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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.

168,657 papers · 148 categories

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130259389518 · Jun 202019922001200920172026
48 results for multi-task linear regression

The paper uses random matrix theory for multi-task regression, improving time series forecasting.

problem Improving time series forecasting using multi-task regression.
method Applying random matrix theory to multi-task regression problems, deriving closed-form solutions for optimization.
result Provides a robust foundation for hyperparameter optimization in multi-task regression scenarios.

Paper estimates noise covariance in correlated multi-task linear models.

problem Estimating noise covariance in multi-task high-dimensional linear models with correlated noise.
method Uses multi-task elastic-net and lasso estimators to estimate noise covariance, correcting bias in squared residual matrix.
result Develops a novel estimator of noise covariance that converges at rate n1/2n^{-1/2}, matching oracle estimator under suitable conditions.

Unified analysis of multi-task functional linear regression with manifold and composite penalties.

problem Estimating slope functions from functional data with multi-task learning.
method Penalized splines with manifold constraint and composite quadratic penalty.
result Unified convergence upper bound and phase transition behaviors for estimators.

Develops a scalable multi-task Gaussian process with neural embedding for improved performance.

problem High model complexity and limited model capability in multi-task Gaussian processes.
method Neural embedding of coregionalization, advanced variational inference, sparse approximation.
result Higher prediction quality and better generalization of the NSVLMC model.

New estimator tackles multi-task linear regression with outliers, avoiding eigenvalue lower bounds.

problem Multi-task linear regression with contaminated tasks and eigenvalue lower bounds failure.
method Matrix-weighted norm regularization and relative balancedness condition.
result Prediction MSE bounds match Duan and Wang (2023) under weaker spectral assumptions.

The one-class kernel spectral regression (OC-KSR), the regression-based formulation of the kernel null-space approach has been found to be an effective Fisher criterion-based methodology for one-class classification (OCC), achieving state-of-the-art performance in one-class classification while providing relatively hig…

2019-05-22abs ↗pdf ↗

We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning prob- lems with nonscalar outputs like multi-task learning and structured out- put prediction. We show that multi-task ke…

2013-06-17abs ↗pdf ↗

Study multi-task learning with low-rank representation in stochastic linear bandits.

problem Transfer learning across multiple linear bandit tasks with shared low-dimensional representation.
method Proposes a greedy policy with trace norm regularization to implicitly learn a low-rank representation without knowing the rank.
result Upper bound on multi-task regret of NdT(T+d)r\sqrt{NdT(T+d)r}, showing benefit over independent task solving.

MTL improves multi-dimensional regression in luminescence sensing.

problem Challenges in modeling multi-dimensional regression problems with classical methods.
method Multi-task learning (MTL) with feed-forward neural networks (FFNNs).
result MTL allows predicting multiple parameters from a single set of measurements.

This work improves multi-task regression performance using approximations of full-conformal prediction.

problem Jointly solve multiple regression tasks with better performance than individual tasks.
method Design an approximating prediction region in RKHS for full-conformal multi-task regression.
result The approximating prediction region improves upon split-conformal prediction on synthetic data.

We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008], we assume that the regression vectors share the same sparsity pattern. This means that the set of relevant predictor var…

2009-03-09abs ↗pdf ↗

A new multi-task learning estimator improves Gaussian graphical regression model fitting.

problem High error rate in fitting Gaussian graphical regression models due to separate node-wise lasso regressions.
method Proposes a multi-task learning estimator with cross-task group sparsity and within-task element-wise sparsity penalties, solved via an efficient augmented Lagrangian algorithm.
result Error rate improvement over separate node-wise lasso estimates, demonstrated through simulations and application to gene co-expression network study.

Extends neural diffusion processes for multi-task regression.

problem Limited to single-task inference, existing formulations cannot capture dependencies across related tasks.
method Introduces a task encoder to condition diffusion model on low-dimensional representations of context observations.
result Improves predictive performance and uncertainty calibration across related functions.

New method generates continuous Pareto sets for multi-task learning.

problem Challenges in finding optimal solutions for correlated multi-task learning problems.
method Efficiently generates locally continuous Pareto sets and fronts in multi-objective optimization problems.
result Demonstrates continuous analysis of Pareto optimal solutions in machine learning problems.

High dimensional regression benefits from sparsity promoting regularizations. Screening rules leverage the known sparsity of the solution by ignoring some variables in the optimization, hence speeding up solvers. When the procedure is proven not to discard features wrongly the rules are said to be \emph{safe}. In this …

2015-06-11abs ↗pdf ↗

Paper extends multi-task Gaussian Cox processes for heterogeneous tasks.

problem Modeling multiple heterogeneous correlated tasks jointly.
method Data augmentation and mean-field approximation for non-conjugate Bayesian inference.
result Demonstrates improved performance and inference on synthetic and real data.

Develops a new fairness learning approach for multi-task regression models.

problem Fairness in multi-task regression models with biased datasets.
method Uses rank-based non-parametric independence test (Mann Whitney U statistic) and reformulates as non-convex optimization problem.
result Outperforms state-of-the-art methods on fairness metrics.

This paper proposes MM-DAGs for analyzing traffic congestion, learning multiple DAGs jointly.

problem Analyzing multi-modal traffic data with overlapping and distinct variables.
method Developed MM-DAGs for multi-task, multi-modal DAG learning, using multi-modal regression and CD measure.
result Proved the effectiveness of MM-DAGs in traffic congestion analysis.

We demystify attention patterns in multi-head softmax models for linear data.

problem Understanding the training dynamics and emergent patterns in multi-head softmax attention models.
method Extensive empirical experiments and rigorous theoretical analysis.
result Multi-head softmax attention models approximate a debiased gradient descent predictor, outperforming single-head attention and achieving near-Bayesian optimality.

Sensors are an integral part of modern Internet of Things (IoT) applications. There is a critical need for the analysis of heterogeneous multivariate temporal data obtained from the individual sensors of these systems. In this paper we particularly focus on the problem of the scarce amount of training data available pe…

2019-05-13abs ↗pdf ↗

The paper develops inference methods for high-dimensional multi-task regression with row-sparse coefficients.

problem Inference for high-dimensional multi-task regression with unknown coefficient matrix under row-sparsity.
method Proposes chi-square and normal inference methodologies using MT Lasso with de-biasing scheme and interaction matrix.
result Derives asymptotic normal and chi-square distribution results for valid confidence intervals and ellipsoids.

This study compares mtl architectures for renewable power generation forecasting.

problem Forecasting expected power generation for renewable power plants.
method Comparative study of mtl architectures including Hard parameter sharing, cross-stitch network, sluice network, and task embedding.
result Emerging Relation Network (ERN) and task embedding provide significant improvements in forecasting.

New algorithm improves learning efficiency in multi-task contextual bandits.

problem Improving learning efficiency in multi-task contextual bandits.
method Alternating projected gradient descent (GD) and minimization estimator for low-rank feature matrix recovery.
result Proved regret bound for multi-task learning algorithm.

The paper shows how multi-task learning in neural networks is similar to kernel regression and Hilbert spaces.

problem Understanding the solutions to multi-task shallow ReLU neural network learning problems.
method Analyzing the properties of solutions to multi-task shallow ReLU neural network learning problems, proving uniqueness and equivalence to minimum-norm interpolation problems in Hilbert spaces.
result The solutions to multi-task neural network interpolation problems are almost always unique and coincide with the solution to a minimum-norm interpolation problem in a Sobolev (Reproducing Kernel) Hilbert Space.

This paper addresses the meta-learning problem in sparse linear regression with infinite tasks. We assume that the learner can access several similar tasks. The goal of the learner is to transfer knowledge from the prior tasks to a similar but novel task. For p parameters, size of the support set k , and l samples per …

2020-02-22abs ↗pdf ↗

SMART transfers knowledge across related studies for multi-task learning.

problem Deterioration of multi-task learning performance with small target sample size.
method SMART assumes spectral similarity between source and target models, estimating target coefficients through structured regularization.
result SMART achieves near-minimax error rates, improving estimation accuracy and robustness to negative transfer.

Meta-learning, or learning-to-learn, seeks to design algorithms that can utilize previous experience to rapidly learn new skills or adapt to new environments. Representation learning -- a key tool for performing meta-learning -- learns a data representation that can transfer knowledge across multiple tasks, which is es…

2020-02-26abs ↗pdf ↗

Develops a method for fairness in multi-task learning using Wasserstein barycenters.

problem Extending fairness to multi-task learning with shared representations.
method Definition of Strong Demographic Parity extended to multi-task learning using multi-marginal Wasserstein barycenters. Closed form solution for optimal fair predictor.
result Empirical results show practical value of post-processing methodology in promoting fair decision-making.

New algorithms minimize regret in multi-task and lifelong linear bandits with shared representation.

problem Minimizing regret in multi-task and lifelong linear bandits with shared representation.
method Novel algorithms using efficient estimator for low-rank linear feature extractor and novel analysis.
result Achieved regret bounds matching minimax lower bound up to logarithmic factors.

Proposes a transductive matrix completion method with calibration for multi-task learning.

problem Improving multi-task learning with multiple related data sources.
method Transductive matrix completion with calibration constraint.
result The proposed algorithm recovers incomplete feature and target matrices with improved results.

We sharply characterize the performance of different penalization schemes for the problem of selecting the relevant variables in the multi-task setting. Previous work focuses on the regression problem where conditions on the design matrix complicate the analysis. A clearer and simpler picture emerges by studying the No…

2010-08-31abs ↗pdf ↗

Proposes a novel MTL approach based on bias-variance analysis.

problem Improving multi-task learning performance through shared knowledge.
method Two-phase iterative aggregation of targets and features using bias-variance analysis.
result Validation on synthetic and real-world datasets demonstrates the effectiveness of the proposed method.

SOFARI improves inference on multi-task learning latent factors.

problem Challenges in precise inference on multi-task learning latent factor matrices.
method High-dimensional manifold-based Neyman near-orthogonality inference on Stiefel manifold structure.
result Easy-to-use bias-corrected estimators for latent factor vectors and singular values with asymptotic normal distributions.

New method for MTL with varying sparsity patterns across tasks.

problem Jointly training multiple linear models with differing sparsity patterns.
method Mixed-integer programming formulation and scalable algorithms.
result Our methods leverage shared support information to improve variable selection.