183 citations · 706 across the 60 of their papers we have counts for
27 papers · 1 filter
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…
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…
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…
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…
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…
Fast rates in structured prediction
Vivien Cabannes, Alessandro Rudi, Francis Bach
Discrete supervised learning problems such as classification are often tackled by introducing a continuous surrogate problem akin to regression. Bounding the original error, betwee…
Overcoming the curse of dimensionality with Laplacian regularization in semi-supervised learning
Vivien Cabannes, Loucas Pillaud-Vivien, Francis Bach +1
As annotations of data can be scarce in large-scale practical problems, leveraging unlabelled examples is one of the most important aspects of machine learning. This is the aim of…
Learning Output Embeddings in Structured Prediction
Luc Brogat-Motte, Alessandro Rudi, Céline Brouard +2
A powerful and flexible approach to structured prediction consists in embedding the structured objects to be predicted into a feature space of possibly infinite dimension by means…
Interpolation and Learning with Scale Dependent Kernels
Nicolò Pagliana, Alessandro Rudi, Ernesto De Vito +1
We study the learning properties of nonparametric ridge-less least squares. In particular, we consider the common case of estimators defined by scale dependent kernels, and focus o…
A General Framework for Consistent Structured Prediction with Implicit Loss Embeddings
Carlo Ciliberto, Lorenzo Rosasco, Alessandro Rudi
We propose and analyze a novel theoretical and algorithmic framework for structured prediction. While so far the term has referred to discrete output spaces, here we consider more…
Gain with no Pain: Efficient Kernel-PCA by Nyström Sampling
Nicholas Sterge, Bharath Sriperumbudur, Lorenzo Rosasco +1
In this paper, we propose and study a Nyström based approach to efficient large scale kernel principal component analysis (PCA). The latter is a natural nonlinear extension of clas…
Efficient online learning with kernels for adversarial large scale problems
Rémi Jézéquel, Pierre Gaillard, Alessandro Rudi
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretica…
Massively scalable Sinkhorn distances via the Nyström method
Jason Altschuler, Francis Bach, Alessandro Rudi +1
The Sinkhorn "distance", a variant of the Wasserstein distance with entropic regularization, is an increasingly popular tool in machine learning and statistical inference. However,…
On Fast Leverage Score Sampling and Optimal Learning
Alessandro Rudi, Daniele Calandriello, Luigi Carratino +1
Leverage score sampling provides an appealing way to perform approximate computations for large matrices. Indeed, it allows to derive faithful approximations with a complexity adap…
Learning with SGD and Random Features
Luigi Carratino, Alessandro Rudi, Lorenzo Rosasco
Sketching and stochastic gradient methods are arguably the most common techniques to derive efficient large scale learning algorithms. In this paper, we investigate their applicati…
Manifold Structured Prediction
Alessandro Rudi, Carlo Ciliberto, Gian Maria Marconi +1
Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure. While classical approaches consider finite,…
Localized Structured Prediction
Carlo Ciliberto, Francis Bach, Alessandro Rudi
Key to structured prediction is exploiting the problem structure to simplify the learning process. A major challenge arises when data exhibit a local structure (e.g., are made by "…
Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance
Giulia Luise, Alessandro Rudi, Massimiliano Pontil +1
Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkh…
Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces
Junhong Lin, Alessandro Rudi, Lorenzo Rosasco +1
In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We inve…
FALKON: An Optimal Large Scale Kernel Method
Alessandro Rudi, Luigi Carratino, Lorenzo Rosasco
Kernel methods provide a principled way to perform non linear, nonparametric learning. They rely on solid functional analytic foundations and enjoy optimal statistical properties.…
Generalization Properties of Learning with Random Features
Alessandro Rudi, Lorenzo Rosasco
We study the generalization properties of ridge regression with random features in the statistical learning framework. We show for the first time that learning boun…