Related papers: Subjects classification from high-dimensional and …
Selection of appropriate collective variables for enhancing sampling of molecular simulations remains an unsolved problem in computational biophysics. In particular, picking initial collective variables (CVs) is particularly challenging in…
This paper introduces a new clustering technique, called {\em dimensional clustering}, which clusters each data point by its latent {\em pointwise dimension}, which is a measure of the dimensionality of the data set local to that point.…
Deep Metric Learning (DML) approaches learn to represent inputs to a lower-dimensional latent space such that the distance between representations in this space corresponds with a predefined notion of similarity. This paper investigates how…
Motivated by the problem of identifying correlations between genes or features of two related biological systems, we propose a model of \emph{feature selection} in which only a subset of the predictors $X_t$ are dependent on the…
Unsupervised estimation of latent variable models is a fundamental problem central to numerous applications of machine learning and statistics. This work presents a principled approach for estimating broad classes of such models, including…
Clustering algorithms are one of the main analytical methods to detect patterns in unlabeled data. Existing clustering methods typically treat samples in a dataset as points in a metric space and compute distances to group together similar…
Gaussian process-based latent variable models are flexible and theoretically grounded tools for nonlinear dimension reduction, but generalizing to non-Gaussian data likelihoods within this nonlinear framework is statistically challenging.…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
Motivation: The high dimensionality of genomic data calls for the development of specific classification methodologies, especially to prevent over-optimistic predictions. This challenge can be tackled by compression and variable selection,…
The success of deep learning in high-dimensional settings is often attributed to the presence of low-dimensional structure in real-world data. While standard theoretical models typically assume that this structure lies in the target…
Feature selection is crucial for pinpointing relevant features in high-dimensional datasets, mitigating the 'curse of dimensionality,' and enhancing machine learning performance. Traditional feature selection methods for classification use…
A serious problem in learning probabilistic models is the presence of hidden variables. These variables are not observed, yet interact with several of the observed variables. Detecting hidden variables poses two problems: determining the…
As technology advanced, collecting data via automatic collection devices become popular, thus we commonly face data sets with lengthy variables, especially when these data sets are collected without specific research goals beforehand. It…
A topic of great current interest is Causal Representation Learning (CRL), whose goal is to learn a causal model for hidden features in a data-driven manner. Unfortunately, CRL is severely ill-posed since it is a combination of the two…
Clustering has long been a popular unsupervised learning approach to identify groups of similar objects and discover patterns from unlabeled data in many applications. Yet, coming up with meaningful interpretations of the estimated clusters…
We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random…
Model-based clustering of moderate or large dimensional data is notoriously difficult. We propose a model for simultaneous dimensionality reduction and clustering by assuming a mixture model for a set of latent scores, which are then linked…
The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…
High-dimensional multivariate longitudinal data, which arise when many outcome variables are measured repeatedly over time, are becoming increasingly common in social, behavioral and health sciences. We propose a latent variable model for…
In the framework of model-based clustering, a model allowing several latent class variables is proposed. This model assumes that the distribution of the observed data can be factorized into several independent blocks of variables. Each…