Related papers: Dos and don'ts of reduced chi-squared
The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this…
Although the theory of constrained least squares (CLS) estimation is well known, it is usually applied with the view that the constraints to be imposed are unavoidable. However, there are cases in which constraints are optional. For…
The extraction of signals from noise is a common problem in all areas of science and engineering. A particularly useful version is that of forecasting: determining a causal filter that estimates a future value of a hidden process from past…
In data mining applications, feature selection is an essential process since it reduces a model's complexity. The cost of obtaining the feature values must be taken into consideration in many domains. In this paper, we study the…
In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and…
Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares…
Many experiments can be interpreted in terms of random processes operating according to some internal protocols. When experiments are costly or cannot be repeated only one or a few finite samples are available. In this paper we study data…
Measurements of ellipticities of background galaxies are sensitive to the reduced shear, the cosmic shear divided by $(1-\kappa)$ where $\kappa$ is the projected density field. We compute the difference between shear and reduced shear both…
The present generation of weak lensing surveys will be superseded by surveys run from space with much better sky coverage and high level of signal to noise ratio, such as SNAP. However, removal of any systematics or noise will remain a…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
Regression models with crossed random effect errors can be very expensive to compute. The cost of both generalized least squares and Gibbs sampling can easily grow as $N^{3/2}$ (or worse) for $N$ observations. Papaspiliopoulos et al. (2020)…
Weak gravitational lensing has the potential to constrain cosmological parameters to high precision. However, as shown by the Shear TEsting Programmes (STEP) and GRavitational lEnsing Accuracy Testing (GREAT) Challenges, measuring galaxy…
We consider the problem of robustly predicting as well as the best linear combination of $d$ given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For…
Segmentation is a fundamental task in medical image analysis. The clinical interest is often to measure the volume of a structure. To evaluate and compare segmentation methods, the similarity between a segmentation and a predefined ground…
Two schemes are presented that mitigate the effect of errors and decoherence in short depth quantum circuits. The size of the circuits for which these techniques can be applied is limited by the rate at which the errors in the computation…
Cone regression is a particular case of quadratic programming that minimizes a weighted sum of squared residuals under a set of linear inequality constraints. Several important statistical problems such as isotonic, concave regression or…
Forthcoming astronomical surveys are expected to detect new sources in such large numbers that measuring their spectroscopic redshift measurements will be not be practical. Thus, there is much interest in using machine learning to yield the…
Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional…
In recent years, it has been convincingly shown that weather forecasting models can be run in single-precision arithmetic. Several models or components thereof have been tested with even lower precision than this. This previous work has…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…