Related papers: Sufficient Dimension Reduction for Interactions
The merit of projecting data onto linear subspaces is well known from, e.g., dimension reduction. One key aspect of subspace projections, the maximum preservation of variance (principal component analysis), has been thoroughly researched…
A guiding principle for data reduction in statistical inference is the sufficiency principle. This paper extends the classical sufficiency principle to decentralized inference, i.e., data reduction needs to be achieved in a decentralized…
The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…
We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first…
Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as…
When estimating the treatment effect in an observational study, we use a semiparametric locally efficient dimension reduction approach to assess both the treatment assignment mechanism and the average responses in both treated and…
When estimating causal effects from observational studies, researchers often need to adjust for many covariates to deconfound the non-causal relationship between exposure and outcome, among which many covariates are discrete. The behavior…
Sufficient dimension reduction (SDR) is continuing an active research field nowadays for high dimensional data. It aims to estimate the central subspace (CS) without making distributional assumption. To overcome the large-$p$-small-$n$…
How should an agent (the sender) observing multi-dimensional data (the state vector) persuade another agent to take the desired action? We show that it is always optimal for the sender to perform a (non-linear) dimension reduction by…
Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association…
We introduce a new method to jointly reduce the dimension of the input and output space of a function between high-dimensional spaces. Choosing a reduced input subspace influences which output subspace is relevant and vice versa.…
This article provides an introduction to the Regression Discontinuity (RD) design, and its application to empirical research in the medical sciences. While the main focus of this article is on causal interpretation, key concepts of…
Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important.…
Empirical studies using Regression Discontinuity (RD) designs often explore heterogeneous treatment effects based on pretreatment covariates, even though no formal statistical methods exist for such analyses. This has led to the widespread…
With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fr\'echet regression model (Peterson & M\"uller 2019) provides a…
A new dimension reduction (DR) method for data sets is proposed by autonomous deforming of data manifolds. The deformation is guided by the proposed deforming vector field, which is defined by two kinds of virtual interactions between data…
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…
We derive an objective function that can be optimized to give an estimator of the Vapnik- Chervonenkis dimension for model selection in regression problems. We verify our estimator is consistent. Then, we verify it performs well compared to…
Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…
We extend the continuity-based framework to Regression Discontinuity Designs (RDDs) to identify and estimate causal effects under interference when units are connected through a network. Assignment to an "effective treatment," combining the…