183 citations · 706 across the 60 of their papers we have counts for
62 papers
Distributionally Faithful Imputation via Positive Semi-Definite Kernel Density Estimation
Andrea Basteri, Carlo Ciliberto, Alessandro Rudi
Missing values undermine statistical inference and machine learning pipelines, yet most imputation methods rely on heuristics or restrictive parametric assumptions that ignore the…
GloptiNets: Scalable Non-Convex Optimization with Certificates
Gaspard Beugnot, Julien Mairal, Alessandro Rudi
We present a novel approach to non-convex optimization with certificates, which handles smooth functions on the hypercube or on the torus. Unlike traditional methods that rely on a…
Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence
Riccardo Bonalli, Alessandro Rudi
We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, wh…
Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Models
Anant Raj, Umut Şimşekli, Alessandro Rudi
This paper deals with the problem of efficient sampling from a stochastic differential equation, given the drift function and the diffusion matrix. The proposed approach leverages…
Approximation of optimization problems with constraints through kernel Sum-Of-Squares
Pierre-Cyril Aubin-Frankowski, Alessandro Rudi
Handling an infinite number of inequality constraints in infinite-dimensional spaces occurs in many fields, from global optimization to optimal transport. These problems have been…
Vector-Valued Least-Squares Regression under Output Regularity Assumptions
Luc Brogat-Motte, Alessandro Rudi, Céline Brouard +2
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study und…
Exponential convergence of sum-of-squares hierarchies for trigonometric polynomials
Francis Bach, Alessandro Rudi
We consider the unconstrained optimization of multivariate trigonometric polynomials by the sum-of-squares hierarchy of lower bounds. We first show a convergence rate of …
Active Labeling: Streaming Stochastic Gradients
Vivien Cabannes, Francis Bach, Vianney Perchet +1
The workhorse of machine learning is stochastic gradient descent. To access stochastic gradients, it is common to consider iteratively input/output pairs of a training dataset. Int…
Non-Convex Optimization with Certificates and Fast Rates Through Kernel Sums of Squares
Blake Woodworth, Francis Bach, Alessandro Rudi
We consider potentially non-convex optimization problems, for which optimal rates of approximation depend on the dimension of the parameter space and the smoothness of the function…
Measuring dissimilarity with diffeomorphism invariance
Théophile Cantelobre, Carlo Ciliberto, Benjamin Guedj +1
Measures of similarity (or dissimilarity) are a key ingredient to many machine learning algorithms. We introduce DID, a pairwise dissimilarity measure applicable to a wide range of…
Second order conditions to decompose smooth functions as sums of squares
Ulysse Marteau-Ferey, Francis Bach, Alessandro Rudi
We consider the problem of decomposing a regular non-negative function as a sum of squares of functions which preserve some form of regularity. In the same way as decomposing non-n…
On the Benefits of Large Learning Rates for Kernel Methods
Gaspard Beugnot, Julien Mairal, Alessandro Rudi
This paper studies an intriguing phenomenon related to the good generalization performance of estimators obtained by using large learning rates within gradient descent algorithms.…
Nyström Kernel Mean Embeddings
Antoine Chatalic, Nicolas Schreuder, Alessandro Rudi +1
Kernel mean embeddings are a powerful tool to represent probability distributions over arbitrary spaces as single points in a Hilbert space. Yet, the cost of computing and storing…
Near-optimal estimation of smooth transport maps with kernel sums-of-squares
Boris Muzellec, Adrien Vacher, Francis Bach +2
It was recently shown that under smoothness conditions, the squared Wasserstein distance between two distributions could be efficiently computed with appealing statistical error up…
Learning PSD-valued functions using kernel sums-of-squares
Boris Muzellec, Francis Bach, Alessandro Rudi
Shape constraints such as positive semi-definiteness (PSD) for matrices or convexity for functions play a central role in many applications in machine learning and sciences, includ…
Sampling from Arbitrary Functions via PSD Models
Ulysse Marteau-Ferey, Francis Bach, Alessandro Rudi
In many areas of applied statistics and machine learning, generating an arbitrary number of independent and identically distributed (i.i.d.) samples from a given distribution is a…
Infinite-Dimensional Sums-of-Squares for Optimal Control
Eloïse Berthier, Justin Carpentier, Alessandro Rudi +1
We introduce an approximation method to solve an optimal control problem via the Lagrange dual of its weak formulation. It is based on a sum-of-squares representation of the Hamilt…
Mixability made efficient: Fast online multiclass logistic regression
Rémi Jézéquel, Pierre Gaillard, Alessandro Rudi
Mixability has been shown to be a powerful tool to obtain algorithms with optimal regret. However, the resulting methods often suffer from high computational complexity which has r…
A Note on Optimizing Distributions using Kernel Mean Embeddings
Boris Muzellec, Francis Bach, Alessandro Rudi
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. Wh…
PSD Representations for Effective Probability Models
Alessandro Rudi, Carlo Ciliberto
Finding a good way to model probability densities is key to probabilistic inference. An ideal model should be able to concisely approximate any probability while being also compati…
Beyond Tikhonov: Faster Learning with Self-Concordant Losses via Iterative Regularization
Gaspard Beugnot, Julien Mairal, Alessandro Rudi
The theory of spectral filtering is a remarkable tool to understand the statistical properties of learning with kernels. For least squares, it allows to derive various regularizati…
On the Consistency of Max-Margin Losses
Alex Nowak-Vila, Alessandro Rudi, Francis Bach
The foundational concept of Max-Margin in machine learning is ill-posed for output spaces with more than two labels such as in structured prediction. In this paper, we show that th…
Online nonparametric regression with Sobolev kernels
Oleksandr Zadorozhnyi, Pierre Gaillard, Sebastien Gerschinovitz +1
In this work we investigate the variation of the online kernelized ridge regression algorithm in the setting of dimensional adversarial nonparametric regression. We derive the…
Disambiguation of weak supervision with exponential convergence rates
Vivien Cabannes, Francis Bach, Alessandro Rudi
Machine learning approached through supervised learning requires expensive annotation of data. This motivates weakly supervised learning, where data are annotated with incomplete y…