Related papers: Robust Extrinsic Regression Analysis for Manifold …

We develop a new robust geographically weighted regression method in the presence of outliers. We embed the standard geographically weighted regression in robust objective function based on $\gamma$-divergence. A novel feature of the…

Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…

In the last decades the estimation of the intrinsic dimensionality of a dataset has gained considerable importance. Despite the great deal of research work devoted to this task, most of the proposed solutions prove to be unreliable when the…

Kernel methods have had great success in Statistics and Machine Learning. Despite their growing popularity, however, less effort has been drawn towards developing kernel based classification methods on Riemannian manifolds due to difficulty…

We present a robust framework to perform linear regression with missing entries in the features. By considering an elliptical data distribution, and specifically a multivariate normal model, we are able to conditionally formulate a…

Functional data analysis offers a diverse toolkit of statistical methods tailored for analyzing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly…

The problem of robust mean estimation in high dimensions is studied, in which a certain fraction (less than half) of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, the robust mean estimation problem is…

We introduce flexible robust functional regression models, using various heavy-tailed processes, including a Student $t$-process. We propose efficient algorithms in estimating parameters for the marginal mean inferences and in predicting…

Data living on manifolds commonly appear in many applications. Often this results from an inherently latent low-dimensional system being observed through higher dimensional measurements. We show that under certain conditions, it is possible…

We introduce a novel concept of coarse extrinsic curvature for Riemannian submanifolds, inspired by Ollivier's notion of coarse Ricci curvature. This curvature is derived from the Wasserstein 1-distance between probability measures…

We propose a robust method for location estimation in various matrix manifolds based on the projected Frobenius median, which is closely related to the spatial median. This method applies broadly to matrix manifolds, including Stiefel and…

This paper presents an integrated perspective on robustness in regression. Specifically, we examine the relationship between traditional outlier-resistant robust estimation and robust optimization, which focuses on parameter estimation…

We propose practical deep Gaussian process models on Riemannian manifolds, similar in spirit to residual neural networks. With manifold-to-manifold hidden layers and an arbitrary last layer, they can model manifold- and scalar-valued…

Many modern datasets are collected automatically and are thus easily contaminated by outliers. This led to a regain of interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the…

Challenges with data in the big-data era include (i) the dimension $p$ is often larger than the sample size $n$ (ii) outliers or contaminated points are frequently hidden and more difficult to detect. Challenge (i) renders most conventional…

We put forward a simple new randomized missing data (RMD) approach to robust filtering of state-space models, motivated by the idea that the inclusion of only a small fraction of available highly precise measurements can still extract most…

The manifold hypothesis suggests that high-dimensional data often lie on or near a low-dimensional manifold. Estimating the dimension of this manifold is essential for leveraging its structure, yet existing work on dimension estimation is…

Geometric representation learning has recently shown great promise in several machine learning settings, ranging from relational learning to language processing and generative models. In this work, we consider the problem of performing…

Conditional estimation given specific covariate values (i.e., local conditional estimation or functional estimation) is ubiquitously useful with applications in engineering, social and natural sciences. Existing data-driven non-parametric…

The ability to learn disentangled representations that split underlying sources of variation in high dimensional, unstructured data is important for data efficient and robust use of neural networks. While various approaches aiming towards…