Related papers: Theoretical Guarantees for the Subspace-Constraine…
This paper deals with subspace estimation in the small sample size regime, where the number of samples is comparable in magnitude with the observation dimension. The traditional estimators, mostly based on the sample correlation matrix, are…
Anomalies (or outliers) are prevalent in real-world empirical observations and potentially mask important underlying structures. Accurate identification of anomalous samples is crucial for the success of downstream data analysis tasks. To…
In this paper, we study problem of estimating a sparse regression vector with correct support in the presence of outlier samples. The inconsistency of lasso-type methods is well known in this scenario. We propose a combinatorial version of…
State space subspace algorithms for input-output systems have been widely applied but also have a reasonably well-developedasymptotic theory dealing with consistency. However, guaranteeing the stability of the estimated system matrix is a…
High-dimensional data often lie in low-dimensional subspaces corresponding to different classes they belong to. Finding sparse representations of data points in a dictionary built using the collection of data helps to uncover…
Model-based deep learning solutions to inverse problems have attracted increasing attention in recent years as they bridge state-of-the-art numerical performance with interpretability. In addition, the incorporated prior domain knowledge…
In this paper, we analyse the recovery properties of nonconvex regularized $M$-estimators, under the assumption that the true parameter is of soft sparsity. In the statistical aspect, we establish the recovery bound for any stationary point…
State estimation aims at approximately reconstructing the solution $u$ to a parametrized partial differential equation from $m$ linear measurements, when the parameter vector $y$ is unknown. Fast numerical recovery methods have been…
We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…
Model estimates obtained from traditional subspace identification methods may be subject to significant variance. This elevated variance is aggravated in the cases of large models or of a limited sample size. Common solutions to reduce the…
We propose a neural network for unsupervised anomaly detection with a novel robust subspace recovery layer (RSR layer). This layer seeks to extract the underlying subspace from a latent representation of the given data and removes outliers…
Learning from data in the presence of outliers is a fundamental problem in statistics. Until recently, no computationally efficient algorithms were known to compute the mean of a high dimensional distribution under natural assumptions in…
Simulated Tempering (ST) is an MCMC algorithm for complex target distributions that operates on a path between the target and a more amenable reference distribution. Crucially, if the reference enables i.i.d. sampling, ST is regenerative…
Over the past decades, there has been a surge of interest in studying low-dimensional structures within high-dimensional data. Statistical factor models $-$ i.e., low-rank plus diagonal covariance structures $-$ offer a powerful framework…
Nonlinear estimation in robotics and vision is typically plagued with outliers due to wrong data association, or to incorrect detections from signal processing and machine learning methods. This paper introduces two unifying formulations…
Using Artificial Neural Networks (ANN) for nonlinear system identification has proven to be a promising approach, but despite of all recent research efforts, many practical and theoretical problems still remain open. Specifically, noise…
This paper studies the problem of recovering a signal from one-bit compressed sensing measurements under a manifold model; that is, assuming that the signal lies on or near a manifold of low intrinsic dimension. We provide a convex recovery…
This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…
In this paper, we present a novel optimization algorithm designed specifically for estimating state-space models to deal with heavy-tailed measurement noise and constraints. Our algorithm addresses two significant limitations found in…
The purpose of this thesis is to develop new theories on high-dimensional structured signal recovery under a rather weak assumption on the measurements that only a finite number of moments exists. High-dimensional recovery has been one of…