相关论文: Coupled regularized sample covariance matrix estim…

In massive multiple-input multiple-output (MIMO) systems, the knowledge of the users' channel covariance matrix is crucial for minimum mean square error (MMSE) channel estimation in the uplink as well as it plays an important role in…

In this paper, we examine the Sample Average Approximation (SAA) procedure within a framework where the Monte Carlo estimator of the expectation is biased. We also introduce Multilevel Monte Carlo (MLMC) in the SAA setup to enhance the…

Support vector machine (SVM) is a well-known statistical technique for classification problems in machine learning and other fields. An important question for SVM is the selection of covariates (or features) for the model. Many studies have…

We study the typical learning properties of the recently introduced Soft Margin Classifiers (SMCs), learning realizable and unrealizable tasks, with the tools of Statistical Mechanics. We derive analytically the behaviour of the learning…

Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…

Maximum likelihood estimation in nonlinear models can exhibit substantial instability in finite samples when the data provide limited information about certain parameters. Such instability is driven by rare but extreme realizations of the…

We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…

We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…

Score matching estimators have gained widespread attention in recent years partly because they are free from calculating the integral of normalizing constant, thereby addressing the computational challenges in maximum likelihood estimation…

Many statistical applications require an estimate of a covariance matrix and/or its inverse. When the matrix dimension is large compared to the sample size, which happens frequently, the sample covariance matrix is known to perform poorly…

Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…

Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…

We derive the form of the variance-covariance matrix for any affine equivariant matrix-valued statistics when sampling from complex elliptical distributions. We then use this result to derive the variance-covariance matrix of the sample…

In imbalanced multi-class classification problems, the misclassification rate as an error measure may not be a relevant choice. Several methods have been developed where the performance measure retained richer information than the mere…

We consider the estimation of a scalar parameter, when two estimators are available. The first is always consistent. The second is inconsistent in general, but has a smaller asymptotic variance than the first, and may be consistent if an…

Adaptive algorithms belong to an important class of algorithms used in radar target detection to overcome prior uncertainty of interference covariance. The contamination of the empirical covariance matrix by the useful signal leads to…

Most modern supervised statistical/machine learning (ML) methods are explicitly designed to solve prediction problems very well. Achieving this goal does not imply that these methods automatically deliver good estimators of causal…

We present a method for calibrating the Ensemble of Exemplar SVMs model. Unlike the standard approach, which calibrates each SVM independently, our method optimizes their joint performance as an ensemble. We formulate joint calibration as a…

Covariance matrix tapers have a long history in signal processing and related fields. Examples of applications include autoregressive models (promoting a banded structure) or beamforming (widening the spectral null width associated with an…

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…