Related papers: A dimensional R2 regression metric
Single Index Models (SIMs) are simple yet flexible semi-parametric models for classification and regression. Response variables are modeled as a nonlinear, monotonic function of a linear combination of features. Estimation in this context…
The recent developments in the machine learning domain have enabled the development of complex multivariate probabilistic forecasting models. Therefore, it is pivotal to have a precise evaluation method to gauge the performance and…
Difference-in-differences (DID) is a widely used approach for drawing causal inference from observational panel data. Two common estimation strategies for DID are outcome regression and propensity score weighting. In this paper, motivated…
High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…
Reversible Instance Normalization (RevIN) is a key technique enabling simple linear models to achieve state-of-the-art performance in time series forecasting. While replacing its non-robust statistics with robust counterparts (termed…
The problem of finding a reduced dimensionality representation of categorical variables while preserving their most relevant characteristics is fundamental for the analysis of complex data. Specifically, given a co-occurrence matrix of two…
Parameter reduction can enable otherwise infeasible design and uncertainty studies with modern computational science models that contain several input parameters. In statistical regression, techniques for sufficient dimension reduction…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
Consider measuring an n-dimensional vector x through the inner product with several measurement vectors, a_1, a_2, ..., a_m. It is common in both signal processing and statistics to assume the linear response model y_i = <a_i, x> + e_i,…
Regression discontinuity (RD) designs are popular quasi-experimental studies in which treatment assignment depends on whether the value of a running variable exceeds a cutoff. RD designs are increasingly popular in educational applications…
This paper introduces a new notion of dimensionality of probabilistic models from an information-theoretic view point. We call it the "descriptive dimension"(Ddim). We show that Ddim coincides with the number of independent parameters for…
Modern datasets are characterized by a large number of features that may conceal complex dependency structures. To deal with this type of data, dimensionality reduction techniques are essential. Numerous dimensionality reduction methods…
Diffusion models have achieved cutting-edge performance in image generation. However, their lengthy denoising process and computationally intensive score estimation network impede their scalability in low-latency and resource-constrained…
Model-assisted regression estimation is fundamental in survey sampling for incorporating auxiliary information. However, when the auxiliary dimension grows with the sample size, the standard Generalized regression (GREG) estimator can…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
This paper presents the Robust Recurrent Deep Network (R2DN), a scalable parameterization of robust recurrent neural networks for machine learning and data-driven control. We construct R2DNs as a feedback interconnection of a linear…
Discovering patterns of the complex high-dimensional data is a long-standing problem. Dimension Reduction (DR) and Intrinsic Dimension Estimation (IDE) are two fundamental thematic programs that facilitate geometric understanding of the…
Precise control over dimension of nanocrystals is critical to tune the properties for various applications. However, the traditional control through experimental optimization is slow, tedious and time consuming. Herein a robust deep neural…
Errors in variables (Deming) regression of measurements spanning a wide range of values requires appropriate weighting to reflect nonconstant variance. Precision profile models, mathematical relationships between measurement variance and…
This work focuses on the issue of variable selection in functional regression. Unlike most work in this framework, our approach does not select isolated points in the definition domain of the predictors, nor does it rely on the expansion of…