Author name cluster

Malik Tiomoko

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

9 papers

2 author rows

NeurIPS Conference 2024 Conference Paper

Analysing Multi-Task Regression via Random Matrix Theory with Application to Time Series Forecasting

Romain Ilbert
Malik Tiomoko
Cosme Louart
Ambroise Odonnat
Vasilii Feofanov
Themis Palpanas
Ievgen Redko

In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models. Our analysis provides valuable insights by linking the multi-task learning performance to various model statistics such as raw data covariances, signal-generating hyperplanes, noise levels, as well as the size and number of datasets. We finally propose a consistent estimation of training and testing errors, thereby offering a robust foundation for hyperparameter optimization in multi-task regression scenarios. Experimental validations on both synthetic and real-world datasets in regression and multivariate time series forecasting demonstrate improvements on univariate models, incorporating our method into the training loss and thus leveraging multivariate information.

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ICML Conference 2024 Conference Paper

Random matrix theory improved Fréchet mean of symmetric positive definite matrices

Florent Bouchard
Ammar Mian
Malik Tiomoko
Guillaume Ginolhac
Frédéric Pascal 0001

In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fréchet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means. Such means are leveraged in numerous machine learning tasks. Relying on advanced statistical tools, we introduce a random matrix theory based method that estimates Fréchet means, which is particularly beneficial when dealing with low sample support and a high number of matrices to average. Our experimental evaluation, involving both synthetic and real-world EEG and hyperspectral datasets, shows that we largely outperform state-of-the-art methods.

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UAI Conference 2023 Conference Paper

Learning from Low Rank Tensor Data: A Random Tensor Theory Perspective

Mohamed El Amine Seddik
Malik Tiomoko
Alexis Decurninge
Maxim Panov
Maxime Guillaud

Under a simplified data model, this paper provides a theoretical analysis of learning from data that have an underlying low-rank tensor structure in both supervised and unsupervised settings. For the supervised setting, we provide an analysis of a Ridge classifier (with high regularization parameter) with and without knowledge of the low-rank structure of the data. Our results quantify analytically the gain in misclassification errors achieved by exploiting the low-rank structure for denoising purposes, as opposed to treating data as mere vectors. We further provide a similar analysis in the context of clustering, thereby quantifying the exact performance gap between tensor methods and standard approaches which treat data as simple vectors.

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ICLR Conference 2023 Conference Paper

Optimizing Spca-based Continual Learning: A Theoretical Approach

Chunchun Yang
Malik Tiomoko
Zengfu Wang

Catastrophic forgetting and the stability-plasticity dilemma are two major obstacles to continual learning. In this paper we first propose a theoretical analysis of a SPCA-based continual learning algorithm using high dimensional statistics. Second, we design OSCL (Optimized Spca-based Continual Learning) which builds on a flexible task optimization based on the theory. By optimizing a single task, catastrophic forgetting can be prevented theoretically. While optimizing multi-tasks, the trade-off between integrating knowledge from the new task and retaining previous knowledge of the old task can be achieved by assigning appropriate weights to corresponding tasks in compliance with the objectives. Experimental results confirm that the various theoretical conclusions are robust to a wide range of data distributions. Besides, several applications on synthetic and real data show that the proposed method while being computationally efficient, achieves comparable results with some state of the art.

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ICML Conference 2023 Conference Paper

PCA-based Multi-Task Learning: a Random Matrix Approach

Malik Tiomoko
Romain Couillet
Frédéric Pascal 0001

The article proposes and theoretically analyses a computationally efficient multi-task learning (MTL) extension of popular principal component analysis (PCA)-based supervised learning schemes. The analysis reveals that (i) by default, learning may dramatically fail by suffering from negative transfer, but that (ii) simple counter-measures on data labels avert negative transfer and necessarily result in improved performances. Supporting experiments on synthetic and real data benchmarks show that the proposed method achieves comparable performance with state-of-the-art MTL methods but at a significantly reduced computational cost.

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ICML Conference 2023 Conference Paper

Random Matrix Analysis to Balance between Supervised and Unsupervised Learning under the Low Density Separation Assumption

Vasilii Feofanov
Malik Tiomoko
Aladin Virmaux

We propose a theoretical framework to analyze semi-supervised classification under the low density separation assumption in a high-dimensional regime. In particular, we introduce QLDS, a linear classification model, where the low density separation assumption is implemented via quadratic margin maximization. The algorithm has an explicit solution with rich theoretical properties, and we show that particular cases of our algorithm are the least-square support vector machine in the supervised case, the spectral clustering in the fully unsupervised regime, and a class of semi-supervised graph-based approaches. As such, QLDS establishes a smooth bridge between these supervised and unsupervised learning methods. Using recent advances in the random matrix theory, we formally derive a theoretical evaluation of the classification error in the asymptotic regime. 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. Finally, we provide extensive illustrations of our framework, as well as an experimental study on several benchmarks to demonstrate that QLDS, while being computationally more efficient, improves over cross-validation for hyperparameter selection, indicating a high promise of the usage of random matrix theory for semi-supervised model selection.

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ICML Conference 2022 Conference Paper

Deciphering Lasso-based Classification Through a Large Dimensional Analysis of the Iterative Soft-Thresholding Algorithm

Malik Tiomoko
Ekkehard Schnoor
Mohamed El Amine Seddik
Igor Colin
Aladin Virmaux

This paper proposes a theoretical analysis of a Lasso-based classification algorithm. Leveraging on a realistic regime where the dimension of the data $p$ and their number $n$ are of the same order of magnitude, the theoretical classification error is derived as a function of the data statistics. As a result, insights into the functioning of the Lasso in classification and its differences with competing algorithms are highlighted. Our work is based on an original novel analysis of the Iterative Soft-Thresholding Algorithm (ISTA), which may be of independent interest beyond the particular problem studied here and may be adapted to similar iterative schemes. A theoretical optimization of the model’s hyperparameters is also provided, which allows for the data- and time-consuming cross-validation to be avoided. Finally, several applications on synthetic and real data are provided to validate the theoretical study and justify its impact in the design and understanding of algorithms of practical interest.

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ICLR Conference 2021 Conference Paper

Deciphering and Optimizing Multi-Task Learning: a Random Matrix Approach

Malik Tiomoko
Hafiz Tiomoko Ali
Romain Couillet

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. By a random matrix analysis applied to a Gaussian mixture data model, the performance of MTL LS-SVM is shown to converge, as $n,p\to\infty$, to a deterministic limit involving simple (small-dimensional) statistics of the data. We prove (i) that the standard MTL LS-SVM algorithm is in general strongly biased and may dramatically fail (to the point that individual single-task LS-SVMs may outperform the MTL approach, even for quite resembling tasks): our analysis provides a simple method to correct these biases, and that we reveal (ii) the sufficient statistics at play in the method, which can be efficiently estimated, even for quite small datasets. The latter result is exploited to automatically optimize the hyperparameters without resorting to any cross-validation procedure. Experiments on popular datasets demonstrate that our improved MTL LS-SVM method is computationally-efficient and outperforms sometimes much more elaborate state-of-the-art multi-task and transfer learning techniques.

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ICML Conference 2019 Conference Paper

Random Matrix Improved Covariance Estimation for a Large Class of Metrics

Malik Tiomoko
Romain Couillet
Florent Bouchard
Guillaume Ginolhac

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 largely outperform the sample covariance matrix estimate and to compete with state-of-the-art methods, while at the same time being computationally simpler and faster. Applications to linear and quadratic discriminant analyses also show significant gains, therefore suggesting practical interest to statistical machine learning.

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