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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.

169,181 papers · 148 categories

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48 results for least-squares models

A fast cross-validation method for high-dimensional data.

problem High computational cost of least-squares models in high-dimensional datasets.
method Analytical approach for k-fold cross-validation without explicit model training.
result Up to 10,000x faster than standard approach in high-dimensional data.

The paper analyzes the risk of a least squares estimator under a spike covariance model.

problem Risk analysis of the least squares estimator under a spike covariance model.
method Assumes spike covariance matrices, studies risk as d/nightarrowd/n ightarrow \infty.
result Risk of the minimum norm least squares estimator vanishes compared to the null estimator.

Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking solutions quality and accuracy becomes the trade-off. In this paper, we investi…

2015-10-16abs ↗pdf ↗

A new method for estimating large-scale linear models with improved precision.

problem Estimating large-scale linear statistical models efficiently.
method Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), integrating Sketch-and-Solve and Iterative-Sketching methods.
result SLSE-FRS produces high-precision estimators, outperforming state-of-the-art methods.

A recently introduced Importance Sampling strategy based on a least squares optimization is applied to the Monte Carlo simulation of Libor Market Models. Such Least Squares Importance Sampling (LSIS) allows the automatic optimization of the sampling distribution within a trial class by means of a quick presimulation al…

2007-11-01abs ↗pdf ↗

This paper compares LSM and ANN/GBM for pricing American put options under a complex model.

problem Pricing American put options using advanced techniques.
method Least-Squares Monte Carlo (LSM) and Artificial Neural Network (ANN) and Gradient Boosted Machine (GBM) Trees.
result LSM outperforms ANN and GBM in pricing American put options.

Ordinary least squares (OLS) is the default method for fitting linear models, but is not applicable for problems with dimensionality larger than the sample size. For these problems, we advocate the use of a generalized version of OLS motivated by ridge regression, and propose two novel three-step algorithms involving l…

2015-06-07abs ↗pdf ↗

The paper proposes a least squares method for binary compressive sampling with low intrinsic dimension signals.

problem Recovering signals from binary measurements with noise and sign flips.
method Least squares decoder for signals with low generative intrinsic dimension.
result The least squares decoder achieves a sharp estimation error of O(klog(Ln)m)O(\sqrt{\frac{k\log (Ln)}{m}}) under certain conditions.

This book introduces linear models and their theories rigorously.

problem Understanding linear models and their theories.
method Explains linear models from three perspectives, introduces maximum likelihood estimation, and proves least squares is the best unbiased linear model.
result Least squares is the best unbiased linear model in terms of mean squared error.

Study improves least squares estimation for heavy-tailed errors.

problem Improving least squares estimation under heteroscedastic and heavy-tailed errors.
method Analyzes the rate of convergence of least squares estimator under bounded conditional variance and finitely many moments of errors.
result Upper bounds on rates of convergence of LSE for heavy-tailed errors are found.

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…

2009-02-25abs ↗pdf ↗

The paper tackles robust reinforcement learning with performance guarantees.

problem Finding a robust policy for RMDP with state space uncertainties.
method Proposes RLSPI algorithm for learning optimal robust policy with performance bounds.
result Demonstrates the performance of RLSPI on standard benchmark problems.

The paper explores how overfitting can lead to better predictions in high-dimensional data.

problem Understanding the behavior of linear models in high-dimensional settings with more predictors than observations.
method Analysis of ordinary least squares, penalized least squares, and spectral shrinkage estimates.
result The phenomenon of double descent, where model performance can improve with increasing model complexity.

Proposes a method to interpret linguistic data models using parse trees and least-squares scores.

problem Interpreting trained classification models in linguistic data sets.
method Assigns least-squares based importance scores to words in a sentence using syntactic constituency structure and relates them to the Banzhaf value in coalitional game theory.
result Demonstrates the effectiveness of the proposed method in aiding interpretability and diagnostics for language models.

We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that …

2011-05-04abs ↗pdf ↗

Unified analysis of reweighted least-squares algorithms for linear models.

problem Recovering unknown signals from linear measurements using reweighted least squares.
method Unified asymptotic analysis of IRLS, lin-RFM, and alternating minimization algorithms.
result The algorithms can achieve favorable performance in a few iterations with appropriate reweighting.

Unified multi-view learning framework using OPLS with regularization and deep extensions.

problem Improving multi-view learning for classification and feature extraction.
method Orthonormalized Partial Least Squares (OPLS) with regularization and deep extensions.
result Unified multi-view learning framework with improved performance.

New algorithms estimate Jacobian matrices for large-scale machine learning.

problem Efficiently computing search directions for large nonlinear least squares.
method Exploit low-rank structure in Hessian to estimate Jacobian matrices.
result Two algorithms perform well compared to state-of-the-art methods.

New algorithm estimates partially-observed linear systems with better rates than previous methods.

problem Estimating parameters of partially-observed linear systems with long-term dependencies and semi-parametric noise.
method Prefiltered least squares estimator with semi-parametric noise model.
result First algorithm provably estimates parameters of partially-observed linear systems with rates not dependent on dependency decay rate.

Bayesian method improves online NARMAX model identification.

problem Online identification of nonlinear systems with small sample sizes and low noise.
method Variational Bayesian inference using message passing algorithm for polynomial NARMAX models.
result Variational Bayesian estimator outperforms recursive and offline least-squares methods.

Study identifies and validates a method for system identification of Markov jump linear systems.

problem System identification for autonomous Markov jump linear systems with complete state observations.
method Proposes switched least squares method for identification and derives rates of convergence.
result Data-independent rate of convergence is O(log(T)/T)\mathcal{O}\big(\sqrt{\log(T)/T} \big), showing strong consistency.

This paper reviews and compares supervised linear dimension-reduction techniques.

problem Lack of information in the response during unsupervised PCA reduces predictive performance.
method Review and comparison of supervised linear dimension-reduction techniques.
result PLS and LSPCA consistently outperform other techniques in simulations.

New algorithm improves online binary classification with constant time complexity.

problem Online binary classification with rebalancing.
method Non-iteratively reweighted recursive least-squares.
result Exacts converges to batch formulation and outperforms existing algorithms.

Reduced-rank method improves least-squares regression under output regularity.

problem Least-squares regression with infinite dimensional outputs.
method Reduced-rank method for solving least-squares problems with output regularity assumptions.
result Learning bounds and improved statistical performance compared to full-rank method.

The paper explores machine learning methods for proxy modeling in life insurance solvency capital requirements.

problem Life insurance companies need to estimate solvency capital requirements from full loss distributions, but computational limitations restrict full simulations.
method The paper presents various adaptive machine learning approaches to approximate the risk-dependent proxy function using least-squares Monte Carlo.
result The machine learning methods significantly improve the accuracy and efficiency of proxy modeling compared to traditional regression techniques.

New deep learning solver for high-dimensional derivative pricing.

problem High-dimensional derivatives pricing problems.
method Combines deep learning with least square regression for backward SDE solving.
result Accurate and efficient pricing of complex derivatives.

ESNs trained with Tikhonov least squares approximate ergodic dynamical systems in L2(μ) norm.

problem Approximating ergodic dynamical systems using ESNs.
method Tikhonov least squares regression on ESNs trained on observations from an ergodic dynamical system.
result ESNs trained with Tikhonov least squares approximate the target function in the L2(μ) norm.

A new algorithm solves nonnegative least squares faster with nonnegative data.

problem Nonnegative least squares problems with nonnegative data.
method Primal-dual perspective accelerated algorithm with adaptive restart.
result Oracle complexity independent of matrix constants, solvable to multiplicative error.

Efficient method for high-dimensional American option pricing and hedging.

problem High-dimensional American option pricing and hedging.
method Gradient-enhanced sparse Hermite polynomial expansions combined with least squares Monte Carlo.
result Outperforms state-of-the-art methods in high dimensions with comparable computational cost.

Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence that was developed for regression diagnostics can be used to detect such corrup…

2014-06-12abs ↗pdf ↗