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Found 34 papers, 6 papers with code
Estimation of multiple mean vectors in high dimension
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples.
Transductive conformal inference with adaptive scores
Conformal inference is a fundamental and versatile tool that provides distribution-free guarantees for many machine learning tasks.
Label Shift Quantification with Robustness Guarantees via Distribution Feature Matching
Quantification learning deals with the task of estimating the target label distribution under label shift.
Covariance Adaptive Best Arm Identification
This framework allows the learner to estimate the covariance among the arms distributions, enabling a more efficient identification of the best arm.
Statistical learning on measures: an application to persistence diagrams
We consider a binary supervised learning classification problem where instead of having data in a finite-dimensional Euclidean space, we observe measures on a compact space $\mathcal{X}$.
Fast rates for prediction with limited expert advice
We investigate the problem of minimizing the excess generalization error with respect to the best expert prediction in a finite family in the stochastic setting, under limited access to information.
Topologically penalized regression on manifolds
We study a regression problem on a compact manifold M. In order to take advantage of the underlying geometry and topology of the data, the regression task is performed on the basis of the first several eigenfunctions of the Laplace-Beltrami operator of the manifold, that are regularized with topological penalties.
Error rate control for classification rules in multiclass mixture models
In the context of finite mixture models one considers the problem of classifying as many observations as possible in the classes of interest while controlling the classification error rate in these same classes.
Nonasymptotic one-and two-sample tests in high dimension with unknown covariance structure
A particular attention is given to the dependence in the pseudo-dimension $d_*$ of the distribution, defined as $d_* := \|\Sigma\|_2^2/\|\Sigma\|_\infty^2$.
Online Orthogonal Matching Pursuit
Greedy algorithms for feature selection are widely used for recovering sparse high-dimensional vectors in linear models.
High-Dimensional Multi-Task Averaging and Application to Kernel Mean Embedding
We propose an improved estimator for the multi-task averaging problem, whose goal is the joint estimation of the means of multiple distributions using separate, independent data sets.
Statistical Learning Guarantees for Compressive Clustering and Compressive Mixture Modeling
We provide statistical learning guarantees for two unsupervised learning tasks in the context of compressive statistical learning, a general framework for resource-efficient large-scale learning that we introduced in a companion paper. The principle of compressive statistical learning is to compress a training collection, in one pass, into a low-dimensional sketch (a vector of random empirical generalized moments) that captures the information relevant to the considered learning task.
Volume Doubling Condition and a Local Poincaré Inequality on Unweighted Random Geometric Graphs
The aim of this paper is to establish two fundamental measure-metric properties of particular random geometric graphs.
Efficient Regularized Piecewise-Linear Regression Trees
We present a detailed analysis of the class of regression decision tree algorithms which employ a regulized piecewise-linear node-splitting criterion and have regularized linear models at the leaves.
Restless dependent bandits with fading memory
The analysis of slow mixing scenario is supported with a minmax lower bound, which (up to a $\log(T)$ factor) matches the obtained upper bound.
Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points.
A minimax near-optimal algorithm for adaptive rejection sampling
Rejection Sampling is a fundamental Monte-Carlo method.
Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods
We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm.
Domain Generalization by Marginal Transfer Learning
In the problem of domain generalization (DG), there are labeled training data sets from several related prediction problems, and the goal is to make accurate predictions on future unlabeled data sets that are not known to the learner.
Early stopping for statistical inverse problems via truncated SVD estimation
We consider truncated SVD (or spectral cut-off, projection) estimators for a prototypical statistical inverse problem in dimension $D$.
Statistics Theory Statistics Theory 65J20, 62G07
Decontamination of Mutual Contamination Models
Many machine learning problems can be characterized by mutual contamination models.
Compressive Statistical Learning with Random Feature Moments
We describe a general framework -- compressive statistical learning -- for resource-efficient large-scale learning: the training collection is compressed in one pass into a low-dimensional sketch (a vector of random empirical generalized moments) that captures the information relevant to the considered learning task.
Kernel regression, minimax rates and effective dimensionality: beyond the regular case
These questions have been considered in past literature, but only under specific assumptions about the decay, typically polynomial, of the spectrum of the the kernel mapping covariance operator.
Parallelizing Spectral Algorithms for Kernel Learning
We consider a distributed learning approach in supervised learning for a large class of spectral regularization methods in an RKHS framework.
Convergence rates of Kernel Conjugate Gradient for random design regression
We prove statistical rates of convergence for kernel-based least squares regression from i. i. d.
Optimal adaptation for early stopping in statistical inverse problems
For linear inverse problems $Y=\mathsf{A}\mu+\xi$, it is classical to recover the unknown signal $\mu$ by iterative regularisation methods $(\widehat \mu^{(m)}, m=0, 1,\ldots)$ and halt at a data-dependent iteration $\tau$ using some stopping rule, typically based on a discrepancy principle, so that the weak (or prediction) squared-error $\|\mathsf{A}(\widehat \mu^{(\tau)}-\mu)\|^2$ is controlled.
Statistics Theory Statistics Theory 65J20, 62G07
Optimal Rates For Regularization Of Statistical Inverse Learning Problems
We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i. i. d.
Permutational Rademacher Complexity: a New Complexity Measure for Transductive Learning
This paper introduces a new complexity measure for transductive learning called Permutational Rademacher Complexity (PRC) and studies its properties.
Localized Complexities for Transductive Learning
We show two novel concentration inequalities for suprema of empirical processes when sampling without replacement, which both take the variance of the functions into account.
Extensions of stability selection using subsamples of observations and covariates
We introduce extensions of stability selection, a method to stabilise variable selection methods introduced by Meinshausen and B\"uhlmann (J R Stat Soc 72:417-473, 2010).
Classification with Asymmetric Label Noise: Consistency and Maximal Denoising
For any label noise problem, there is a unique pair of true class-conditional distributions satisfying the proposed conditions, and we argue that this pair corresponds in a certain sense to maximal denoising of the observed distributions.
The Local Rademacher Complexity of Lp-Norm Multiple Kernel Learning
We derive an upper bound on the local Rademacher complexity of Lp-norm multiple kernel learning, which yields a tighter excess risk bound than global approaches.
Generalizing from Several Related Classification Tasks to a New Unlabeled Sample
We develop a distribution-free, kernel-based approach to the problem.
Optimal learning rates for Kernel Conjugate Gradient regression
Lower bounds on attainable rates depending on these two quantities were established in earlier literature, and we obtain upper bounds for the considered method that match these lower bounds (up to a log factor) if the true regression function belongs to the reproducing kernel Hilbert space.
