Related papers: Computational barriers in minimax submatrix detect…
We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…
We investigate the problem of center estimation in the high dimensional binary sub-Gaussian Mixture Model with Hidden Markov structure on the labels. We first study the limitations of existing results in the high dimensional setting and…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…
Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To…
We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency…
The covariance matrix of a $p$-dimensional random variable is a fundamental quantity in data analysis. Given $n$ i.i.d. observations, it is typically estimated by the sample covariance matrix, at a computational cost of $O(np^{2})$…
We consider the problem of sequential (online) estimation of a single change point in a piecewise linear regression model under a Gaussian setup. We demonstrate that certain CUSUM-type statistics attain the minimax optimal rates for…
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…
The information-theoretic limits of community detection have been studied extensively for network models with high levels of symmetry or homogeneity. The contribution of this paper is to study a broader class of network models that allow…
Given a heterogeneous Gaussian sequence model with unknown mean $\theta \in \mathbb R^d$ and known covariance matrix $\Sigma = \operatorname{diag}(\sigma_1^2,\dots, \sigma_d^2)$, we study the signal detection problem against sparse…
We consider the problem of identifying the densest k-node subgraph in a given graph. We write this problem as an instance of rank-constrained cardinality minimization and then relax using the nuclear and 11 norms. Although the original…
We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an…
Researchers currently use a number of approaches to predict and substantiate information-computation gaps in high-dimensional statistical estimation problems. A prominent approach is to characterize the limits of restricted models of…
Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of…
This paper investigates the computational and statistical limits in clustering matrix-valued observations. We propose a low-rank mixture model (LrMM), adapted from the classical Gaussian mixture model (GMM) to treat matrix-valued…
The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of…
Multiplicative noise makes stochastic dynamics depend on how the white-noise limit is interpreted. In multidimensional systems with matrix-valued noise amplitudes $\sigma(x)$, this dependence includes a local Jacobian contribution that is…
Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, $N$, due to the cubic (in…
Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…