A new optimizer, MVO, improves nonlinear regression performance.
problem Finding optimal coefficients in nonlinear regression models.
method Multi-Verse Optimizer (MVO) compared to Particle Swarm Optimizer (PSO).
result MVO statistically outperforms PSO in 10 nonlinear regression problems.
Proposes a multivariate regression model for better analysis of multiple datasets.
problem Insufficient performance of single-dataset analysis in integrative studies.
method Sparse estimation for variable and group selection, alternating direction method of multipliers algorithm.
result Demonstrated improved performance through simulations and real data analysis.
This work analyzes Fréchet regression using comparison geometry, providing theoretical and practical insights.
problem Analyzing data on complex structures like manifolds and graphs.
method Theoretical analysis through comparison geometry, focusing on existence, uniqueness, and stability of the Fréchet mean.
result Key results on the existence, uniqueness, and stability of the Fréchet mean, along with statistical guarantees for nonparametric regression.
Study on reducing dimensionality in high-dimensional regression with kernel methods and stability analysis.
problem Analyzing errors in high-dimensional regression with dimensionality reduction and kernel regression.
method Derive a stability result for kernel regression with Wasserstein distance and apply it to PCA to deduce convergence rates.
result Two-step procedure yields useful convergence rates in semi-supervised settings.
Tensor Regression tackles high-dimensional data analysis.
problem Challenges in traditional data representation methods for high-dimensional data.
method Systematic study and analysis of tensor-based regression models.
result Provides solutions for specific regression tasks with multiway data.
Improved regression analysis using Padé approximants with new residuals and regularization.
problem Improving regression analysis with Padé approximants for accuracy and avoiding overfitting.
method New residuals in least squares method, system of linear equations for rational functions, Tikhonov regularization.
result Demonstrated efficiency in practical cases from physics and reliability theory.
Study uses regression and ML for COVID-19 mortality forecasting.
problem Forecasting COVID-19 mortality during the first wave in Spain.
method Cyclical curve log-regression, multivariate time series spatial residual correlation analysis, Bayesian approach, machine learning.
result Empirical analysis shows ML regression models perform better than traditional methods.
This paper explores the impact of metric choice on Fréchet regression.
problem Choosing the right metric for Fréchet regression in complex data.
method Review and extensive numerical studies of existing dimension reduction methods.
result Different metrics significantly affect the estimation of central and central mean space.
Novel Fréchet regression method handles errors-in-variables with low-rank covariates.
problem Regression with noisy and limited covariate data.
method Combines global Fréchet regression and principal component regression for low-rank structure.
result Improved efficiency and accuracy in high-dimensional and noisy data settings.
In this paper we develop the theory of parametric polynomial regression in Riemannian manifolds and Lie groups. We show application of Riemannian polynomial regression to shape analysis in Kendall shape space. Results are presented, showing the power of polynomial regression on the classic rat skull growth data of Book…
Short proof shows how ridge regression works with random data.
problem Understanding prediction error in ridge regression with random design.
method Combination of exchangeability arguments, matrix perturbation, and operator convexity.
result Elementary proof of prediction error without complex inequalities.
Tensor Neural Networks improve regression accuracy and efficiency.
problem Nonparametric regression problems with complex, high-dimensional functions.
method Integrates statistical regression and numerical integration within a tensor neural network framework.
result Superior performance in approximation accuracy and generalization capacity compared to FFNs and RBNs.
Study uses ML and causal analysis to predict student performance factors.
problem Understanding socio-academic and economic factors affecting student performance.
method Employed machine learning techniques and causal analysis on 1,050 student profiles.
result Ridge Regression achieved robust predictions with MAE of 0.12 and MSE of 0.024.
Simplified analysis of SGD for linear regression with weight averaging.
problem Understanding SGD optimization in linear regression models.
method Simplified analysis using linear algebra tools, bypassing complex operator manipulations.
result Recovery of bias and variance bounds for SGD in linear regression.
Study improves H-consistency bounds for regression analysis.
problem Improving H-consistency bounds for regression analysis. method Generalized theorems and novel H-consistency bounds for various surrogate loss functions. result Derives principled surrogate losses for adversarial regression.
A new model explains relative spreads between economies using dynamic Nelson-Siegel and functional regression.
problem Analyzing and predicting relative spreads between economies in fixed income markets.
method State-space functional regression model incorporating dynamic Nelson-Siegel model and kernel PCA.
result The new model outperforms the dynamic Nelson-Siegel model in explaining relative spreads.
We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We…
New deep Cox mixture model improves survival analysis performance.
problem Challenges in survival analysis due to censoring and healthcare applications.
method Learning mixtures of Cox regressions with deep neural networks for hazard ratios and non-parametric baseline hazard.
result Our approach outperforms classical and modern survival analysis methods, especially in minority demographics.
Overview of high-dimensional time series regression methods.
problem Estimation and inference with high-dimensional time series data.
method Limit theory for high-dimensional dependent data, asymptotic theory for time series regression, statistical learning methods.
result Main limit theory results and asymptotic theory for high-dimensional time series regression.
Study on online nonparametric regression using Sobolev kernel methods.
problem Adversarial nonparametric regression in high dimensions.
method Online kernelized ridge regression with Sobolev kernel analysis.
result Upper bounds on regret for Sobolev space classes, revealing optimality in certain cases.
PLS-Lasso integrates dimension reduction into regression for financial index tracking.
problem Dimension reduction and regression are traditionally treated separately in multivariate data analysis.
method PLS-Lasso integrates dimension reduction directly into the regression process, presenting two formulations: PLS-Lasso-v1 and PLS-Lasso-v2.
result PLS-Lasso-v1 and PLS-Lasso-v2 outperform Lasso in financial index tracking.
Proposes an online method for high-dimensional streaming data.
problem Increasing variable dimensions with sample size in online kernel sliced inverse regression.
method Introduces approximate linear dependence condition and dictionary variable sets to address the problem. Transforms into online generalized eigen-decomposition problem and uses stochastic optimization for updates.
result Achieves close performance to batch processing kernel sliced inverse regression.
Bias - variance decomposition of the expected error defined for regression and classification problems is an important tool to study and compare different algorithms, to find the best areas for their application. Here the decomposition is introduced for the survival analysis problem. In our experiments, we study bias -…
New algorithm broadens BART models applicability.
problem Limited applicability of Bayesian additive regression trees (BART) models due to conditional conjugacy.
method Introduces a reversible jump Markov chain Monte Carlo algorithm for generalized BART models.
result Extends BART models to arbitrary generalized BART models without conditional conjugacy.
New analysis improves SGD for robust and quantile regression with sub-quadratic convergence.
problem Improving SGD for robust and quantile regression with sub-quadratic convergence.
method Piecewise Lyapunov function for first-order differentiable functions.
result First geometrical convergence result for sub-quadratic SGD.
CNNs outperform standard chemometric methods for spectral data classification.
problem Reducing the need for pre-processing steps in spectral data analysis.
method Convolutional neural networks (CNNs) compared with SVMs and PLSR for classification and regression of spectral data.
result CNNs outperform standard chemometric methods, especially for classification tasks.
Study optimizes linear regression analysis for high-dimensional settings.
problem Understanding high-dimensional linear regression with interpolation and regularization.
method Localized uniform convergence analysis of optimistic rates for linear regression.
result Recover guarantees for ridge and LASSO regression under random designs.
We discuss the development of novel deep learning algorithms to enable real-time regression analysis for time series data. We showcase the application of this new method with a timely case study, and then discuss the applicability of this approach to tackle similar challenges across science domains.
We apply network Lasso to semi-supervised regression problems involving network structured data. This approach lends quite naturally to highly scalable learning algorithms in the form of message passing over an empirical graph which represents the network structure of the data. By using a simple non-parametric regressi…
Study compares BERT with other sentiment analysis models.
problem Comparing sentiment analysis techniques.
method Used four models: Sent WordNet, logistic regression, LSTM, and BERT on IMDB movie reviews.
result BERT outperformed other models in sentiment classification.
Extends multivariate regression for tensor-variate data, identifying brain regions and facial characteristics.
problem Challenges in fitting regression models with multivariate responses and covariates.
method Low-rank tensor formats on regression coefficients and tensor-variate normal distribution for errors.
result Maximum likelihood estimators for tensor-on-tensor regression via block-relaxation algorithms.
The paper examines the consistency of Lasso regression applied to signature analysis of time series data.
problem Consistency of Lasso regression in signature analysis of time series data.
method The paper studies the consistency of Lasso regression applied to signature analysis of time series data, both theoretically and numerically.
result The Lasso regression is consistent both asymptotically and in finite sample for certain types of time series and processes.
The paper shows how data and algorithm interactions affect overparameterized linear regression generalization.
problem Understanding generalization in overparameterized linear regression.
method Introducing data-algorithm compatibility and performing data-dependent trajectory analysis with gradient descent.
result Early stopping iterates lead to better generalization than last-iterate analysis, with weaker restrictions.
PROD method improves high-dimensional regression by handling strong correlations.
problem Violation of Irrepresentable Condition in LASSO for high-dimensional data.
method PROD procedure based on orthogonal decomposition of design matrix.
result PROD enhances performance of high-dimensional penalized regression.
Study shows double descent curve in high-dimensional linear regression with random projections.
problem Understanding the generalization performance in high-dimensional settings with random projections.
method Fixed prediction problem, ridge regression estimator, minimum norm least-squares fit, random matrix theory, asymptotic equivalents.
result Exhibit a double descent curve for high-dimensional linear regression with random projections.
Regression Trees analyze stock returns, revealing market excess return as the most informative factor.
problem Understanding informational content of three factors in stock returns.
method Joint regression tree analysis of daily stock return data for 5 major US corporations.
result The market excess return factor is always the most informative in all cases (solo and joint).
Regression trees learn gradients of differentiable functions.
problem Understanding gradients of differentiable functions using regression trees.
method Developed a method to estimate gradients of differentiable functions using regression trees and exposed quantities from tree learning libraries.
result Gradient estimates from regression trees can be used to improve predictive analysis and solve tasks in uncertainty quantification.
Two models predict net loan losses using Bayesian and frequentist regression.
problem Predicting net loan losses using financial and sociological data.
method Bayesian and frequentist regression analysis.
result Improved understanding of net loan loss relationships.
Sparse symmetric tensor regression reduces brain connectivity complexity.
problem Complex brain connectivity analysis in neuroimaging.
method Sparse symmetric tensor regression model for functional connectivity.
result Superior performance in Alzheimer's disease detection.
Prototypal analysis is introduced to overcome two shortcomings of archetypal analysis: its sensitivity to outliers and its non-locality, which reduces its applicability as a learning tool. Same as archetypal analysis, prototypal analysis finds prototypes through convex combination of the data points and approximates th…
In this work, we study the use of logistic regression in manufacturing failures detection. As a data set for the analysis, we used the data from Kaggle competition Bosch Production Line Performance. We considered the use of machine learning, linear and Bayesian models. For machine learning approach, we analyzed XGBoost…
This paper applies deep learning to ordinal regression, modeling it as a binary search.
problem Ordinal regression with deep learning models.
method Formulated ordinal regression as a binary search problem, using recurrent neural networks.
result Deep learning model shows comparable or better predictive power compared to traditional methods.
The paper analyzes how adversarial attacks affect sparse regression models.
problem Effects of adversarial attacks on sparse regression models.
method Primal-dual witness paradigm to analyze support of estimated regression parameter vector.
result Adversaries can influence sample complexity by corrupting irrelevant features.
Differentially private log-location-scale regression models improve privacy in statistical analysis.
problem Ensuring privacy in statistical regression models while maintaining accuracy.
method Integrates differential privacy into LLS regression using the functional mechanism.
result Proposed DP-LLS models satisfy ε-differential privacy and perform well under various conditions.
Tomal et al. (2015) introduced the notion of "phalanxes" in the context of rare-class detection in two-class classification problems. A phalanx is a subset of features that work well for classification tasks. In this paper, we propose a different class of phalanxes for application in regression settings. We define a "R…
Proposes mutual information for regression without prior knowledge.
problem Regression tasks without prior model knowledge.
method Mutual information learning formulation, SGD convergence analysis.
result High dimensionality can be beneficial with a threshold.
Improved SGD for robust linear and ReLU regression with adversarial corruptions.
problem Robust regression with adversarial corruptions in streaming data.
method Stochastic gradient descent (SGD-exp) with exponentially decaying step size.
result Nearly linear convergence to true parameter with up to 50% Massart corruption rate.
Motivated by the Bagging Partial Least Squares (PLS) and Principal Component Analysis (PCA) algorithms, we propose a Principal Model Analysis (PMA) method in this paper. In the proposed PMA algorithm, the PCA and the PLS are combined. In the method, multiple PLS models are trained on sub-training sets, derived from the…