}$…
Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
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…
Many Bayesian inference problems involve high-dimensional models where the performance of standard importance sampling (IS) methods often degrades rapidly as the dimensionality increases. Classical analyses of IS typically rely on the…
In this work, we propose a smart idea to couple importance sampling and Multilevel Monte Carlo (MLMC). We advocate a per level approach with as many importance sampling parameters as the number of levels, which enables us to compute the…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…