Related papers: Generative Flexible Latent Structure Regression (G…
Methods based on partial least squares (PLS) regression, which has recently gained much attention in the analysis of high-dimensional genomic datasets, have been developed since the early 2000s for performing variable selection. Most of…
A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…
Partial least squares (PLS) regression combines dimensionality reduction and prediction using a latent variable model. Since partial least squares regression (PLS-R) does not require matrix inversion or diagonalization, it can be applied to…
As a popular tool for producing meaningful and interpretable models, large-scale sparse learning works efficiently when the underlying structures are indeed or close to sparse. However, naively applying the existing regularization methods…
A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the…
Relating a set of variables X to a response y is crucial in chemometrics. A quantitative prediction objective can be enriched by qualitative data interpretation, for instance by locating the most influential features. When high-dimensional…
Estimating graphical model structure from high-dimensional and undersampled data is a fundamental problem in many scientific fields. Existing approaches, such as GLASSO, latent variable GLASSO, and latent tree models, suffer from high…
Partial Least Squares (PLS) methods have been heavily exploited to analyse the association between two blocs of data. These powerful approaches can be applied to data sets where the number of variables is greater than the number of…
A body of recent work in modeling neural activity focuses on recovering low-dimensional latent features that capture the statistical structure of large-scale neural populations. Most such approaches have focused on linear generative models,…
Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its…
Predicting stable and metastable structures is central to molecular and materials discovery, but remains limited by the cost of searching high-dimensional energy landscapes. Deep generative models offer efficient structure sampling, yet…
With massive high-dimensional data now commonplace in research and industry, there is a strong and growing demand for more scalable computational techniques for data analysis and knowledge discovery. Key to turning these data into knowledge…
We introduce and study the Group Square-Root Lasso (GSRL) method for estimation in high dimensional sparse regression models with group structure. The new estimator minimizes the square root of the residual sum of squares plus a penalty…
Kernel Regularized Least Squares (KRLS) is a popular method for flexibly estimating models that may have complex relationships between variables. However, its usefulness to many researchers is limited for two reasons. First, existing…
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.…
In many applications, particularly in the natural sciences, the available high-dimensional set of features may contain variables that are not correlated with the response under consideration. Such irrelevant features can, in certain cases,…
In this paper, we introduce a novel high-dimensional Factor-Adjusted sparse Partially Linear regression Model (FAPLM), to integrate the linear effects of high-dimensional latent factors with the nonparametric effects of low-dimensional…
Learning vector autoregressive models from multivariate time series is conventionally approached through least squares or maximum likelihood estimation. These methods typically assume a fully connected model which provides no direct insight…
Generalized linear model or GLM constitutes a large class of models and essentially extends the ordinary linear regression by connecting the mean of the response variable with the covariate through appropriate link functions. On the other…
We propose a novel method to model nonlinear regression problems by adapting the principle of penalization to Partial Least Squares (PLS). Starting with a generalized additive model, we expand the additive component of each variable in…