Related papers: Canonical Correlation and Assortative Matching: A …
We devise a method that reduces the problem of classifying systems of forms and linear mappings to the problem of classifying systems of linear mappings. Canonical matrices of (i) bilinear or sesquilinear forms, (ii) pairs of symmetric,…
We propose a new perspective for the evaluation of matching procedures by considering the complexity of the function class they belong to. Under this perspective we provide theoretical guarantees on post-matching covariate balance through a…
It is well known that parameters for strongly correlated predictor variables in a linear model cannot be accurately estimated. We look for linear combinations of these parameters that can be. Under a uniform model, we find such linear…
The machine learning community has recently devoted much attention to the problem of inferring causal relationships from statistical data. Most of this work has focused on uncovering connections among scalar random variables. We generalize…
Pairwise comparison matrices are widely used in Multicriteria Decision Making. This article applies incomplete pairwise comparison matrices in the area of sport tournaments, namely proposing alternative rankings for the 2010 Chess Olympiad…
We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. Matching methods are heavily used in the social sciences due to their interpretability, but most matching…
Analogical reasoning depends fundamentally on the ability to learn and generalize about relations between objects. We develop an approach to relational learning which, given a set of pairs of objects…
Statistical matching is an effective method for estimating causal effects in which treated units are paired with control units with ``similar'' values of confounding covariates prior to performing estimation. In this way, matching helps…
We propose a method for summarizing the strength of association between a set of variables and a multivariate outcome. Classical summary measures are appropriate when linear relationships exist between covariates and outcomes, while our…
This paper studies inference on the average treatment effect in experiments in which treatment status is determined according to "matched pairs" and it is additionally desired to adjust for observed, baseline covariates to gain further…
To estimate casual treatment effects, we propose a new matching approach based on the reduced covariates obtained from sufficient dimension reduction. Compared to the original covariates and the propensity score, which are commonly used for…
Some mathematical theorems represent ideas that are discovered again and again in different forms. One such theorem is Hall's marriage theorem. This theorem is equivalent to several other theorems in combinatorics and optimization theory,…
We present a fast algorithm for approximate Canonical Correlation Analysis (CCA). Given a pair of tall-and-thin matrices, the proposed algorithm first employs a randomized dimensionality reduction transform to reduce the size of the input…
The relationship between linear relations and matrix pencils is investigated. Given a linear relation, we introduce its Weyr characteristic. If the linear relation is the range (or the kernel) representation of a given matrix pencil, we…
We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for…
Under the potential outcomes framework, we introduce matched-pair factorial designs, and propose the matched-pair estimator of the factorial effects. We also calculate the randomization-based covariance matrix of the matched-pair estimator,…
Becker (1973) presents a bilateral matching model in which scalar types describe agents. For this framework, he establishes the conditions under which positive sorting between agents' attributes is the unique market outcome. Becker's…
Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance…
The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so general that it requires an exponential number of oracle calls. Nevertheless, Lov\'asz (1980)…
Many major works in social science employ matching to make causal conclusions, but different matches on the same data may produce different treatment effect estimates, even when they achieve similar balance or minimize the same loss…