Related papers: Minimax rates for sparse signal detection under co…
Bayesian hypothesis testing and minimax hypothesis testing represent extreme instances of detection in which the prior probabilities of the hypotheses are either completely and precisely known, or are completely unknown. Group minimax, also…
We consider detecting change points in the correlation structure of streaming data with minimum assumptions posed on the underlying data distribution. Detection statistics are constructed for dense and sparse change settings, based on…
Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…
In this paper, we provide a general methodology to draw statistical inferences on individual signal coordinates or linear combinations of them in sparse phase retrieval. Given an initial estimator for the targeting parameter (some simple…
In the corrupted compass model on a vertex-transitive graph, a neighbouring edge of every vertex is chosen uniformly at random and opened. Additionally, with probability $p$, independently for every vertex, every neighbouring edge is…
Compressed sensing posits that, within limits, one can undersample a sparse signal and yet reconstruct it accurately. Knowing the precise limits to such undersampling is important both for theory and practice. We present a formula that…
We consider parameter estimation under sparse linear regression -- an extensively studied problem in high-dimensional statistics and compressed sensing. While the minimax framework has been one of the most fundamental approaches for…
This paper gives performance limits of the segmented compressive sampling (CS) which collects correlated samples. It is shown that the effect of correlation among samples for the segmented CS can be characterized by a penalty term in the…
We consider testing for presence of a signal in Gaussian white noise with intensity 1/sqrt(n), when the alternatives are given by smoothness ellipsoids with an L2-ball of (squared) radius rho removed. It is known that, for a fixed Sobolev…
We investigate high-dimensional sparse regression when both the noise and the design matrix exhibit heavy-tailed behavior. Standard algorithms typically fail in this regime, as heavy-tailed covariates distort the empirical risk geometry. We…
We consider estimating the predictive density under Kullback-Leibler loss in an $\ell_0$ sparse Gaussian sequence model. Explicit expressions of the first order minimax risk along with its exact constant, asymptotically least favorable…
There is a growing interest in signaling schemes that operate in the wideband regime due to the crowded frequency spectrum. However, a downside of the wideband regime is that obtaining channel state information is costly, and the capacity…
The ferromagnetic XY model on sparse random graphs in a randomly oriented field is analyzed via the belief propagation algorithm. At variance with the fully connected case and with the random field Ising model on the same topology, we find…
In a sparse high-dimensional elliptical model we consider a hard threshold estimator for the correlation matrix based on Kendall's tau with threshold level $\alpha(\frac{\log p}{n})^{1/2}$. Parameters $\alpha$ are identified such that the…
This paper studies a statistical network model generated by a large number of randomly sized overlapping communities, where any pair of nodes sharing a community is linked with probability $q$ via the community. In the special case with…
Consider the communication-constrained problem of nonparametric function estimation, in which each distributed terminal holds multiple i.i.d. samples. Under certain regularity assumptions, we characterize the minimax optimal rates for all…
We study statistical and computational limits of clustering when the means of the centres are sparse and their dimension is possibly much larger than the sample size. Our theoretical analysis focuses on the model $X_i = z_i \theta +…
The stochastic block model is a canonical model of communities in random graphs. It was introduced in the social sciences and statistics as a model of communities, and in theoretical computer science as an average case model for graph…
The functional significance of correlations between action potentials of neurons is still a matter of vivid debates. In particular it is presently unclear how much synchrony is caused by afferent synchronized events and how much is…
In the problem of asymptotic binary i.i.d. state discrimination, the optimal asymptotics of the type I and the type II error probabilities is in general an exponential decrease to zero as a function of the number of samples; the set of…