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Found 9 papers, 2 papers with code
Random matrix theory improved Fréchet mean of symmetric positive definite matrices
In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fr\'echet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means.
Random Matrix Analysis to Balance between Supervised and Unsupervised Learning under the Low Density Separation Assumption
As an application, we derive a hyperparameter selection policy that finds the best balance between the supervised and the unsupervised terms of our learning criterion.
PCA-based Multi Task Learning: a Random Matrix Approach
The article proposes and theoretically analyses a \emph{computationally efficient} multi-task learning (MTL) extension of popular principal component analysis (PCA)-based supervised learning schemes \cite{barshan2011supervised, bair2006prediction}.
Multi-task learning on the edge: cost-efficiency and theoretical optimality
This article proposes a distributed multi-task learning (MTL) algorithm based on supervised principal component analysis (SPCA) which is: (i) theoretically optimal for Gaussian mixtures, (ii) computationally cheap and scalable.
Deciphering and Optimizing Multi-Task Learning: a Random Matrix Approach
This article provides theoretical insights into the inner workings of multi-task and transfer learning methods, by studying the tractable least-square support vector machine multi-task learning (LS-SVM MTL) method, in the limit of large ($p$) and numerous ($n$) data.
Large Dimensional Analysis and Improvement of Multi Task Learning
Multi Task Learning (MTL) efficiently leverages useful information contained in multiple related tasks to help improve the generalization performance of all tasks.
Random Matrix-Improved Estimation of the Wasserstein Distance between two Centered Gaussian Distributions
This article proposes a method to consistently estimate functionals $\frac1p\sum_{i=1}^pf(\lambda_i(C_1C_2))$ of the eigenvalues of the product of two covariance matrices $C_1, C_2\in\mathbb{R}^{p\times p}$ based on the empirical estimates $\lambda_i(\hat C_1\hat C_2)$ ($\hat C_a=\frac1{n_a}\sum_{i=1}^{n_a} x_i^{(a)}x_i^{(a){{\sf T}}}$), when the size $p$ and number $n_a$ of the (zero mean) samples $x_i^{(a)}$ are similar.
Random Matrix Improved Covariance Estimation for a Large Class of Metrics
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.
Random matrix-improved estimation of covariance matrix distances
Given two sets $x_1^{(1)},\ldots, x_{n_1}^{(1)}$ and $x_1^{(2)},\ldots, x_{n_2}^{(2)}\in\mathbb{R}^p$ (or $\mathbb{C}^p$) of random vectors with zero mean and positive definite covariance matrices $C_1$ and $C_2\in\mathbb{R}^{p\times p}$ (or $\mathbb{C}^{p\times p}$), respectively, this article provides novel estimators for a wide range of distances between $C_1$ and $C_2$ (along with divergences between some zero mean and covariance $C_1$ or $C_2$ probability measures) of the form $\frac1p\sum_{i=1}^n f(\lambda_i(C_1^{-1}C_2))$ (with $\lambda_i(X)$ the eigenvalues of matrix $X$).
