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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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48 results for local linear regression

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.

New GP model estimates piecewise continuous functions.

problem Piecewise continuous regression functions in scientific and engineering applications.
method Local Gaussian process model with partitioned local data and joint estimation of boundaries.
result Superior performance over conventional GP models in estimating piecewise regression functions.

The network Lasso (nLasso) has been proposed recently as an efficient learning algorithm for massive networked data sets (big data over networks). It extends the well-known least absolute shrinkage and selection operator (Lasso) from learning sparse (generalized) linear models to network models. Efficient implementatio…

2019-03-26abs ↗pdf ↗

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.

New algorithms improve Bayesian linear regression with spike-and-slab priors.

problem Efficiently sampling from Bayesian linear regression models with sparsity-inducing priors.
method Design of two sampling algorithms: Gibbs sampling and Stochastic Localization.
result Stochastic Localization sampler shows significant advantage for poorly designed data matrices.

Neural Local Wasserstein Regression models distribution-on-distribution regression with flexible, localized transport maps.

problem Estimating distribution-on-distribution regression with global optimal transport maps or linearization limitations.
method Proposes Neural Local Wasserstein Regression, a flexible nonparametric framework using locally defined transport maps in Wasserstein space.
result Demonstrates effective capture of nonlinear and high-dimensional distributional relationships.

Proposes a new random forest weighted local Fréchet regression method.

problem Complex metric space valued responses and curse of dimensionality in Fréchet regression.
method Locally adaptive kernel generated by random forests for local average and local linear Fréchet regression.
result Significantly improves existing Fréchet regression methods with theoretical guarantees.

Discriminative latent-variable models are typically learned using EM or gradient-based optimization, which suffer from local optima. In this paper, we develop a new computationally efficient and provably consistent estimator for a mixture of linear regressions, a simple instance of a discriminative latent-variable mode…

2013-06-17abs ↗pdf ↗

BART and MOTR-BART improve tree-based predictions with local linear models.

problem Non-linearity and high-order interactions in data.
method Bayesian Additive Regression Trees (BART) and Model Trees BART (MOTR-BART) using piecewise linear functions.
result MOTR-BART achieves equal or better performance with fewer trees than BART.

New method for private linear regression under privacy constraints, achieving optimal rates.

problem Statistical complexity of private linear regression under unknown, ill-conditioned covariates.
method Information-Weighted Regression method
result Optimal convergence rates for both central and local privacy models.

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamenta…

2012-10-22abs ↗pdf ↗

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.

Paper presents ABGD for efficient piecewise linear regression in high dimensions.

problem Efficiently solving piecewise linear regression in high-dimensional spaces.
method Parametrizes piecewise linear functions as difference of max-affine functions, using ABGD algorithm.
result ABGD converges linearly to an ε-accurate estimate with optimal sample complexity.

This paper achieves optimal regret bounds for locally private linear contextual bandit.

problem Designing locally private linear contextual bandit algorithms with optimal regret bounds.
method New algorithmic and analytical ideas, including mean absolute deviation analysis and layered principal component regression.
result Achieves an ildeO(T) ilde O(\sqrt{T}) regret upper bound for locally private linear contextual bandit.

Random forests are a powerful method for non-parametric regression, but are limited in their ability to fit smooth signals, and can show poor predictive performance in the presence of strong, smooth effects. Taking the perspective of random forests as an adaptive kernel method, we pair the forest kernel with a local li…

2018-07-30abs ↗pdf ↗

We study the convergence of the Expectation-Maximization (EM) algorithm for mixtures of linear regressions with an arbitrary number kk of components. We show that as long as signal-to-noise ratio (SNR) is Ω~(k)\tildeΩ(k), well-initialized EM converges to the true regression parameters. Previous results for k3k \geq 3 hav…

2019-05-28abs ↗pdf ↗

We tackle permutation in linear regression with a new inference framework.

problem Statistical investigation of permutation in linear regression models.
method Localization step followed by conditional Monte Carlo test and coefficient inference.
result Valid statistical inference procedures for permutation and regression coefficients.

Develops privacy-preserving methods for longitudinal linear regression.

problem Protecting individual information in longitudinal data with privacy-preserving statistics.
method Proposes a user-level private regression estimator and a privatized covariance estimator for longitudinal linear regression under user-level differential privacy.
result Establishes theoretical guarantees for practical user-level differential privacy estimation and inference in longitudinal linear regression.

This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression, spline smoothing or locally weighted regression, and the choice of a kernel in multiple kern…

2009-09-10abs ↗pdf ↗

We study online linear regression problems in a distributed setting, where the data is spread over a network. In each round, each network node proposes a linear predictor, with the objective of fitting the \emph{network-wide} data. It then updates its predictor for the next round according to the received local feedbac…

2019-02-13abs ↗pdf ↗

Distributed statistical learning problems arise commonly when dealing with large datasets. In this setup, datasets are partitioned over machines, which compute locally, and communicate short messages. Communication is often the bottleneck. In this paper, we study one-step and iterative weighted parameter averaging in s…

2018-09-30abs ↗pdf ↗

Improved locally private sparse estimation with multiple samples per user.

problem Challenges in high-dimensional locally private sparse estimation.
method Proposes a framework for user-level locally private sparse linear regression with multiple samples per user.
result Eliminates the dependency of dimensionality on error bounds, achieving tighter error bounds.

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.

Improved interpretability methods for ML models using local regressions and variable importance.

problem Inability of existing interpretability methods to provide reliable explanations for ML models, especially in high-dimensional problems with irrelevant features and non-linear relationships.
method Introduces VarImp and SupClus methods using local regressions with weighted distance considering variable importance.
result VarImp and SupClus methods yield better explanations than state-of-the-art approaches, especially in high-dimensional problems with irrelevant features and non-linear relationships.

Sharp risk bounds for early-stopping in Gaussian linear regression are derived.

problem Minimizing in-sample mean squared error in high-dimensional Gaussian linear regression.
method Early-stopped mirror descent (ESMD) with local Gaussian width bounds.
result Sharp risk bounds extend to early-stopped mirror descent for least squares estimator (LSE).

Paper solves NP-hard sparse mixed linear regression problem with provable guarantees.

problem Sparse mixed linear regression on unlabeled data.
method Invex relaxation for intractable problem with theoretical guarantees.
result Exact recovery of data labels and close approximation of regression parameters.

New insights into continual learning for deep models, showing convergence issues but local linear solutions.

problem Challenges in continual learning for homogeneous deep models.
method Sequential projections onto task margin sets, leveraging nonconvex projection theory.
result Local linear convergence under certain conditions for homogeneous deep networks.

Single index model is a powerful yet simple model, widely used in statistics, machine learning, and other scientific fields. It models the regression function as g(<a,x>)g(<a,x>), where a is an unknown index vector and x are the features. This paper deals with a nonlinear generalization of this framework to allow for a regre…

2019-02-24abs ↗pdf ↗

Analog forecasting uses local dynamics to predict chaotic systems.

problem Theoretical connections between analog forecasting and dynamical systems are overlooked.
method Local approximations of the system's dynamics, linear regression, and estimation of analog forecasting errors.
result Analog forecasting performances are highly linked to the local Jacobian matrix of the flow map.

The paper develops a minimax optimal method for high-dimensional regression using auxiliary data.

problem High-dimensional additive regression with heavy-tailed errors and transfer learning.
method Smooth backfitting estimator with local linear smoothing, followed by a two-stage estimation method.
result The method achieves the minimax optimal rate under certain conditions.

Optimal multiscale learning of linear operators

problem Statistical and computational limits of learning bounded linear operators between Sobolev spaces
method Reformulate as an infinite-dimensional matrix regression problem with heterogeneous multiscale structure
result Establish minimax rates and construct a finite-resolution blockwise least-squares estimator attaining these rates

Proposes RLAR for efficient labeled data classification with robust margin and manifold structure.

problem Clear margin representation and data manifold structure difficulty in linear discriminant methods.
method Introduces retargeted regression for adaptive margin learning and locality-aware strategy for compact data manifold.
result RLAR outperforms state-of-the-art approaches in UCI and benchmark data sets.

Recently, it was demonstrated in [CS2012,CS2013] that the robustness of the classical Non-Local Means (NLM) algorithm [BCM2005] can be improved by incorporating p(0<p2)\ell^p (0 < p \leq 2) regression into the NLM framework. This general optimization framework, called Non-Local Patch Regression (NLPR), contains NLM as a spe…

2013-03-02abs ↗pdf ↗

Paper studies IPG method's robustness in noisy distributed linear regression.

problem Distributed linear regression with noise.
method Iteratively Pre-conditioned Gradient-descent (IPG) method.
result IPG method's robustness against noise compared favorably to state-of-the-art algorithms.