Related papers: Optimal Detection For Sparse Mixtures
This work considers the problem of quickest detection of signals in a coupled system of $N$ sensors, which receive continuous sequential observations from the environment. It is assumed that the signals, which are modeled by general It\^{o}…
A key recent advance in face recognition models a test face image as a sparse linear combination of a set of training face images. The resulting sparse representations have been shown to possess robustness against a variety of distortions…
A major challenge in sparsity pattern estimation is that small modes are difficult to detect in the presence of noise. This problem is alleviated if one can observe samples from multiple realizations of the nonzero values for the same…
Sparse inverse covariance estimation (i.e., edge de-tection) is an important research problem in recent years, wherethe goal is to discover the direct connections between a set ofnodes in a networked system based upon the observed…
A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is…
Understanding the dynamics of complex systems is a central task in many different areas ranging form biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even systems failure is sometimes difficult…
This paper studies the classical problem of detecting the locations of signal occurrences in a one-dimensional noisy measurement. Assuming the signal occurrences do not overlap, we formulate the detection task as a constrained likelihood…
We consider a finite mixture of Gaussian regression model for high- dimensional data, where the number of covariates may be much larger than the sample size. We propose to estimate the unknown conditional mixture density by a maximum…
We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. The alternative is independent identically distributed zero-mean Gaussian random variables with…
We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…
This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise…
The change detection problem is to determine if the Markov network structures of two Markov random fields differ from one another given two sets of samples drawn from the respective underlying distributions. We study the trade-off between…
We generalize the classic change-point problem to a "change-set" framework: a spatial Poisson process changes its intensity on an unobservable random set. Optimal detection of the set is defined by maximizing the expected value of a gain…
We consider the classical Neymann-Pearson hypothesis testing problem of signal detection, where under the null hypothesis ($\calH_0$), the received signal is white Gaussian noise, and under the alternative hypothesis ($\calH_1$), the…
In multiple-input multiple-output (MIMO) spatially multiplexing (SM) systems, achievable error rate performance is determined by signal detection strategy. The optimal maximum-likelihood detection (MLD) that exhaustively examines all symbol…
Clustering is a pivotal challenge in unsupervised machine learning and is often investigated through the lens of mixture models. The optimal error rate for recovering cluster labels in Gaussian and sub-Gaussian mixture models involves ad…
The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by…
New problems arise when the standard theory of joint detection and estimation is applied to a set of signals drawn from a continuous family; decision thresholds must be determined as a function of the continuous parameter x characterizing…
We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and submatrix localization. Each of these problems is…
Recent attention in quickest change detection in the multi-sensor setting has been on the case where the densities of the observations change at the same instant at all the sensors due to the disruption. In this work, a more general…