# Essential regression

@inproceedings{Bing2019EssentialR, title={Essential regression}, author={Xin Bing and Florentina Bunea and Marten H. Wegkamp and Seth Strimas-Mackey}, year={2019} }

Essential Regression is a new type of latent factor regression model, where unobserved factors Z ∈ R influence linearly both the response Y ∈ R and the covariates X ∈ R with K p. Its novelty consists in the conditions that give Z interpretable meaning and render the regression coefficients β ∈ R relating Y to Z – along with other important parameters of the model – identifiable. It provides tools for high dimensional regression modelling that are especially powerful when the relationship…

## 5 Citations

### Inference in latent factor regression with clusterable features

- 2022

Mathematics, Computer Science

Bernoulli

Inferential tools for β are developed in a class of factor regression models in which the observed features are signed mixtures of the latent factors, and the proposed estimator (cid:2) β is minimax-rate adaptive, which enables the determination of the top latent antibody-centric mechanisms associated with the vaccine response.

### Interpolating Predictors in High-Dimensional Factor Regression

- 2022

Computer Science

J. Mach. Learn. Res.

The minimum-norm interpolating predictor analyzed under the factor regression model, despite being model-agnostic and devoid of tuning parameters, can have similar risk to predictors based on principal components regression and ridge regression, and can improve over LASSO based predictors, in the high-dimensional regime.

### Inference in Interpretable Latent Factor Regression Models

- 2019

Mathematics

Regression models, in which the observed features $X \in \R^p$ and the response $Y \in \R$ depend, jointly, on a lower dimensional, unobserved, latent vector $Z \in \R^K$, with $K n$.

### Adaptive Estimation of Multivariate Regression with Hidden Variables.

- 2020

Mathematics, Computer Science

A identifiability proof is constructive and leads to a novel and computationally efficient estimation algorithm, called HIVE, which is further extended to the setting with heteroscedastic errors.

### Nonsparse Learning with Latent Variables

- 2021

Computer Science

Oper. Res.

A new Nonsparse Learning Methodology for high-Dimensional data analysis is coming and it’s going to be pretty good.

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