Related papers: Dos and don'ts of reduced chi-squared
In various capacities of statistical signal processing two-dimensional (2-D) chirp models have been considered significantly, particularly in image processing$-$ to model gray-scale and texture images, magnetic resonance imaging, optical…
This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
In this paper, we consider the estimation of the unknown parameters of the multiple chirp signal model in presence of additive error. The chirp signals are quite common in many areas of science and engineering, specially sonar, radar, audio…
Ordinary least-squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. This article…
We develop a technique for establishing lower bounds on the sample complexity of Least Squares (or, Empirical Risk Minimization) for large classes of functions. As an application, we settle an open problem regarding optimality of Least…
Weak gravitational lensing surveys using photometric redshifts can have their cosmological constraints severely degraded by errors in the photo-z scale. We explore the cosmological degradation vs the size of the spectroscopic survey…
Since cosmic shear was first observed in 2000, it has become a key cosmological probe and promises to deliver exquisite dark energy constraints. However, shear is inferred from coherent distortions of galaxy shapes, and the relation between…
Data dimensionality reduction techniques are often utilized in the implementation of Quantum Machine Learning models to address two significant issues: the constraints of NISQ quantum devices, which are characterized by noise and a limited…
For more that seventy years, the measurements of fluxes of galaxies at different wavelengths and derived colours have been used to estimate their corresponding cosmological distances. From the fields of galaxy and AGN evolution to precision…
Overparametrization often helps improve the generalization performance. This paper presents a dual view of overparametrization suggesting that downsampling may also help generalize. Focusing on the proportional regime $m\asymp n \asymp p$,…
We explore linear and non-linear dimensionality reduction techniques for statistical inference of parameters in cosmology. Given the importance of compressing the increasingly complex data vectors used in cosmology, we address questions…
This chapter considers the computational and statistical aspects of learning linear thresholds in presence of noise. When there is no noise, several algorithms exist that efficiently learn near-optimal linear thresholds using a small amount…
Ellipse and ellipsoid fitting has been extensively researched and widely applied. Although traditional fitting methods provide accurate estimation of ellipse parameters in the low-noise case, their performance is compromised when the noise…
We study a minimax risk of estimating inverse functions on a plane, while keeping an estimator is also invertible. Learning invertibility from data and exploiting an invertible estimator are used in many domains, such as statistics,…
Nested-error regression models are widely used for analyzing clustered data. For example, they are often applied to two-stage sample surveys, and in biology and econometrics. Prediction is usually the main goal of such analyses, and…
We propose a goodness-of-fit test for degree-corrected stochastic block models (DCSBM). The test is based on an adjusted chi-square statistic for measuring equality of means among groups of $n$ multinomial distributions with $d_1,\dots,d_n$…
Suppose data are fitted to some parametric model but that the true model happens to be one with an additional parameter. When a parameter is to be estimated one can use likelihood estimation in the wider model or in the narrow model.…
In tomographic weak lensing surveys, the presence of nulling properties reveals symmetries inherent in the data, which rely solely on the geometrical properties of the Universe. Ensuring its validity thus provides us with constraints on the…
The inverse problem methodology is a commonly-used framework in the sciences for parameter estimation and inference. It is typically performed by fitting a mathematical model to noisy experimental data. There are two significant sources of…