28,822 research outputs found
Adaptive Relaxed ADMM: Convergence Theory and Practical Implementation
Many modern computer vision and machine learning applications rely on solving
difficult optimization problems that involve non-differentiable objective
functions and constraints. The alternating direction method of multipliers
(ADMM) is a widely used approach to solve such problems. Relaxed ADMM is a
generalization of ADMM that often achieves better performance, but its
efficiency depends strongly on algorithm parameters that must be chosen by an
expert user. We propose an adaptive method that automatically tunes the key
algorithm parameters to achieve optimal performance without user oversight.
Inspired by recent work on adaptivity, the proposed adaptive relaxed ADMM
(ARADMM) is derived by assuming a Barzilai-Borwein style linear gradient. A
detailed convergence analysis of ARADMM is provided, and numerical results on
several applications demonstrate fast practical convergence.Comment: CVPR 201
Recursive Partitioning for Heterogeneous Causal Effects
In this paper we study the problems of estimating heterogeneity in causal
effects in experimental or observational studies and conducting inference about
the magnitude of the differences in treatment effects across subsets of the
population. In applications, our method provides a data-driven approach to
determine which subpopulations have large or small treatment effects and to
test hypotheses about the differences in these effects. For experiments, our
method allows researchers to identify heterogeneity in treatment effects that
was not specified in a pre-analysis plan, without concern about invalidating
inference due to multiple testing. In most of the literature on supervised
machine learning (e.g. regression trees, random forests, LASSO, etc.), the goal
is to build a model of the relationship between a unit's attributes and an
observed outcome. A prominent role in these methods is played by
cross-validation which compares predictions to actual outcomes in test samples,
in order to select the level of complexity of the model that provides the best
predictive power. Our method is closely related, but it differs in that it is
tailored for predicting causal effects of a treatment rather than a unit's
outcome. The challenge is that the "ground truth" for a causal effect is not
observed for any individual unit: we observe the unit with the treatment, or
without the treatment, but not both at the same time. Thus, it is not obvious
how to use cross-validation to determine whether a causal effect has been
accurately predicted. We propose several novel cross-validation criteria for
this problem and demonstrate through simulations the conditions under which
they perform better than standard methods for the problem of causal effects. We
then apply the method to a large-scale field experiment re-ranking results on a
search engine
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