Related papers: Statistical Mechanics of MAP Estimation: General R…
This paper addresses the adaptive radar target detection problem in the presence of Gaussian interference with unknown statistical properties. To this end, the problem is first formulated as a binary hypothesis test, and then we derive a…
We study the performance of a Bayesian statistician who estimates a rank-one signal corrupted by non-symmetric rotationally invariant noise with a generic distribution of singular values. As the signal-to-noise ratio and the noise structure…
A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…
A new statistical model designed for regression analysis with a sparse design matrix is proposed. This new model utilizes the positions of the limited non-zero elements in the design matrix to decompose the regression model into…
Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae…
This work presents a novel general regularized distributed solution for the state estimation problem in networked systems. Resting on the graph-based representation of sensor networks and adopting a multivariate least-squares approach, the…
Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations…
The traditional sparse modeling approach, when applied to inverse problems with large data such as images, essentially assumes a sparse model for small overlapping data patches. While producing state-of-the-art results, this methodology is…
Error-mitigation methods for Ising machines are reexamined not merely as noise-suppression techniques but as a structural design problem of replica-coupled Ising models. Using simulated annealing as a hardware-noise-free testbed, we…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
This study introduces Mean Averaging Smoothed Product (MASP) Spectrum, which is a modified version of the Harmonic Product Spectrum, designed to enhance pitch estimation for many algorithm-wise deceptive frequency spectra that still lead…
Snapshot mosaic multispectral imagery acquires an undersampled data cube by acquiring a single spectral measurement per spatial pixel. Sensors which acquire $p$ frequencies, therefore, suffer from severe $1/p$ undersampling of the full data…
A fundamental problem in supervised learning is to find a good set of features or distance measures. If the new set of features is of lower dimensionality and can be obtained by a simple transformation of the original data, they can make…
Distributed statistical learning has become a popular technique for large-scale data analysis. Most existing work in this area focuses on dividing the observations, but we propose a new algorithm, DDAC-SpAM, which divides the features under…
We study the problem of signal estimation from non-linear observations when the signal belongs to a low-dimensional set buried in a high-dimensional space. A rough heuristic often used in practice postulates that non-linear observations may…
This note addresses the question of optimally estimating a linear functional of an object acquired through linear observations corrupted by random noise, where optimality pertains to a worst-case setting tied to a symmetric, convex, and…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
Support points summarize a large dataset through a smaller set of representative points that can be used for data operations, such as Monte Carlo integration, without requiring access to the full dataset. In this sense, support points offer…
The Lasso regression is a popular regularization method for feature selection in statistics. Prior to computing the Lasso estimator in both linear and generalized linear models, it is common to conduct a preliminary rescaling of the feature…
The generalized linear model (GLM), where a random vector $\boldsymbol{x}$ is observed through a noisy, possibly nonlinear, function of a linear transform output $\boldsymbol{z}=\boldsymbol{Ax}$, arises in a range of applications such as…