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The vertices of an interval graph represent intervals over a real line where overlapping intervals denote that their corresponding vertices are adjacent. This implies that the vertices are measurable by a metric and there exists a linear…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
Combining additive models and neural networks allows to broaden the scope of statistical regression and extend deep learning-based approaches by interpretable structured additive predictors at the same time. Existing attempts uniting the…
In the mixture of experts model, a common assumption is the linearity between a response variable and covariates. While this assumption has theoretical and computational benefits, it may lead to suboptimal estimates by overlooking potential…
The stochastic expansion of the marginal quasi-likelihood function associated with a class of generalized linear models is shown. Based on the expansion, a quasi-Bayesian information criterion is proposed that is able to deal with…
This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…
We study asymptotic properties of $M$-estimates of regression parameters in linear models in which errors are dependent. Weak and strong Bahadur representations of the $M$-estimates are derived and a central limit theorem is established.…
We discuss pattern languages for closed pattern mining and learning of interval data and distributional data. We first introduce pattern languages relying on pairs of intersection-based constraints or pairs of inclusion based constraints,…
An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the…
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…
We fit the exponent of the Pareto distribution, that is equivalent or can approximate the continuous power law distribution given a cutoff point, using linear regression (LR). We use LR on the logged variables of the empirical tail (one…
This paper proposes an algorithm for computing regularized solutions to linear rational expectations models. The algorithm allows for regularization cross-sectionally as well as across frequencies. A variety of numerical examples illustrate…
In this paper we present theory, algorithms and applications for regression over the max- plus semiring. We show how max-plus 2-norm regression can be used to obtain maximum likelihood estimates for three different inverse problems. Namely…
Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least…
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…
With the development of new sensors and monitoring devices, more sources of data become available to be used as inputs for machine learning models. These can on the one hand help to improve the accuracy of a model. On the other hand,…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…
Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting…