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In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…
Partially linear additive models generalize linear ones since they model the relation between a response variable and covariates by assuming that some covariates have a linear relation with the response but each of the others enter through…
In the age of big data and interpretable machine learning, approaches need to work at scale and at the same time allow for a clear mathematical understanding of the method's inner workings. While there exist inherently interpretable…
In generalized regression models the effect of continuous covariates is commonly assumed to be linear. This assumption, however, may be too restrictive in applications and may lead to biased effect estimates and decreased predictive…
Multiple regression has been the go-to method for data analysis for generations of scholars due to its transparency, interpretability, and desirable theoretical properties. However, the method's simplicity precludes the discovery of complex…
This study proposes a novel method for estimation and hypothesis testing in high-dimensional single-index models. We address a common scenario where the sample size and the dimension of regression coefficients are large and comparable.…
The weights of a neural network are typically initialized at random, and one can think of the functions produced by such a network as having been generated by a prior over some function space. Studying random networks, then, is useful for a…
Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…
We introduce a new regression framework designed to deal with large-scale, complex data that lies around a low-dimensional manifold with noises. Our approach first constructs a graph representation, referred to as the skeleton, to capture…
Traditional methods for linear regression generally assume that the underlying error distribution, equivalently the distribution of the responses, is normal. Yet, sometimes real life response data may exhibit a skewed pattern, and assuming…
We consider the problem of impulse response estimation of stable linear single-input single-output systems. It is a well-studied problem where flexible non-parametric models recently offered a leap in performance compared to the classical…
For many real data, long term observation consists of different processes that coexist or occur one after the other. Those processes very often exhibit different statistical properties and thus before the further analysis the observed data…
This paper looks at effects, due to the boundary, on inference in logistic regression. It shows that first -- and, indeed, higher -- order asymptotic results are not uniform across the model. Near the boundary, effects such as high…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
The term structure of credit spreads is studied with an aim to predict its future movements. A completely new approach to tackle this problem is presented, which utilizes nonlinear parametric models. The Brain-Cousens regression model with…
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…
This paper studies a linear model for multidimensional panel data of three or more dimensions with unobserved interactive fixed-effects. The main estimator uses a Neyman-orthogonal approach, and requires two preliminary steps. First, the…
We propose a novel approach for detecting change points in high-dimensional linear regression models. Unlike previous research that relied on strict Gaussian/sub-Gaussian error assumptions and had prior knowledge of change points, we…
Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…
We study a linear observation model with an unknown permutation called \textit{permuted/shuffled linear regression}, where responses and covariates are mismatched and the permutation forms a discrete, factorial-size parameter. The…