Related papers: Estimation of matrix trace using machine learning
In addition to recent developments in computing speed and memory, methodological advances have contributed to significant gains in the performance of stochastic simulation. In this paper, we focus on variance reduction for matrix…
Most data for evaluating and training recommender systems is subject to selection biases, either through self-selection by the users or through the actions of the recommendation system itself. In this paper, we provide a principled approach…
Three classes of stochastic networks and their performance measures are considered. These performance measures are defined as the expected value of some random variables and cannot normally be obtained analytically as functions of network…
To explore the limits of a stochastic gradient method, it may be useful to consider an example consisting of an infinite number of quadratic functions. In this context, it is appropriate to determine the expected value and the covariance…
Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators,…
We consider the problem of minimizing the number of matrix-vector queries needed for accurate trace estimation in the dynamic setting where our underlying matrix is changing slowly, such as during an optimization process. Specifically, for…
In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…
Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation.…
The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data. An algorithm based on the least-squares method and multiple-trajectory data is proposed for joint estimation of the nominal system…
In this paper we consider the trace regression model where $n$ entries or linear combinations of entries of an unknown $m_1\times m_2$ matrix $A_0$ corrupted by noise are observed. We establish for the nuclear-norm penalized estimator of…
We study an online linear regression setting in which the observed feature vectors are corrupted by noise and the learner can pay to reduce the noise level. In practice, this may happen for several reasons: for example, because features can…
A novel single-frame quaternion estimator processing two vector observations is introduced. The singular cases are examined, and appropriate rotational solutions are provided. Additionally, an alternative method involving sequential…
High-dimensional inference refers to problems of statistical estimation in which the ambient dimension of the data may be comparable to or possibly even larger than the sample size. We study an instance of high-dimensional inference in…
Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a…
Robustness to outliers is often a desirable property of statistical estimators. Indeed many well known estimators offer very good optimal performance in theory but are unusable in applied contexts because of their sensitivity to outliers.…
Many tasks in explainable machine learning, such as data valuation and feature attribution, perform expensive computation for each data point and are intractable for large datasets. These methods require efficient approximations, and…
In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not…
Deep learning models frequently make incorrect predictions with high confidence when presented with test examples that are not well represented in their training dataset. We propose a novel and straightforward approach to estimate…
This work presents a novel matrix-based method for constructing an approximation Hessian using only function evaluations. The method requires less computational power than interpolation-based methods and is easy to implement in matrix-based…
We consider an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and Gaussian noise. Using an integral representation of the evolution operator we investigate the high order corrections to the…