Related papers: Local Linear Regression on Manifolds and its Geome…
Manifold learning-based encoders have been playing important roles in nonlinear dimensionality reduction (NLDR) for data exploration. However, existing methods can often fail to preserve geometric, topological and/or distributional…
Subspace data representation has recently become a common practice in many computer vision tasks. It demands generalizing classical machine learning algorithms for subspace data. Low-Rank Representation (LRR) is one of the most successful…
We are interested in derivative-free optimization of high-dimensional functions. The sample complexity of existing methods is high and depends on problem dimensionality, unlike the dimensionality-independent rates of first-order methods.…
For supervised classification problems, this paper considers estimating the query's label probability through local regression using observed covariates. Well-known nonparametric kernel smoother and $k$-nearest neighbor ($k$-NN) estimator,…
Compared to facial expression recognition, expression synthesis requires a very high-dimensional mapping. This problem exacerbates with increasing image sizes and limits existing expression synthesis approaches to relatively small images.…
We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…
In this paper, we study linear regression applied to data structured on a manifold. We assume that the data manifold is smooth and is embedded in a Euclidean space, and our objective is to reveal the impact of the data manifold's extrinsic…
Geodesic regression has been proposed for fitting the geodesic curve. However, it cannot automatically choose the dimensionality of data. In this paper, we develop a Bayesian geodesic regression model on Riemannian manifolds (BGRM) model.…
The model of low-dimensional manifold and sparse representation are two well-known concise models that suggest each data can be described by a few characteristics. Manifold learning is usually investigated for dimension reduction by…
Collaborative learning through latent shared feature representations enables heterogeneous clients to train personalized models with improved performance and reduced sample complexity. Despite empirical success and extensive study, the…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time…
Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…
Many machine learning problems involve regressing variables on a non-Euclidean manifold -- e.g. a discrete probability distribution, or the 6D pose of an object. One way to tackle these problems through gradient-based learning is to use a…
This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…
We study the problem of finding the best linear model that can minimize least-squares loss given a data-set. While this problem is trivial in the low dimensional regime, it becomes more interesting in high dimensions where the population…
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 study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this "independence" approach delivers an increased flexibility…
Wide accessibility of imaging and profile sensors in modern industrial systems created an abundance of high-dimensional sensing variables. This led to a a growing interest in the research of high-dimensional process monitoring. However,…
We provide a way to infer about existence of topological circularity in high-dimensional data sets in $\mathbb{R}^d$ from its projection in $\mathbb{R}^2$ obtained through a fast manifold learning map as a function of the high-dimensional…