Introduces a new model for mapping matrices to matrices, subsuming linear regression.
problem Learning matrix-to-matrix mappings from data.
method Partial trace regression model, leveraging quantum information theory.
result Relevance demonstrated in matrix-to-matrix regression and positive semidefinite matrix completion.
Method estimates sparse inverse covariance and partial correlation matrices efficiently.
problem Sparse high-dimensional inverse covariance and partial correlation matrix estimation.
method Two-stage estimation method using partial regression with positive semi-definiteness.
result Efficient estimation of inverse covariance and partial correlation matrices with derived non-asymptotic rates.
Test partial effects in Frechet regression on Bures-Wasserstein manifolds.
problem Assessing partial effects in Frechet regression on complex manifolds.
method Sample splitting strategy to estimate covariance matrices and test statistic convergence.
result The test statistic converges to a weighted mixture of chi squared components.
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as e.g. Ridge Regression or Principal Components Regression, as it is not defined as…
Paper tackles blind polynomial regression for unknown inputs.
problem Fitting a polynomial to unknown or partially known input data.
method Formally defines the problem, proposes algorithmic approaches, and applies to jitter-correction.
result Proposes effective methods for blind polynomial regression.
In this paper, we introduce a new machine learning (ML) model for nonlinear regression called the Boosted Smooth Transition Regression Trees (BooST), which is a combination of boosting algorithms with smooth transition regression trees. The main advantage of the BooST model is the estimation of the derivatives (partial…
A new screening method for high-dimensional data reduces computational cost.
problem Challenges in variable selection for ultrahigh-dimensional linear regression.
method Ordering absolute sample ridge partial correlations to screen variables.
result The method provides sure screening property without strong assumptions.
Paper addresses linear regression with partially mismatched data using local search with theoretical guarantees.
problem Linear regression with partially mismatched data.
method Optimization formulation and greedy local search algorithm with theoretical guarantees.
result Local search algorithm converges to nearly-optimal solution at a linear rate under certain conditions.
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.
The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this typically leads to good performance and interpretable models in practice, it ma…
In modern data science, dynamic tensor data is prevailing in numerous applications. An important task is to characterize the relationship between such dynamic tensor and external covariates. However, the tensor data is often only partially observed, rendering many existing methods inapplicable. In this article, we deve…
Volunteer labor can temporarily yield lower benefits to charities than its costs. In such instances, organizations may wish to defer volunteer donations to a later date. Exploiting a discontinuity in blood donations' eligibility criteria, we show that deferring donors reduces their future volunteerism. In our setting, …
This paper reviews SDR methods for multivariate response regression.
problem Handling sufficient dimension reduction for multivariate response regression.
method Characterizes SDR estimators as inverse or forward regression methods.
result Pooled marginal, projective resampling, distance-based, ordinary least squares, partial least squares, and semiparametric SDR estimators are discussed.
We consider the finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. T…
Automates discovering PDEs from data in dynamical systems.
problem Identifying PDEs from data in dynamical systems is challenging.
method ARGOS-RAL framework using sparse regression with recurrent adaptive lasso.
result ARGOS-RAL effectively identifies PDEs from noisy and non-uniformly distributed data.
Gradient boosting with randomized trees reduces discontinuities and complexity.
problem Discontinuities in regression functions due to sparse training data.
method Gradient boosting machine with partially randomized decision trees.
result Improves robustness and computational efficiency of gradient boosting.
New method for causal inference with observed covariates improves learning rates.
problem Causal inference with observed covariates in nonparametric instrumental variable regression.
method Introduces novel Fourier measure for partial smoothing and adapts kernel lengthscales for anisotropic smoothness.
result Upper and lower learning rates for KIV-O show interpolation between NPIV and NPR rates.
Paper develops DP algorithms for isotonic regression over posets.
problem Differential privacy in isotonic regression over partially ordered sets.
method Developed pure-DP and near-matching lower bound algorithms for isotonic regression.
result Achieved near-matching bounds for isotonic regression with and without poset structure.
Develops a theory for equivariant networks with partial domain symmetry.
problem Limited analysis of equivariant networks with partial domain symmetry.
method Proposes pointwise definitions of correct, incorrect, and extrinsic equivariance.
result Establishes error lower bounds for networks with partial symmetry.
Auto-regressive models learn latent states from partially observed linear dynamical systems.
problem Understanding how auto-regressive models learn latent representations from partially observed linear dynamical systems.
method Empirical risk minimization on partially observed linear dynamical systems.
result Two-layer linear auto-regressive models learn to approximate Kalman filtering, coinciding with optimal state estimates.
Paper introduces methods to handle missing data in probabilistic regression trees.
problem Handling missing data in probabilistic regression trees.
method Three approaches: uniform probability, partial observation, and dimension-reduced smoothing.
result Preserves interpretability while extending applicability to incomplete datasets.
Fenrir uses probabilistic numerics to simplify solving initial value problems.
problem Solving initial value problems in ordinary differential equations.
method Probabilistic numerics and Gauss--Markov regression.
result The method simplifies parameter estimation in ODEs, making it easier and more robust.
In this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response, such that the low-dimensional variable becomes the regressor, and which is tract…
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…
We consider the problem of nonparametric regression under shape constraints. The main examples include isotonic regression (with respect to any partial order), unimodal/convex regression, additive shape-restricted regression, and constrained single index model. We review some of the theoretical properties of the least …
Introduces a rule-based Bayesian regression for better uncertainty quantification and expert knowledge integration.
problem Handling regression problems with uncertainty quantification and expert intuition.
method Combines Bayesian inference and rule-based systems for better model performance.
result Improves model performance with better uncertainty quantification and point predictions.
Dual-sPLS improves feature selection and prediction in high-dimensional data.
problem Relating variables to a response in high-dimensional chemometric problems.
method Generalizes PLS1 algorithm with dual norm penalizations and a shrinking ratio parameter.
result Favorably compares to similar regression methods on simulated and real chemical data.
Infinite BART model selects number of trees and allows different functions for clusters.
problem Regression and classification analysis with automatic tree selection and cluster-specific functions.
method Incorporates an Indian Buffet process prior to select a subset of decision trees for each observation.
result Infinite BART model outperforms classic BART on simulated and real datasets.
Bayesian method learns PDEs from noisy data.
problem Discovering PDEs from noisy data.
method Combining variational Bayes and sparse linear regression.
result Proposes a new method to discover PDEs accurately.
This paper presents regression models obtained from a process of blind prediction of peptide binding affinity from provided descriptors for several distinct datasets as part of the 2006 Comparative Evaluation of Prediction Algorithms (COEPRA) contest. This paper finds that kernel partial least squares, a nonlinear part…
A new method improves active learning for large batch sizes.
problem Challenges in scaling Bayesian active learning to large batch sizes.
method Derives Partial Batch Label Sampling (ParBaLS) for EPIG algorithm.
result ParBaLS EPIG outperforms top-B selection and BatchBALD. New kernel speeds up graph regression in physics.
problem Handling large, sparse graphs with continuous node attributes in physics.
method Introduced Sliced Wasserstein Weisfeiler-Lehman (SWWL) graph kernel for Gaussian process regression.
result The SWWL kernel is efficient and positive definite, reducing complexity.
Sparse regression models CMs from oscillatory shear data efficiently.
problem Discovering parsimonious constitutive models from oscillatory shear experiments.
method Sparse regression with tensor basis functions, l1 regularization, and greedy two-stage algorithm.
result Inferred CMs extrapolate well beyond training data and flow conditions.
Zoetrope Genetic Programming improves symbolic regression performance.
problem Evolutionary symbolic regression for complex mathematical expressions.
method Zoetropic representation, repeated fusion operations, linear combination, crossover, mutation, selection.
result Zoetrope Genetic Programming achieves state-of-the-art performance and low computational time.
The paper improves count data regression models for overdispersed data.
problem Improving regression models for overdispersed count data.
method Double ℓ1-regularized negative binomial regressions. result Oracle inequalities and consistency for Lasso estimators of partial regression coefficients.
New method uses sparse deep neural networks for high-dimensional regression with improved parameter estimation.
problem Improving parameter estimation in high-dimensional sparse regression models.
method Proposes nonparametric estimation of partial derivatives in sparse deep neural networks.
result Established convergence rate of nonparametric estimation of partial derivatives as O(n−1/4). Paper tackles active labeling for partial supervision.
problem Accessing stochastic gradients with partial supervision.
method Streaming technique to minimize generalization error.
result Proves minimization of generalization error ratio.
The major perspective of this paper is to provide more evidence into the empirical determinants of capital structure adjustment in different macroeconomics states by focusing and discussing the relative importance of firm-specific and macroeconomic characteristics from an alternative scope in U.S. This study extends th…
Partial dependence curves (FPD) introduced by Friedman, are an important model interpretation tool, but are often not accessible to business analysts and scientists who typically lack the skills to choose, tune, and assess machine learning models. It is also common for the same partial dependence algorithm on the same …
New method stabilizes machine learning for physics-informed inverse problems.
problem Reconstructing physical quantities from PDE-compliant measurements.
method Physics-informed learning with smooth inductive bias.
result PDE operators stabilize variance and prevent overfitting in fixed dimensions.
Research in statistical relational learning has produced a number of methods for learning relational models from large-scale network data. While these methods have been successfully applied in various domains, they have been developed under the unrealistic assumption of full data access. In practice, however, the data …
Algorithm identifies bilinear dynamical systems from noisy data.
problem Learning a realization of a partially observed bilinear dynamical system.
method Regression of outputs to highly correlated covariates for Markov-like parameters.
result High probability error bounds on identification algorithm under uniform stability assumption.
Neighborhood regression has been a successful approach in graphical and structural equation modeling, with applications to learning undirected and directed graphical models. We extend these ideas by defining and studying an algebraic structure called the neighborhood lattice based on a generalized notion of neighborhoo…
This study examines the relationship between PLS and OLS regression using eigenvalue distributions.
problem Analyzing the difference between PLS and OLS regression in terms of eigenvalue distributions.
method Examined the distance between PLS and OLS regression coefficients using the Mahalanobis distance and eigenvalue distributions of the regressor covariance matrix.
result Provided a bound on the distance between PLS and OLS regression coefficients that depends only on the eigenvalue distribution of the regressor covariance matrix.
PCBM improves neural network generalization by partially observing concepts.
problem Decreased generalization performance due to observing all concepts in CBM.
method Developed a theoretical analysis of PCBM's Bayesian generalization error.
result PCBM's generalization error is lower than CBM's due to partial concept observation.
Conditional probabilistic graphical models provide a powerful framework for structured regression in spatio-temporal datasets with complex correlation patterns. However, in real-life applications a large fraction of observations is often missing, which can severely limit the representational power of these models. In t…
A new training method uses multilevel minimization for machine learning.
problem Training machine learning models with high variance and low efficiency.
method Constructs a multilevel hierarchy by reducing sample size and internally trains surrogate models with fewer samples.
result The multilevel method enhances model training efficiency compared to subsampled Newton's and variance reduction methods.
Study efficient inference for network quantile causal effects with partial interference.
problem Estimating network causal effects on outcome quantiles with partial interference.
method Developed a nonparametric efficiency theory and a nonparametrically efficient estimator using a three-way cross-fitting procedure.
result Proposed estimator is consistent, asymptotically normal, and allows flexible estimation of nuisance functions.