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Register a new userMatching on What Matters: A Pseudo-Metric Learning Approach to Matching Estimation in High Dimensions
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When pre-processing observational data via matching, we seek to approximate each unit with maximally similar peers that had an alternative treatment status--essentially replicating a randomized block design. However, as one considers a growing number of continuous features, a curse of dimensionality applies making asymptotically valid inference impossible (Abadie and Imbens, 2006). The alternative of ignoring plausibly relevant features is certainly no better, and the resulting trade-off substantially limits the application of matching methods to wide datasets. Instead, Li and Fu (2017) recasts the problem of matching in a metric learning framework that maps features to a low-dimensional space that facilitates closer matches while still capturing important aspects of unit-level heterogeneity. However, that method lacks key theoretical guarantees and can produce inconsistent estimates in cases of heterogeneous treatment effects. Motivated by straightforward extension of existing results in the matching literature, we present alternative techniques that learn latent matching features through either MLPs or through siamese neural networks trained on a carefully selected loss function. We benchmark the resulting alternative methods in simulations as well as against two experimental data sets--including the canonical NSW worker training program data set--and find superior performance of the neural-net-based methods.
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This paper provides an introduction to structural estimation methods for matching markets with transferable utility.
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the `labels are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm.
Score matching is a popular method for estimating unnormalized statistical models. However, it has been so far limited to simple, shallow models or low-dimensional data, due to the difficulty of computing the Hessian of log-density functions. We show this difficulty can be mitigated by projecting the scores onto random vectors before comparing them. This objective, called sliced score matching, only involves Hessian-vector products, which can be easily implemented using reverse-mode automatic differentiation. Therefore, sliced score matching is amenable to more complex models and higher dimensional data compared to score matching. Theoretically, we prove the consistency and asymptotic normality of sliced score matching estimators. Moreover, we demonstrate that sliced score matching can be used to learn deep score estimators for implicit distributions. In our experiments, we show sliced score matching can learn deep energy-based models effectively, and can produce accurate score estimates for applications such as variational inference with implicit distributions and training Wasserstein Auto-Encoders.
Matching two different sets of items, called heterogeneous set-to-set matching problem, has recently received attention as a promising problem. The difficulties are to extract features to match a correct pair of different sets and also preserve two types of exchangeability required for set-to-set matching: the pair of sets, as well as the items in each set, should be exchangeable. In this study, we propose a novel deep learning architecture to address the abovementioned difficulties and also an efficient training framework for set-to-set matching. We evaluate the methods through experiments based on two industrial applications: fashion set recommendation and group re-identification. In these experiments, we show that the proposed method provides significant improvements and results compared with the state-of-the-art methods, thereby validating our architecture for the heterogeneous set matching problem.
We study the minimum-cost metric perfect matching problem under online i.i.d arrivals. We are given a fixed metric with a server at each of the points, and then requests arrive online, each drawn independently from a known probability distribution over the points. Each request has to be matched to a free server, with cost equal to the distance. The goal is to minimize the expected total cost of the matching. Such stochastic arrival models have been widely studied for the maximization variants of the online matching problem; however, the only known result for the minimization problem is a tight $O(log n)$-competitiveness for the random-order arrival model. This is in contrast with the adversarial model, where an optimal competitive ratio of $O(log n)$ has long been conjectured and remains a tantalizing open question. In this paper, we show improved results in the i.i.d arrival model. We show how the i.i.d model can be used to give substantially better algorithms: our main result is an $O((log log log n)^2)$-competitive algorithm in this model. Along the way we give a $9$-competitive algorithm for the line and tree metrics. Both results imply a strict separation between the i.i.d model and the adversarial and random order models, both for general metrics and these much-studied metrics.
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