no code implementations • 25 Jul 2024 • Sinho Chewi, Jonathan Niles-Weed, Philippe Rigollet

We present an introduction to the field of statistical optimal transport, based on lectures given at \'Ecole d'\'Et\'e de Probabilit\'es de Saint-Flour XLIX.

1 code implementation • 17 Dec 2023 • Borjan Geshkovski, Cyril Letrouit, Yury Polyanskiy, Philippe Rigollet

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

no code implementations • 22 Nov 2023 • Yanjun Han, Philippe Rigollet, George Stepaniants

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

1 code implementation • 5 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.

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.

no code implementations • 4 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.

1 code implementation • 12 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.

1 code implementation • 31 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.

no code implementations • 15 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.

no code implementations • 19 Nov 2021 • Subhro Ghosh, Philippe Rigollet

Determinantal point processes (a. k. a.

no code implementations • 24 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.

no code implementations • 29 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.

no code implementations • 29 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.

no code implementations • 23 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.

no code implementations • 10 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.

no code implementations • 10 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.

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.

no code implementations • 24 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.

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).

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.

no code implementations • 5 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.

no code implementations • 27 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 $\mathbb{E}[y_i]=f(x_i), i=1, \ldots n$.

no code implementations • 19 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.

no code implementations • 2 Apr 2018 • Nilin Abrahamsen, Philippe Rigollet

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

no code implementations • 25 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.

no code implementations • 28 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.

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.

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.

no code implementations • 8 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.

no code implementations • 18 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.

no code implementations • 12 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.

no code implementations • 3 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.

no code implementations • 23 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.

no code implementations • 27 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.

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