Search Results for author: Philippe Rigollet

Found 33 papers, 6 papers with code

A mathematical perspective on Transformers

1 code implementation17 Dec 2023 Borjan Geshkovski, Cyril Letrouit, Yury Polyanskiy, Philippe Rigollet

Transformers play a central role in the inner workings of large language models.

Covariance alignment: from maximum likelihood estimation to Gromov-Wasserstein

no code implementations22 Nov 2023 Yanjun Han, Philippe Rigollet, George Stepaniants

Feature alignment methods are used in many scientific disciplines for data pooling, annotation, and comparison.

Optimal transport for automatic alignment of untargeted metabolomic data

1 code implementation5 Jun 2023 Marie Breeur, George Stepaniants, Pekka Keski-Rahkonen, Philippe Rigollet, Vivian Viallon

Untargeted metabolomic profiling through liquid chromatography-mass spectrometry (LC-MS) measures a vast array of metabolites within biospecimens, advancing drug development, disease diagnosis, and risk prediction.

The emergence of clusters in self-attention dynamics

1 code implementation NeurIPS 2023 Borjan Geshkovski, Cyril Letrouit, Yury Polyanskiy, Philippe Rigollet

Cluster locations are determined by the initial tokens, confirming context-awareness of representations learned by Transformers.

Learning Gaussian Mixtures Using the Wasserstein-Fisher-Rao Gradient Flow

no code implementations4 Jan 2023 Yuling Yan, Kaizheng Wang, Philippe Rigollet

Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications.

GULP: a prediction-based metric between representations

1 code implementation12 Oct 2022 Enric Boix-Adsera, Hannah Lawrence, George Stepaniants, Philippe Rigollet

Comparing the representations learned by different neural networks has recently emerged as a key tool to understand various architectures and ultimately optimize them.

Variational inference via Wasserstein gradient flows

1 code implementation31 May 2022 Marc Lambert, Sinho Chewi, Francis Bach, Silvère Bonnabel, Philippe Rigollet

Along with Markov chain Monte Carlo (MCMC) methods, variational inference (VI) has emerged as a central computational approach to large-scale Bayesian inference.

Bayesian Inference Variational Inference

An algorithmic solution to the Blotto game using multi-marginal couplings

no code implementations15 Feb 2022 Vianney Perchet, Philippe Rigollet, Thibaut Le Gouic

In the case of asymmetric values where optimal solutions need not exist but Nash equilibria do, our algorithm samples from an $\varepsilon$-Nash equilibrium with similar complexity but where implicit constants depend on various parameters of the game such as battlefield values.

Sparse Multi-Reference Alignment : Phase Retrieval, Uniform Uncertainty Principles and the Beltway Problem

no code implementations24 Jun 2021 Subhro Ghosh, Philippe Rigollet

Our techniques have implications for the problem of crystallographic phase retrieval, indicating a certain local uniqueness for the recovery of sparse signals from their power spectrum.

Combinatorial Optimization Retrieval

The query complexity of sampling from strongly log-concave distributions in one dimension

no code implementations29 May 2021 Sinho Chewi, Patrik Gerber, Chen Lu, Thibaut Le Gouic, Philippe Rigollet

We establish the first tight lower bound of $\Omega(\log\log\kappa)$ on the query complexity of sampling from the class of strongly log-concave and log-smooth distributions with condition number $\kappa$ in one dimension.

Rejection sampling from shape-constrained distributions in sublinear time

no code implementations29 May 2021 Sinho Chewi, Patrik Gerber, Chen Lu, Thibaut Le Gouic, Philippe Rigollet

We consider the task of generating exact samples from a target distribution, known up to normalization, over a finite alphabet.

Optimal dimension dependence of the Metropolis-Adjusted Langevin Algorithm

no code implementations23 Dec 2020 Sinho Chewi, Chen Lu, Kwangjun Ahn, Xiang Cheng, Thibaut Le Gouic, Philippe Rigollet

Conventional wisdom in the sampling literature, backed by a popular diffusion scaling limit, suggests that the mixing time of the Metropolis-Adjusted Langevin Algorithm (MALA) scales as $O(d^{1/3})$, where $d$ is the dimension.

A Statistical Perspective on Coreset Density Estimation

no code implementations10 Nov 2020 Paxton Turner, Jingbo Liu, Philippe Rigollet

Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information.

Density Estimation

Efficient Interpolation of Density Estimators

no code implementations10 Nov 2020 Paxton Turner, Jingbo Liu, Philippe Rigollet

We study the problem of space and time efficient evaluation of a nonparametric estimator that approximates an unknown density.

SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence

1 code implementation NeurIPS 2020 Sinho Chewi, Thibaut Le Gouic, Chen Lu, Tyler Maunu, Philippe Rigollet

Stein Variational Gradient Descent (SVGD), a popular sampling algorithm, is often described as the kernelized gradient flow for the Kullback-Leibler divergence in the geometry of optimal transport.

Projection to Fairness in Statistical Learning

no code implementations24 May 2020 Thibaut Le Gouic, Jean-Michel Loubes, Philippe Rigollet

In the context of regression, we consider the fundamental question of making an estimator fair while preserving its prediction accuracy as much as possible.

Fairness regression

Exponential ergodicity of mirror-Langevin diffusions

no code implementations NeurIPS 2020 Sinho Chewi, Thibaut Le Gouic, Chen Lu, Tyler Maunu, Philippe Rigollet, Austin J. Stromme

Motivated by the problem of sampling from ill-conditioned log-concave distributions, we give a clean non-asymptotic convergence analysis of mirror-Langevin diffusions as introduced in Zhang et al. (2020).

Power analysis of knockoff filters for correlated designs

no code implementations NeurIPS 2019 Jingbo Liu, Philippe Rigollet

We introduce a simple functional called effective signal deficiency (ESD) of the covariance matrix $\Sigma$ that predicts consistency of various variable selection methods.

Variable Selection

Estimation of Monge Matrices

no code implementations5 Apr 2019 Jan-Christian Hütter, Cheng Mao, Philippe Rigollet, Elina Robeva

Monge matrices and their permuted versions known as pre-Monge matrices naturally appear in many domains across science and engineering.

Uncoupled isotonic regression via minimum Wasserstein deconvolution

no code implementations27 Jun 2018 Philippe Rigollet, Jonathan Weed

Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown nondecreasing regression function $f$ from independent pairs $(x_i, y_i)$ where $\mathbb{E}[y_i]=f(x_i), i=1, \ldots n$.

regression

Statistical Optimal Transport via Factored Couplings

no code implementations19 Jun 2018 Aden Forrow, Jan-Christian Hütter, Mor Nitzan, Philippe Rigollet, Geoffrey Schiebinger, Jonathan Weed

We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension.

Domain Adaptation

Sparse Gaussian ICA

no code implementations2 Apr 2018 Nilin Abrahamsen, Philippe Rigollet

Independent component analysis (ICA) is a cornerstone of modern data analysis.

Teacher Improves Learning by Selecting a Training Subset

no code implementations25 Feb 2018 Yuzhe Ma, Robert Nowak, Philippe Rigollet, Xuezhou Zhang, Xiaojin Zhu

We call a learner super-teachable if a teacher can trim down an iid training set while making the learner learn even better.

General Classification regression

Minimax Rates and Efficient Algorithms for Noisy Sorting

no code implementations28 Oct 2017 Cheng Mao, Jonathan Weed, Philippe Rigollet

There has been a recent surge of interest in studying permutation-based models for ranking from pairwise comparison data.

Learning Determinantal Point Processes with Moments and Cycles

no code implementations ICML 2017 John Urschel, Victor-Emmanuel Brunel, Ankur Moitra, Philippe Rigollet

Determinantal Point Processes (DPPs) are a family of probabilistic models that have a repulsive behavior, and lend themselves naturally to many tasks in machine learning where returning a diverse set of objects is important.

Point Processes

Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration

no code implementations NeurIPS 2017 Jason Altschuler, Jonathan Weed, Philippe Rigollet

Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision.

BIG-bench Machine Learning

Optimal Rates of Statistical Seriation

no code implementations8 Jul 2016 Nicolas Flammarion, Cheng Mao, Philippe Rigollet

Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing.

Denoising

Online learning in repeated auctions

no code implementations18 Nov 2015 Jonathan Weed, Vianney Perchet, Philippe Rigollet

To our knowledge, this is the first complete set of strategies for bidders participating in auctions of this type.

Aggregation of Affine Estimators

no code implementations12 Nov 2013 Dong Dai, Philippe Rigollet, Lucy Xia, Tong Zhang

While results indicate that the same aggregation scheme may not satisfy sharp oracle inequalities with high probability, we prove that a weaker notion of oracle inequality for EW that holds with high probability.

Model Selection

Computational Lower Bounds for Sparse PCA

no code implementations3 Apr 2013 Quentin Berthet, Philippe Rigollet

In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency.

Computational Efficiency

Optimal detection of sparse principal components in high dimension

no code implementations23 Feb 2012 Quentin Berthet, Philippe Rigollet

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix.

Vocal Bursts Intensity Prediction

The multi-armed bandit problem with covariates

no code implementations27 Oct 2011 Vianney Perchet, Philippe Rigollet

We consider a multi-armed bandit problem in a setting where each arm produces a noisy reward realization which depends on an observable random covariate.

Cannot find the paper you are looking for? You can Submit a new open access paper.