Related papers: The least squares method for option pricing revisi…
Consider linear regression where the examples are generated by an unknown distribution on $R^d\times R$. Without any assumptions on the noise, the linear least squares solution for any i.i.d. sample will typically be biased w.r.t. the least…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
Nonparametric regression subject to convexity or concavity constraints is increasingly popular in economics, finance, operations research, machine learning, and statistics. However, the conventional convex regression based on the least…
The so-called constrained least mean-square algorithm is one of the most commonly used linear-equality-constrained adaptive filtering algorithms. Its main advantages are adaptability and relative simplicity. In order to gain analytical…
In approximation of functions based on point values, least-squares methods provide more stability than interpolation, at the expense of increasing the sampling budget. We show that near-optimal approximation error can nevertheless be…
In this article the issues are discussed with the Bayesian approach, least-square fits, and most-likely fits. Trying to counter these issues, a method, based on weighted confidence, is proposed for estimating probabilities and other…
Model averaging methods have become an increasingly popular tool for improving predictions and dealing with model uncertainty, especially in Bayesian settings. Recently, frequentist model averaging methods such as information theoretic and…
The least squares Monte Carlo algorithm has become popular for solving portfolio optimization problems. A simple approach is to approximate the value functions on a discrete grid of portfolio weights, then use control regression to…
This article introduces a novel approach to the mathematical development of Ordinary Least Squares and Neural Network regression models, diverging from traditional methods in current Machine Learning literature. By leveraging Tensor…
Least squares estimation, a regression technique based on minimisation of residuals, has been invaluable in bringing the best fit solutions to parameters in science and engineering. However, in dynamic environments such as in Geomatics…
This paper investigates some theoretical properties of the Partial Least Square (PLS) method. We focus our attention on the single component case, that provides a useful framework to understand the underlying mechanism. We provide a…
Penalized least squares estimation is a popular technique in high-dimensional statistics. It includes such methods as the LASSO, the group LASSO, and the nuclear norm penalized least squares. The existing theory of these methods is not…
We propose an abstract framework for analyzing the convergence of least-squares methods based on residual minimization when feasible solutions are neural networks. With the norm relations and compactness arguments, we derive error estimates…
We define and analyse a least-squares finite element method for a first-order reformulation of the obstacle problem. Moreover, we derive variational inequalities that are based on similar but non-symmetric bilinear forms. A priori error…
In this paper we propose a novel dual regression-based approach for pricing American options. This approach reduces the complexity of the nested Monte Carlo method and has especially simple form for time discretised diffusion processes. We…
We consider a resampling scheme for parameters estimates in nonlinear regression models. We provide an estimation procedure which recycles, via random weighting, the relevant parameters estimates to construct consistent estimates of the…
The approximation of tensors has important applications in various disciplines, but it remains an extremely challenging task. It is well known that tensors of higher order can fail to have best low-rank approximations, but with an important…
Nonparametric partitioning-based least squares regression is an important tool in empirical work. Common examples include regressions based on splines, wavelets, and piecewise polynomials. This article discusses the main methodological and…
Least-squares refitting is widely used in high dimensional regression to reduce the prediction bias of l1-penalized estimators (e.g., Lasso and Square-Root Lasso). We present theoretical and numerical results that provide new insights into…
A few iterations of alternating least squares with a random starting point provably suffice to produce nearly optimal spectral- and Frobenius-norm accuracies of low-rank approximations to a matrix; iterating to convergence is unnecessary.…