Related papers: Optimal detection of multi-sample aligned sparse s…
We propose an approach to rapidly find the upper limit of separability between datasets that is directly applicable to HEP classification problems. The most common HEP classification task is to use $n$ values (variables) for an object…
Motivated by cutting-edge applications like cryo-electron microscopy (cryo-EM), the Multi-Reference Alignment (MRA) model entails the learning of an unknown signal from repeated measurements of its images under the latent action of a group…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
This paper investigates the detection and estimation of a single change in high-dimensional linear models. We derive minimax lower bounds for the detection boundary and the estimation rate, which uncover a phase transition governed by the…
We consider the problem of detecting a sparse mixture as studied by Ingster (1997) and Donoho and Jin (2004). We consider a wide array of base distributions. In particular, we study the situation when the base distribution has polynomial…
When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…
We consider the problem of testing whether a correlation matrix of a multivariate normal population is the identity matrix. We focus on sparse classes of alternatives where only a few entries are nonzero and, in fact, positive. We derive a…
We study the problem of detection of a p-dimensional sparse vector of parameters in the linear regression model with Gaussian noise. We establish the detection boundary, i.e., the necessary and sufficient conditions for the possibility of…
We consider the problem of sequential signal detection in a multichannel system where the number and location of signals is a priori unknown. We assume that the data in each channel are sequentially observed and follow a general non-i.i.d.…
Assume that we observe a sample of size n composed of p-dimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensity. We are interested in estimating the sum of the n unknown…
Sparse phase retrieval aims to recover a $k$-sparse signal from $m$ phaseless measurements. While the theoretically optimal sample complexity for successful recovery is $\Omega(k \log n)$, existing algorithms can only achieve this bound for…
For decades researchers have studied the On/Off counting problem, where a measured rate consists of two parts. One due to a signal process and another due to a background process, of which both magnitudes are unknown. While most frequentist…
We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…
We develop a multiscale scanning method to find anomalies in a $d$-dimensional random field in the presence of nuisance parameters. This covers the common situation that either the baseline-level or additional parameters such as the…
This paper investigates the fundamental limits for detecting a high-dimensional sparse matrix contaminated by white Gaussian noise from both the statistical and computational perspectives. We consider $p\times p$ matrices whose rows and…
This work considers the problem of detecting signals from multiple sequentially observed data streams, where only one stream can be observed at every time instant. The goal is to detect signals as quickly as possible while controlling the…
We consider the problem of detecting jumps in an otherwise smoothly evolving trend whilst the covariance and higher-order structures of the system can experience both smooth and abrupt changes over time. The number of jump points is allowed…
A Bayesian analysis of the probability of a signal in the presence of background is developed, and criteria are proposed for claiming evidence for, or the discovery of a signal. The method is general and in particular applicable to sparsely…
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}…
Verification of a quantum advantage in the presence of noise is a key open problem in the study of near-term quantum devices. In this work, we show how to assess the quality of photonic interference in a linear optical quantum device (boson…