Related papers: Extrinsic local regression on manifold-valued data
Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two…
The intrinsic dimensionality refers to the ``true'' dimensionality of the data, as opposed to the dimensionality of the data representation. For example, when attributes are highly correlated, the intrinsic dimensionality can be much lower…
We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…
Many unsupervised representation learning methods belong to the class of similarity learning models. While various modality-specific approaches exist for different types of data, a core property of many methods is that representations of…
Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which…
The discovering of low-dimensional manifolds in high-dimensional data is one of the main goals in manifold learning. We propose a new approach to identify the effective dimension (intrinsic dimension) of low-dimensional manifolds. The scale…
A fundamental problem in manifold learning is to approximate a functional relationship in a data chosen randomly from a probability distribution supported on a low dimensional sub-manifold of a high dimensional ambient Euclidean space. The…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…
Determining the optimal model for a given task often requires training multiple models from scratch, which becomes impractical as dataset and model sizes grow. A more efficient alternative is to expand smaller pre-trained models, but this…
Modern technology often generates data with complex structures in which both response and explanatory variables are matrix-valued. Existing methods in the literature are able to tackle matrix-valued predictors but are rather limited for…
We solve a regularized weighted low-rank approximation problem by a stochastic gradient descent on a manifold. To guarantee the convergence of our stochastic gradient descent, we establish a convergence theorem on manifolds for…
Mixed effect modeling for longitudinal data is challenging when the observed data are random objects, which are complex data taking values in a general metric space without linear structure. In such settings the classical additive error…
Semi-structured regression models enable the joint modeling of interpretable structured and complex unstructured feature effects. The structured model part is inspired by statistical models and can be used to infer the input-output…
Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic…
This paper proposes a new methodology for performing Bayesian inference in imaging inverse problems where the prior knowledge is available in the form of training data. Following the manifold hypothesis and adopting a generative modelling…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
We present a novel framework for estimation and inference with the broad class of universal approximators. Estimation is based on the decomposition of model predictions into Shapley values. Inference relies on analyzing the bias and…
Delineating the associations between images and a vector of covariates is of central interest in medical imaging studies. To tackle this problem of image response regression, we propose a novel nonparametric approach in the framework of…
Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean…