Valentin Leplat
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View article: Market-Driven Subset Selection for Budgeted Training
Market-Driven Subset Selection for Budgeted Training Open
Training large language models on massive datasets is computationally expensive, yet empirical evidence suggests that substantial portions of training examples contribute minimally to final performance. Data subset selection addresses this…
View article: Pass-efficient Randomized Algorithms for Low-rank Approximation of Quaternion Matrices
Pass-efficient Randomized Algorithms for Low-rank Approximation of Quaternion Matrices Open
Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input matrix-w…
View article: Nonnegative Tensor Decomposition Via Collaborative Neurodynamic Optimization
Nonnegative Tensor Decomposition Via Collaborative Neurodynamic Optimization Open
This paper introduces a novel collaborative neurodynamic model for computing nonnegative Canonical Polyadic Decomposition (CPD). The model relies on a system of recurrent neural networks to solve the underlying nonconvex optimization probl…
View article: Ruppert-Polyak averaging for Stochastic Order Oracle
Ruppert-Polyak averaging for Stochastic Order Oracle Open
Black-box optimization, a rapidly growing field, faces challenges due to limited knowledge of the objective function's internal mechanisms. One promising approach to address this is the Stochastic Order Oracle Concept. This concept, simila…
View article: An alternating minimization algorithm with trajectory for direct exoplanet detection
An alternating minimization algorithm with trajectory for direct exoplanet detection Open
Context . Effective image post-processing algorithms are vital for the successful direct imaging of exoplanets. Standard point spread function (PSF) subtraction methods use techniques based on a low-rank approximation to separate the rotat…
View article: An Alternating Minimization Algorithm with Trajectory for Direct Exoplanet Detection -- The AMAT Algorithm
An Alternating Minimization Algorithm with Trajectory for Direct Exoplanet Detection -- The AMAT Algorithm Open
Effective image post-processing algorithms are vital for the successful direct imaging of exoplanets. Standard PSF subtraction methods use techniques based on a low-rank approximation to separate the rotating planet signal from the quasi-s…
View article: Efficient Algorithms for Regularized Nonnegative Scale-invariant Low-rank Approximation Models
Efficient Algorithms for Regularized Nonnegative Scale-invariant Low-rank Approximation Models Open
Regularized nonnegative low-rank approximations, such as sparse Nonnegative Matrix Factorization or sparse Nonnegative Tucker Decomposition, form an important branch of dimensionality reduction models known for their enhanced interpretabil…
View article: Block Majorization Minimization with Extrapolation and Application to $β$-NMF
Block Majorization Minimization with Extrapolation and Application to $β$-NMF Open
We propose a Block Majorization Minimization method with Extrapolation (BMMe) for solving a class of multi-convex optimization problems. The extrapolation parameters of BMMe are updated using a novel adaptive update rule. By showing that b…
View article: Asymptotic Analysis of the Ruppert – Polyak Averaging for Stochastic Order Oracle
Asymptotic Analysis of the Ruppert – Polyak Averaging for Stochastic Order Oracle Open
Black-box optimization, a rapidly growing field, faces challenges due to limited knowledge of the objective function’s internal mechanisms. One promising approach to addressing this is the Stochastic Order Oracle Concept. This concept, sim…
View article: DATA FUSION AND UNMIXING WITH THE REGULARIZED NON-NEGATIVE BLOCK-TERM DECOMPOSITION: JOINT PROBLEMS, BLIND APPROACH AND AUTOMATIC MODEL ORDER SELECTION
DATA FUSION AND UNMIXING WITH THE REGULARIZED NON-NEGATIVE BLOCK-TERM DECOMPOSITION: JOINT PROBLEMS, BLIND APPROACH AND AUTOMATIC MODEL ORDER SELECTION Open
This paper introduces a family of coupled tensor optimization problems for joint super-resolution and unmixing in remote sensing. Using β-divergences allows the proposed methods to account for various noise statistics. A family of simple, …
View article: Deep Nonnegative Matrix Factorization with Beta Divergences
Deep Nonnegative Matrix Factorization with Beta Divergences Open
Deep Nonnegative Matrix Factorization (deep NMF) has recently emerged as a valuable technique for extracting multiple layers of features across different scales. However, all existing deep NMF models and algorithms have primarily centered …
View article: Conic optimization-based algorithms for nonnegative matrix factorization
Conic optimization-based algorithms for nonnegative matrix factorization Open
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix V and a factorization rank K, compute two nonnegative matrices, W with K columns and H with K rows, such that WH approximates V as well as possible…
View article: Direct Exoplanet Detection Using L1 Norm Low-Rank Approximation
Direct Exoplanet Detection Using L1 Norm Low-Rank Approximation Open
We propose to use low-rank matrix approximation using the component-wise L1-norm for direct imaging of exoplanets. Exoplanet detection by direct imaging is a challenging task for three main reasons: (1) the host star is several orders of m…
View article: NONNEGATIVE BLOCK-TERM DECOMPOSITION WITH THE β-DIVERGENCE:JOINT DATA FUSION AND BLIND SPECTRAL UNMIXING
NONNEGATIVE BLOCK-TERM DECOMPOSITION WITH THE β-DIVERGENCE:JOINT DATA FUSION AND BLIND SPECTRAL UNMIXING Open
We present a new method for solving simultaneously two problems: (1) hyperspectral and multispectral image fusion, and (2) the blind spectral unmixing of the unknown super-resolution image. The method, dubbed as β-(Lr ,Lr ,1)-NBTD, relies …
View article: NAG-GS: Semi-Implicit, Accelerated and Robust Stochastic Optimizer
NAG-GS: Semi-Implicit, Accelerated and Robust Stochastic Optimizer Open
Classical machine learning models such as deep neural networks are usually trained by using Stochastic Gradient Descent-based (SGD) algorithms. The classical SGD can be interpreted as a discretization of the stochastic gradient flow. In th…
View article: Nonnegative Tucker Decomposition with Beta-divergence for Music\n Structure Analysis of Audio Signals
Nonnegative Tucker Decomposition with Beta-divergence for Music\n Structure Analysis of Audio Signals Open
Nonnegative Tucker decomposition (NTD), a tensor decomposition model, has\nreceived increased interest in the recent years because of its ability to\nblindly extract meaningful patterns, in particular in Music Information\nRetrieval. Never…
View article: Nonnegative Tucker Decomposition with Beta-divergence for Music Structure Analysis of Audio Signals
Nonnegative Tucker Decomposition with Beta-divergence for Music Structure Analysis of Audio Signals Open
Nonnegative Tucker decomposition (NTD), a tensor decomposition model, has received increased interest in the recent years because of its ability to blindly extract meaningful patterns, in particular in Music Information Retrieval. Neverthe…
View article: Conic-Optimization Based Algorithms for Nonnegative Matrix Factorization
Conic-Optimization Based Algorithms for Nonnegative Matrix Factorization Open
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix $V$ and a factorization rank $K$, compute two nonnegative matrices, $W$ with $K$ columns and $H$ with $K$ rows, such that $WH$ approximates $V$ as …
View article: Exact Nonnegative Matrix Factorization via Conic Optimization
Exact Nonnegative Matrix Factorization via Conic Optimization Open
In this paper, we present two new approaches for computing exact nonnegative matrix factorizations (NMFs). Exact NMF can be defined as follows: given an input nonnegative matrix $V \in \mathbb{R}_+^{F \times N}$ and a factorization rank $K…
View article: Distributionally Robust and Multi-Objective Nonnegative Matrix Factorization
Distributionally Robust and Multi-Objective Nonnegative Matrix Factorization Open
This Matlab code allows you to solve the NMF problem where the objective function is a weighted sum of several β-divergences measuring the error between the input matrix X and the factorization WH, where W≥0 and H ≥0. It also allows you to…
View article: Blind Audio Source Separation With Minimum-Volume Beta-Divergence NMF
Blind Audio Source Separation With Minimum-Volume Beta-Divergence NMF Open
Considering a mixed signal composed of various audio sources and recorded\nwith a single microphone, we consider on this paper the blind audio source\nseparation problem which consists in isolating and extracting each of the\nsources. To p…