Related papers: Toward Variation-Independent Regression by Composi…
In this paper, we consider the problem of treating linear regression equation coefficients in the case of correlated predictors. It is shown that in general there are no natural ways of interpreting these coefficients similar to the case of…
Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for…
Compositional data are met in many different fields, such as economics, archaeometry, ecology, geology and political sciences. Regression where the dependent variable is a composition is usually carried out via a log-ratio transformation of…
Rejoinder to "Brownian distance covariance" by G\'abor J. Sz\'ekely and Maria L. Rizzo [arXiv:1010.0297]
Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…
In this paper we improve the probabilistic approach to compositions of Ehrenborg, Levin and Readdy by introducing a simpler but more general probabilistic model. As consequence we get some new estimates on the behavior of a uniform random…
Time-varying parameter vector autoregression provides a flexible framework to capture structural changes within time series. However, when applied to high-dimensional data, this model encounters challenges of over-parametrization and…
Should prediction models always deliver a prediction? In the pursuit of maximum predictive performance, critical considerations of reliability and fairness are often overshadowed, particularly when it comes to the role of uncertainty.…
We consider regression in which one predicts a response $Y$ with a set of predictors $X$ across different experiments or environments. This is a common setup in many data-driven scientific fields and we argue that statistical inference can…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
This chapter reviews the instrumental variable quantile regression model of Chernozhukov and Hansen (2005). We discuss the key conditions used for identification of structural quantile effects within this model which include the…
This paper introduces multimodal conformal regression. Traditionally confined to scenarios with solely numerical input features, conformal prediction is now extended to multimodal contexts through our methodology, which harnesses internal…
This handbook chapter gives an introduction to the sharp regression discontinuity design, covering identification, estimation, inference, and falsification methods.
We review previous work of Alain Connes, and its extension by the author, on some conformal invariants obtained from the noncommutative residue on even dimensional compact manifolds without boundary. Inspired by recent work of Yong Wang, we…
We introduce a new version of forward stepwise regression. Our modification finds solutions to regression problems where the selected predictors appear in a structured pattern, with respect to a predefined distance measure over the…
Discussion of "Instrumental Variables: An Econometrician's Perspective" by Guido W. Imbens [arXiv:1410.0163].
We demonstrate a conditional autoregressive pipeline for efficient music recomposition, based on methods presented in van den Oord et al.(2017). Recomposition (Casal & Casey, 2010) focuses on reworking existing musical pieces, adhering to…
In this paper we present a method ofcomputing the posterior probability ofconditional independence of two or morecontinuous variables from data,examined at several resolutions. Ourapproach is motivated by theobservation that the appearance…
Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded…
Unsupervised representation learning with variational inference relies heavily on independence assumptions over latent variables. Causal representation learning (CRL), however, argues that factors of variation in a dataset are, in fact,…