Two novel approaches improve prediction with Clusterwise Linear Regression.
problem Predicting cluster labels for unseen test points in CLR.
method Two novel approaches: Predictive CLR and Constrained CLR.
result Both approaches significantly improve over known CLR-based regression methods.
A new framework for predictive clustering and optimization.
problem Finding clusters of data that yield low error on a supervised target.
method Generalized optimization framework using MILP and MM for scalability.
result Models can uncover different interpretable discrete cluster structures.
System uses TDA for user segmentation and demand forecasting.
problem User loyalty and demand forecasting challenges.
method TDA-based clustering of time series data with matrix factorization.
result Significantly higher accuracy in clustering and demand forecasting.
The Baire metric induces an ultrametric on a dataset and is of linear computational complexity, contrasted with the standard quadratic time agglomerative hierarchical clustering algorithm. We apply the Baire distance to spectrometric and photometric redshifts from the Sloan Digital Sky Survey using, in this work, about…
The Baire metric induces an ultrametric on a dataset and is of linear computational complexity, contrasted with the standard quadratic time agglomerative hierarchical clustering algorithm. In this work we evaluate empirically this new approach to hierarchical clustering. We compare hierarchical clustering based on the …
The paper addresses misspecification in econometric models of discrete unobserved heterogeneity.
problem Misspecification in econometric models of discrete unobserved heterogeneity.
method Generalizing previous approaches to allow multiple latent variables, developing inference results for a k-means style estimator, and proposing information criteria for model selection.
result Over-fitting can be severe in k-means style estimators when the number of clusters is over-specified.
A new procedure aggregates models to predict data from multiple clusters.
problem Predicting data from multiple clusters with different underlying models.
method Three-step procedure: clustering, model fitting, and aggregation.
result The method outperforms existing models in various prediction problems.
The paper improves SVR with linear constraints for better model properties.
problem Improving Support Vector Regression with linear constraints.
method Generalized SMO algorithm for solving optimization with linear constraints.
result The proposed method shows better practical performance on various datasets.
We simplify complex regression coefficients using linearization and feature comparison.
problem Interpreting high-dimensional regression coefficients from nonlinear responses.
method Developed a linearization method to derive feature coefficients and compare them with regression coefficients.
result Shows how regression coefficients relate to linearized feature coefficients and how they change under regularization.
Linearized probit regression matches nonlinear methods in accuracy.
problem Binary regression accuracy with nonlinear methods.
method Linearizing probit model with linear estimators.
result Linearized estimators perform similarly to nonlinear methods.
Robust learning mixtures of linear regressions improve robustness.
problem Improving robustness in learning mixtures of linear regressions.
method Connecting mixtures of linear regressions and mixtures of Gaussians with thresholding for a quasi-polynomial time algorithm.
result The algorithm has significantly better robustness than previous results.
Paper proposes robust regression methods using depth functions.
problem Robust regression in Huber's ε ε ε -contamination models. method Maximizers of multivariate regression depth functions.
result Achieves minimax rates in various regression problems.
DualIV simplifies non-linear IV regression via dual formulation.
problem Non-linear instrumental variable regression with potential first-stage regression bottleneck.
method Dual formulation of non-linear IV regression as a convex-concave saddle-point problem, leading to a kernel-based algorithm with analytic solution.
result Empirical results show competitive performance compared to existing algorithms.
Locally adaptive interpretable regression improves linear regression's predictability.
problem Linear regression's predictability is limited; it lacks adaptability.
method Locally adaptive interpretable regression (LoAIR) uses neural networks to predict percentile of a Gaussian distribution for regression coefficients.
result LoAIR achieves comparable or better predictive performance than state-of-the-art baselines.
The paper analyzes the generalizability of linear autoencoders and multivariate linear regression.
problem Limited theoretical understanding of linear autoencoders' performance.
method Proposes a PAC-Bayes bound for multivariate linear regression and shows LAEs as constrained models.
result The proposed PAC-Bayes bound is tight and correlates with practical metrics.
Efficient algorithm for conditional linear regression.
problem Building models that accurately predict a specific segment of data.
method Efficient algorithm for identifying a significant segment of the population and its linear regression fit.
result Theoretical analysis and efficient algorithm for conditional linear regression.
Study on thermodynamic costs of simple linear regression.
problem Understanding thermodynamic costs in machine learning models.
method Approximated thermodynamic lower bounds for exact and stochastic linear regression.
result Derived scaling laws for optimal dataset size based on generalization error.
PARC uses piecewise linear predictors for regression and classification.
problem Multivariate regression and classification problems.
method Alternates between ridge and softmax regression, and cluster assignment based on accuracy and separability.
result Converges to a local minimum in a finite number of steps.
Secure linear regression at speed of plaintext methods.
problem Secure multiparty linear regression and feature selection.
method Distributed algorithms combining geometric ideas.
result Efficient and secure genome-wide association studies.
Paper introduces semi-supervised linear extremile regression for high-dimensional data.
problem Challenges in high-dimensional extremile regression due to data sparsity and overfitting.
method Proposes semi-supervised learning for linear extremile regression, achieving n \sqrt{n} n -consistency. result Demonstrates improved estimation efficiency and performance in high-dimensional settings.
Proposes a method for differentially private linear regression and synthetic data generation.
problem Lack of valid inference and synthetic data generation methods for small-scale datasets in privacy-aware settings.
method Gaussian differentially private linear regression with bias-corrected estimator and SDG procedure.
result Improves accuracy and provides valid confidence intervals for downstream tasks.
Develops fast approximations for conditional Shapley values in linear and polynomial models.
problem Estimating conditional Shapley values using regression models is computationally expensive.
method A new approximative estimation method for conditional Shapley values using linear and polynomial regression models.
result Our method significantly reduces computation time compared to existing methods.
Efficient estimator for non-linear regression problems using convex programming.
problem Non-linear regression problems with difference of convex (DC) non-linearities.
method Formulated as a convex program, using an approximation oracle for gradients.
result Produces accurate estimates with high probability under certain assumptions.
Analyzes neural networks using linear models to understand their behavior.
problem Understanding multi-layer neural networks through linear models.
method Recalls and reviews four models: linear regression with concentrated features, kernel ridge regression, random feature model, and neural tangent model.
result Highlights limitations of linear theory and discusses approaches to overcome them.
Unified derivation of high-dimensional linear models using stochastic gradient descent.
problem Performance analysis of high-dimensional linear models trained with stochastic gradient descent.
method Derivation of a deterministic equivalence for the two-point function of a random matrix resolvent.
result Unified understanding of model performance including previously known and novel results.
We analyzed optimism in linear and kernel regression models.
problem Understanding predictive complexity in regression models.
method Derived closed-form asymptotic optimism for linear and kernel regression models.
result Scaled optimism is a useful measure for model complexity.
Faster and versatile sampler for Bayesian linear regression.
problem Efficiently sampling from Bayesian linear regression models with arbitrary priors.
method Slice sampler exploiting linear regression likelihood structure.
result Better effective sample size per second than alternatives.
Proposes FARM model combining latent factor and sparse regression.
problem Testing adequacy of latent factor and sparse regression models.
method Factor Augmented sparse linear Regression Model (FARM) with FabTest and ANOVA type tests.
result Model robustness and effectiveness validated through experiments.
Lecture notes on advanced linear regression methods.
problem Understanding the properties of linear regression estimators in high dimensions.
method Proposition-proof exploration of least squares, ridgeless, ridge, and lasso estimators.
result Detailed analysis of the existence, uniqueness, relations, computation, and non-asymptotic properties of these estimators.
Algorithm optimizes quantized isotonic regression with log-linear time updates.
problem Optimizing quantized isotonic regression estimations.
method Modified PAVA algorithm for sequential optimization.
result Log-linear time updates for optimal quantized mapping.
Develops estimators for near-optimal linear regression under distribution shift.
problem Linear regression under distribution shift with scarce target domain data.
method Minimax linear risk estimators covering various transfer learning settings.
result Achieves near-optimal risk for linear regression problems under distribution shift.
Neural linear model performs well on simple regression tasks but requires tuning.
problem Characterizing the neural linear model's performance on simple regression tasks.
method Characterized the neural linear model on UCI and gap datasets.
result The neural linear model shows good performance but requires good hyperparameter tuning.
Paper analyzes nLasso for localized linear regression in networked data.
problem Learning sparse linear models from networked data.
method Extends nLasso to network models using convex optimization.
result Sufficient condition for nLasso to accurately learn localized linear regression.
Lower bounds show linear complexity for linear regression.
problem Computational complexity of linear regression.
method Reduction to estimating the least eigenvalue of a random Wishart matrix.
result Θ(d) calls to the oracle are necessary and sufficient for polynomial accuracy.
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.
AM converges super-linearly for solving mixed linear regression problems.
problem Learning linear regressors from unlabeled observations in multiple linear regression models.
method Alternating Minimization (AM) algorithm, which alternates between label estimation and regression solving.
result AM converges super-linearly in certain parameter regimes, requiring only O(log log(1/ε)) iterations to achieve an error of ε.
Proof of Gaussian ML estimator consistency in linear auto-regressive models.
problem Consistency of Gaussian maximum likelihood estimator in linear auto-regressive models.
method Information-theoretic proof without stability assumptions.
result Nearly optimal non-asymptotic rates for parameter recovery.
This paper compares linear regression and neural networks for pricing swing options.
problem Pricing swing options using approximation methods.
method Linear regression and neural networks for approximating the continuation value and swing price.
result The approximation methods converge to the actual swing price as the number of functions or Monte Carlo samples increases.
Piecewise-linear regression trees improve tree-based regression with theoretical and practical benefits.
problem Improving tree-based regression models with theoretical guarantees and practical tractability.
method Regularized piecewise-linear node-splitting criterion, LASSO-type and ℓ 2 \ell_{2} ℓ 2 regularization, variable selection procedure. result New high-probability generalization error bounds for piecewise-linear regression trees.
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.
Improves Bayesian linear regression for private data analysis.
problem Bayesian linear regression with privacy guarantees.
method Develops noise-aware methods for inference over privacy mechanisms.
result Correct posterior distributions can be computed for private data.
Improved linear regression with privacy and robustness guarantees.
problem Private and robust linear regression with adversarial corruption.
method Differentially private stochastic gradient descent with full-batch gradient descent and adaptive clipping.
result Near optimal sample complexity for both private and robust linear regression.
Private sketches protect linear regression data privacy.
problem Protecting sensitive information in linear regression.
method Release private sketches of datasets, compute approximate solutions.
result Private sketches maintain good approximation guarantees to the original problem.
Paper analyzes agnostic learning of mixed linear regression without generative models.
problem Learning mixed linear regression without assuming stochastic generation.
method Expectation Maximization (EM) and Alternating Minimization (AM) algorithms.
result AM and EM algorithms converge to population loss minimizers under standard conditions.
Neural networks can be simplified to linear regression for easier understanding by statisticians.
problem Introducing neural networks to statisticians who are not familiar with them.
method Describing neural networks that approximate linear regression and discussing customizations.
result Statisticians can now understand neural networks by focusing on linear regression.
EM algorithm converges globally for two-component mixed linear regression.
problem Global convergence of EM algorithm for mixed linear regression.
method Developed new theoretical analysis for EM algorithm convergence in mixed linear regression.
result EM algorithm converges globally for two-component mixed linear regression.
New methods combine low and high-fidelity data for accurate surrogate modeling.
problem Challenges in surrogate modeling for high-dimensional outputs with limited training data.
method Projection-based multifidelity linear regression methods integrating low-fidelity and high-fidelity data.
result Multifidelity methods achieve up to 12% improvement in median accuracy compared to single-fidelity methods.
ILTS iteratively refines linear regression models on subsets of data.
problem Linear regression with corruptions and outliers.
method Iteratively selects and refits the subset of samples with lowest loss.
result ILTS converges linearly to the closest mixture component under certain conditions.