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The Adaptive Multilevel Splitting (AMS) algorithm is a powerful and versatile method for the simulation of rare events. It is based on an interacting (via a mutation-selection procedure) system of replicas, and depends on two integer…
This paper studies Graphical SLOPE for precision matrix estimation, with emphasis on its ability to recover both sparsity and clusters of edges with equal or similar strength. In a fixed-dimensional regime, we establish that the root-$n$…
The sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis, and sparse canonical correlation analysis.…
Constructing an occupancy representation of the environment is a fundamental problem for robot autonomy. Many accurate and efficient methods exist that address this problem but most assume that the occupancy states of different elements in…
In this paper, we consider a compressed sensing problem of reconstructing a sparse signal from an undersampled set of noisy linear measurements. The regularized least squares or least absolute shrinkage and selection operator (LASSO)…
Inducing-point-based sparse variational Gaussian processes have become the standard workhorse for scaling up GP models. Recent advances show that these methods can be improved by introducing a diagonal scaling matrix to the conditional…
Pan-sharpening algorithms utilize a panchromatic image and a multispectral image to generate a high spatial and high spectral image. However, the optimizations of the algorithms are designed with different standards. We employ a simple…
We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…
Consider a spectrally sparse signal $\boldsymbol{x}$ that consists of $r$ complex sinusoids with or without damping. We study the robust recovery problem for the spectrally sparse signal under the fully observed setting, which is about…
A multi-species generalization of the asymmetric simple exclusion process (ASEP) is studied in ordered sequential and sub-lattice parallel updating schemes. In this model particles hop with their own specific probabilities to their…
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…
Approximate message passing algorithm enjoyed considerable attention in the last decade. In this paper we introduce a variant of the AMP algorithm that takes into account glassy nature of the system under consideration. We coin this…
We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical…
This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized Tikhonov regularization, providing a rational…
We consider the problem of reconstructing the signal and the hidden variables from observations coming from a multi-layer network with rotationally invariant weight matrices. The multi-layer structure models inference from deep generative…
[Abridged.] It is conceivable that no single statistical estimator can be sensitive to all forms and levels of non-Gaussianity that may be present in observed CMB data. In recent works a statistical procedure based upon the calculation of…
We analyse the asymptotic behaviour of random instances of the Maximum Set Packing (MSP) optimization problem, also known as Maximum Matching or Maximum Strong Independent Set on Hypergraphs. We give an analytical prediction of the MSPs…
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…
Performance of regularized least-squares estimation in noisy compressed sensing is analyzed in the limit when the dimensions of the measurement matrix grow large. The sensing matrix is considered to be from a class of random ensembles that…
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…