arXiv subjects

Emmanuel Pilliat

Publications and source records attributed to Emmanuel Pilliat.

6 recordsLinked to original sources

arXiv2026

High-Performance Portable GPU Primitives for Arbitrary Types and Operators in Julia

Portable GPU frameworks such as Kokkos and RAJA reduce the burden of cross-architecture development but typically incur measurable overhead on fundamental parallel primitives relative to vendor-optimized libraries. We present KernelForge.jl, a Julia library that implements scan, mapreduce, and matrix-vector primitives through a two-layer portable architecture: KernelIntrinsics.jl provides backend-agnostic abstractions for warp-level shuffles, memory fences, and vectorized memory access, while KernelForge.jl builds high-performance algorithms exclusively on top of these interfaces. Evaluated on an NVIDIA A40 and an AMD MI300X, KernelForge.jl matches or exceeds CUB kernel execution time on scan and mapreduce on the A40, and matches cuBLAS throughput on matrix-vector operations across most tested configurations-demonstrating, as a proof of concept, that portable JIT-compiled abstractions can achieve vendor-level throughput without sacrificing generality.

cs.DC↗

arXiv2025

Adaptive Algorithms for Infinitely Many-Armed Bandits: A Unified Framework

We consider a bandit problem where the buget is smaller than the number of arms, which may be infinite. In this regime, the usual objective in the literature is to minimize simple regret. To analyze broad classes of distributions with potentially unbounded support, where simple regret may not be well-defined, we take a slightly different approach and seek to maximize the expected simple reward of the recommended arm, providing anytime guarantees. To that end, we introduce a distribution-free algorithm, OSE, that adapts to the distribution of arm means and achieves near-optimal rates for several distribution classes. We characterize the sample complexity through the rank-corrected inverse squared gap function. In particular, we recover known upper bounds and transition regimes for $\alpha$ less or greater than $1/2$ when the quantile function is $\lambda_\eta = 1-\eta^{\alpha}$. We additionally identify new transition regimes depending on the noise level relative to $\alpha$, which we conjecture to be nearly optimal. Additionally, we introduce an enhanced practical version, PROSE, that achieves state-of-the-art empirical performance for the main distribution classes considered in the literature.

math.ST↗

arXiv2024

On Sparsity and Sub-Gaussianity in the Johnson-Lindenstrauss Lemma

We provide a simple proof of the Johnson-Lindenstrauss lemma for sub-Gaussian variables. We extend the analysis to identify how sparse projections can be, and what the cost of sparsity is on the target dimension.The Johnson-Lindenstrauss lemma is the theoretical core of the dimensionality reduction methods based on random projections. While its original formulation involves matrices with Gaussian entries, the computational cost of random projections can be drastically reduced by the use of simpler variables, especially if they vanish with a high probability. In this paper, we propose a simple and elementary analysis of random projections under classical assumptions that emphasizes the key role of sub-Gaussianity. Furthermore, we show how to extend it to sparse projections, emphasizing the limits induced by the sparsity of the data itself.

math.ST↗

arXiv2023

Optimal rates for ranking a permuted isotonic matrix in polynomial time

We consider a ranking problem where we have noisy observations from a matrix with isotonic columns whose rows have been permuted by some permutation $π$ *. This encompasses many models, including crowd-labeling and ranking in tournaments by pair-wise comparisons. In this work, we provide an optimal and polynomial-time procedure for recovering $π$ * , settling an open problem in [7]. As a byproduct, our procedure is used to improve the state-of-the art for ranking problems in the stochastically transitive model (SST). Our approach is based on iterative pairwise comparisons by suitable data-driven weighted means of the columns. These weights are built using a combination of spectral methods with new dimension-reduction techniques. In order to deal with the important case of missing data, we establish a new concentration inequality for sparse and centered rectangular Wishart-type matrices.

math.ST↗

arXiv2023

Optimal Permutation Estimation in Crowd-Sourcing problems

Motivated by crowd-sourcing applications, we consider a model where we have partial observations from a bivariate isotonic n x d matrix with an unknown permutation $π$ * acting on its rows. Focusing on the twin problems of recovering the permutation $π$ * and estimating the unknown matrix, we introduce a polynomial-time procedure achieving the minimax risk for these two problems, this for all possible values of n, d, and all possible sampling efforts. Along the way, we establish that, in some regimes, recovering the unknown permutation $π$ * is considerably simpler than estimating the matrix.

math.ST↗

arXiv2022

Optimal multiple change-point detection for high-dimensional data

This manuscript makes two contributions to the field of change-point detection. In a generalchange-point setting, we provide a generic algorithm for aggregating local homogeneity testsinto an estimator of change-points in a time series. Interestingly, we establish that the errorrates of the collection of tests directly translate into detection properties of the change-pointestimator. This generic scheme is then applied to various problems including covariance change-point detection, nonparametric change-point detection and sparse multivariate mean change-point detection. For the latter, we derive minimax optimal rates that are adaptive to theunknown sparsity and to the distance between change-points when the noise is Gaussian. Forsub-Gaussian noise, we introduce a variant that is optimal in almost all sparsity regimes.

math.ST↗