相关论文: Transcending The Least Squares

We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined and the possible impact of…

The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the…

It is shown that the the popular least squares method of option pricing converges even under very general assumptions. This substantially increases the freedom of creating different implementations of the method, with varying levels of…

Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…

A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.

A numerical method optimizing the coefficients of the semi empirical mass formula or those of similar mass formulas is presented. The optimization is based on the least-squares adjustments method and leads to the resolution of a linear…

An effective two-stage method for an estimation of parameters of the linear regression is considered. For this purpose we introduce a certain quasi-estimator that, in contrast to usual estimator, produces two alternative estimates. It is…

The method of quasi-optimal observables [hep-ph/0001019] offers a fundamental yet simple and flexible algorithmic framework for data processing in high energy physics to improve upon the practice of event selection cuts.

A novel regression method is introduced and studied. The procedure weights squared residuals based on their magnitude. Unlike the classic least squares which treats every squared residual equally important, the new procedure exponentially…

Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…

This is a brief tutorial on the least square estimation technique that is straightforward yet effective for parameter estimation. The tutorial is focused on the linear LSEs instead of nonlinear versions, since most nonlinear LSEs can be…

We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions into conforming functions before applying the load functional.…

In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…

Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to…

We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer…

The statistical method of quasi-optimal weights can be used to derive criteria for searches of anomalies. As an example we derive a convenient statistical criterion for step-like anomalies in cumulative spectra such as measured in the…

Weighting methods are widely used to adjust for covariates in observational studies, sample surveys, and regression settings. In this paper, we study a class of recently proposed weighting methods which find the weights of minimum…

Markov parameters play a key role in system identification. There exists many algorithms where these parameters are estimated using least-squares in a first, pre-processing, step, including subspace identification and multi-step…

Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a…

As quantum tomography is becoming a key component of the quantum engineering toolbox, there is a need for a deeper understanding of the multitude of estimation methods available. Here we investigate and compare several such methods: maximum…