arXiv research

Improved fMRI analysis models enhance classification performance and select relevant brain regions.

PLS-Lasso integrates dimension reduction into regression for financial index tracking.

Two Kähler structures are PCR equivalent in the Siegel domain.

PCR-LE achieves optimal rates for nonparametric regression over Sobolev spaces.

CPCR mitigates bias in PCR for overparameterized models.

VC-PCR improves prediction by clustering correlated variables.

New approach to quantify posterior concentration rates using Wasserstein dynamics.

Principal component regression (PCR) is a simple, but powerful and ubiquitously utilized method. Its effectiveness is well established when the covariates exhibit low-rank structure. However, its ability to handle settings with noisy, missing, and mixed-valued, i.e., discrete and continuous, covariates is not understoo…

Noisy Pooled PCR tests large groups more efficiently.

This study analyzes prediction risk for PCR method in latent factor regression models.

Deep learning accelerators efficiently train over vast and growing amounts of data, placing a newfound burden on commodity networks and storage devices. A common approach to conserve bandwidth involves resizing or compressing data prior to training. We introduce Progressive Compressed Records (PCRs), a data format that…

Principal Components Regression (PCR) is a traditional tool for dimension reduction in linear regression that has been both criticized and defended. One concern about PCR is that obtaining the leading principal components tends to be computationally demanding for large data sets. While random projections do not possess…

Adaptive PCR improves panel data analysis with uniform guarantees.

A new PCR method using SVD with sparse regularization.

We solve principal component regression (PCR), up to a multiplicative accuracy $1+γ$, by reducing the problem to $\tilde{O}(γ^{-1})$ black-box calls of ridge regression. Therefore, our algorithm does not require any explicit construction of the top principal components, and is suitable for large-scale PCR instances. In…

New method infers viral load from pooled tests.

We identify and validate a model for PCR in high dimensions, improving prediction guarantees.

Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from only explanatory variables and not considered with the response variable. To addre…

Consider a regression problem where there is no labeled data and the only observations are the predictions $f_i(x_j)$ of $m$ experts $f_{i}$ over many samples $x_j$. With no knowledge on the accuracy of the experts, is it still possible to accurately estimate the unknown responses $y_{j}$? Can one still detect the leas…

Software helps teach latent variable methods in multivariate data analytics.

Technological change and innovation are vitally important, especially for high-tech companies. However, factors influencing their future research and development (R&D) trends are both complicated and various, leading it a quite difficult task to make technology tracing for high-tech companies. To this end, in this pape…

Gradient-free ensemble learns sector forecasts from diverse models.

A new debiasing method for high-dimensional regression with applications to PCR.

New method speeds up learning of complex dynamical systems.

This paper investigates the efficacy of a regularized multi-task learning (MTL) framework based on SVM (M-SVM) to answer whether MTL always provides reliable results and how MTL outperforms independent learning. We first find that M-SVM is Bayes risk consistent in the limit of large sample size. This implies that despi…

Machine learning predicts ship performance changes over time.

Principal component regression (PCR) is a widely used two-stage procedure: principal component analysis (PCA), followed by regression in which the selected principal components are regarded as new explanatory variables in the model. Note that PCA is based only on the explanatory variables, so the principal components a…

The paper examines Adaptive Lasso and Transfer Lasso, highlighting their differences and proposing a new method.

Machine learning model diagnoses COVID-19 from routine blood tests.

A new method improves target selection for manipulating complex systems like the brain.

DFR reduces the computational cost of sparse-group lasso and adaptive sparse-group lasso.

A fast method for Lasso and Logistic Lasso problems.

We leverage recent advances in high-dimensional statistics to derive new L2 estimation upper bounds for Lasso and Group Lasso in high-dimensions. For Lasso, our bounds scale as $(k^*/n) \log(p/k^*)$---$n\times p$ is the size of the design matrix and $k^*$ the dimension of the ground truth $\boldsymbolβ^*$---and match t…

We analyze optimal weighted ridge regression in overparameterized linear models.

We introduce an application of the group lasso to design of experiments. Note that we are NOT trying to explain experimental design for the group lasso. Conversely, we explain how we can use the idea of the group lasso in experimental design, showing that the problem of constructing an optimal design matrix can be tran…

New method for tuning Graphical Lasso hyperparameters.

The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that takes the hierarchical model formulation of the Bayesian Lasso. The main differenc…

LLM-Lasso uses LLMs to improve feature selection in Lasso regression.

The solution path of the 1D fused lasso for an $n$-dimensional input is piecewise linear with $\mathcal{O}(n)$ segments (Hoefling et al. 2010 and Tibshirani et al 2011). However, existing proofs of this bound do not hold for the weighted fused lasso. At the same time, results for the generalized lasso, of which the wei…

Proposes MM-DUST for efficient generalized lasso solution paths.

Bayesian approach improves network lasso for multi-task learning.

We propose a method for finding alternate features missing in the Lasso optimal solution. In ordinary Lasso problem, one global optimum is obtained and the resulting features are interpreted as task-relevant features. However, this can overlook possibly relevant features not selected by the Lasso. With the proposed met…

This review summarizes five Lasso optimization algorithms.

In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods, the Lasso being a canonical example, are popular candidates to address high dim…

We propose an improved LASSO estimation technique based on Stein-rule. We shrink classical LASSO estimator using preliminary test, shrinkage, and positive-rule shrinkage principle. Simulation results have been carried out for various configurations of correlation coefficients ($r$), size of the parameter vector ($β$), …

Paper examines LASSO for high-dimensional predictive regression, improving its performance in forecasting unemployment.

Exponential Lasso improves Lasso's robustness to outliers and heavy-tailed noise.

Exclusive Group Lasso improves feature selection in correlated biological data.