相关论文: Robust Kernel (Cross-) Covariance Operators in Rep…

We study the covariance of the cross-power spectrum of different tracers for the large-scale structure. We develop the counts-in-cells framework for the multi-tracer approach, and use this to derive expressions for the full non-Gaussian…

We propose kernel PCA as a method for analyzing the dependence structure of multivariate extremes and demonstrate that it can be a powerful tool for clustering and dimension reduction. Our work provides some theoretical insight into the…

Kernel methods map data into high-dimensional spaces, enabling linear algorithms to learn nonlinear functions without explicitly storing the feature vectors. Quantum kernel methods promise efficient learning by encoding feature maps into…

We propose a method of analysis of dynamical networks based on a recent measure of Granger causality between time series, based on kernel methods. The generalization of kernel Granger causality to the multivariate case, here presented,…

Deep neural network based question answering (QA) models are neither robust nor explainable in many cases. For example, a multiple-choice QA model, tested without any input of question, is surprisingly "capable" to predict the most of…

This paper considers the problem of supervised learning with linear methods when both features and labels can be corrupted, either in the form of heavy tailed data and/or corrupted rows. We introduce a combination of coordinate gradient…

Survival analysis aims to explore the relationship between covariates and the time until the occurrence of an event. The Cox proportional hazards model is commonly used for right-censored data, but it is not strictly limited to this type of…

Solving combinatorial optimization (CO) on graphs is among the fundamental tasks for upper-stream applications in data mining, machine learning and operations research. Despite the inherent NP-hard challenge for CO, heuristics,…

Kernel methods have been proven to be a powerful tool for the integration and analysis of highthroughput technologies generated data. Kernels offer a nonlinear version of any linear algorithm solely based on dot products. The kernelized…

While probabilistic models describe the dependence structure between observed variables, causal models go one step further: they predict, for example, how cognitive functions are affected by external interventions that perturb neuronal…

Principal component analysis (PCA) is a fundamental tool for analyzing multivariate data. Here the focus is on dimension reduction to the principal subspace, characterized by its projection matrix. The classical principal subspace can be…

Imitation learning in robotics faces significant challenges in generalization due to the complexity of robotic environments and the high cost of data collection. We introduce RoCoDA, a novel method that unifies the concepts of invariance,…

Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few…

We consider a robust version of multiple-set linear canonical analysis obtained by using a S-estimator of covariance operator. The related influence functions are derived. Asymptotic properties of this robust method are obtained and a…

Representing images by compact codes has proven beneficial for many visual recognition tasks. Most existing techniques, however, perform this coding step directly in image feature space, where the distributions of the different classes are…

Bilevel optimization has emerged as a technique for addressing a wide range of machine learning problems that involve an outer objective implicitly determined by the minimizer of an inner problem. While prior works have primarily focused on…

A number of machine learning tasks entail a high degree of invariance: the data distribution does not change if we act on the data with a certain group of transformations. For instance, labels of images are invariant under translations of…

Building on the functional-analytic framework of operator-valued kernels and un-truncated signature kernels, we propose a scalable, provably convergent signature-based algorithm for a broad class of high-dimensional, path-dependent hedging…

Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…