Related papers: Polynomial Time Algorithms for Dual Volume Samplin…
The paper considers the problem of finding a submatrix $X_{\mathcal{S}} \in \mathbb{R}^{m \times k}$ in a matrix $X \in \mathbb{R}^{m \times n}$, such that the spectral or Frobenius norm of $X_{\mathcal{S}}^{\dag} X$ is limited, which…
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 give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem…
A wide variety of optimization techniques, both exact and heuristic, tend to be biased samplers. This means that when attempting to find multiple uncorrelated solutions of a degenerate Boolean optimization problem a subset of the solution…
We study the low rank approximation problem of any given matrix $A$ over $\mathbb{R}^{n\times m}$ and $\mathbb{C}^{n\times m}$ in entry-wise $\ell_p$ loss, that is, finding a rank-$k$ matrix $X$ such that $\|A-X\|_p$ is minimized. Unlike…
This paper addresses the problem of sequential submodular maximization: selecting and ranking items in a sequence to optimize some composite submodular function. In contrast to most of the previous works, which assume access to the utility…
An efficient simulation-based methodology is proposed for the rolling window estimation of state space models, called particle rolling Markov chain Monte Carlo (MCMC) with double block sampling. In our method, which is based on Sequential…
We study parallel sampling from high-dimensional strongly log-concave distributions. Langevin-based samplers converge rapidly in continuous time, but their discretizations are typically sequential and often require polynomially many steps…
Two-sample feature selection is the problem of finding features that describe a difference between two probability distributions, which is a ubiquitous problem in both scientific and engineering studies. However, existing methods have…
Since its introduction Boson Sampling has been the subject of intense study in the world of quantum computing. The task is to sample independently from the set of all $n \times n$ submatrices built from possibly repeated rows of a larger $m…
We investigate the problem of transforming an input sequence into a high-dimensional output sequence in order to transcribe polyphonic audio music into symbolic notation. We introduce a probabilistic model based on a recurrent neural…
Data reduction is a fundamental challenge of modern technology, where classical statistical methods are not applicable because of computational limitations. We consider multiple linear regression for an extraordinarily large number of…
In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification.…
A number of problems in a variety of fields are characterised by target distributions with a multimodal structure in which the presence of several isolated local maxima dramatically reduces the efficiency of Markov Chain Monte Carlo…
Performing exact Bayesian inference for complex models is computationally intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are expensive for large datasets and…
The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy…
We study the column subset selection problem with respect to the entrywise $\ell_1$-norm loss. It is known that in the worst case, to obtain a good rank-$k$ approximation to a matrix, one needs an arbitrarily large $n^{\Omega(1)}$ number of…
We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or…
Subsampling is one of the popular methods to balance statistical efficiency and computational efficiency in the big data era. Most approaches aim at selecting informative or representative sample points to achieve good overall information…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…