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. 2019 Apr:89:2445-2453.

Interpretable Almost-Exact Matching for Causal Inference

Awa Dieng  1 , Yameng Liu  1 , Sudeepa Roy  1 , Cynthia Rudin  1 , Alexander Volfovsky  1
Affiliations

Interpretable Almost-Exact Matching for Causal Inference

Awa Dieng et al. Proc Mach Learn Res. 2019 Apr.

Abstract

Matching methods are heavily used in the social and health sciences due to their interpretability. We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. The method proposed in this work aims to match units on a weighted Hamming distance, taking into account the relative importance of the covariates; the algorithm aims to match units on as many relevant variables as possible. To do this, the algorithm creates a hierarchy of covariate combinations on which to match (similar to downward closure), in the process solving an optimization problem for each unit in order to construct the optimal matches. The algorithm uses a single dynamic program to solve all of the units' optimization problems simultaneously. Notable advantages of our method over existing matching procedures are its high-quality interpretable matches, versatility in handling different data distributions that may have irrelevant variables, and ability to handle missing data by matching on as many available covariates as possible.

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Figures

Figure 1:
Figure 1:
Estimated CATT vs. True CATT (Conditional Average Treatment Effect on the Treated). DAME and FLAME perfectly estimate the CATTs before dropping important covariates. DAME matches all units without dropping important covariates, but FLAME needs to stop early in order to avoid poor matches. All other methods are sensitive to irrelevant covariates and give poor estimates. The two numbers on each plot are the number of matched units and MSE.
Figure 2:
Figure 2:
DAME makes higher quality matches early on. Rows correspond to stopping thresholds (top row 30%, bottom row 50%). DAME matches on more covariates than FLAME, yielding lower MSE from matched groups.
Figure 3:
Figure 3:
Run-time comparison between DAME FLAME, and brute force. Left: varying number of units. Right: varying number of covariates.
Figure 4:
Figure 4:
Number Matched: Number of units matched per covariates for the BTC data
Figure 5:
Figure 5:
Histogram of estimated CATE by DAME. For individuals where the CATE is negative, it means that BTC was estimated to reduce crime.
Figure 6:
Figure 6:
Comparison between DAME and SVM-based method
See this image and copyright information in PMC

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