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Why Propensity Scores Should Not Be Used for Matching
We show that propensity score matching (PSM), an enormously popular method of preprocessing data for causal inference, often accomplishes the opposite of its intended goal—thus increasing imbalance, inefficiency, model dependence, and bias. The weakness of PSM comes from its attempts to approximate a completely randomized experiment, rather than, as with other matching methods, a more efficient fully blocked randomized experiment. PSM is thus uniquely blind to the often large portion of imbalance that can be eliminated by approximating full blocking with other matching methods. Moreover, in data balanced enough to approximate complete randomization, either to begin with or after pruning some observations, PSM approximates random matching which, we show, increases imbalance even relative to the original data. Although these results suggest researchers replace PSM with one of the other available matching methods, propensity scores have other productive uses.
Journal Article
Image Matching from Handcrafted to Deep Features: A Survey
As a fundamental and critical task in various visual applications, image matching can identify then correspond the same or similar structure/content from two or more images. Over the past decades, growing amount and diversity of methods have been proposed for image matching, particularly with the development of deep learning techniques over the recent years. However, it may leave several open questions about which method would be a suitable choice for specific applications with respect to different scenarios and task requirements and how to design better image matching methods with superior performance in accuracy, robustness and efficiency. This encourages us to conduct a comprehensive and systematic review and analysis for those classical and latest techniques. Following the feature-based image matching pipeline, we first introduce feature detection, description, and matching techniques from handcrafted methods to trainable ones and provide an analysis of the development of these methods in theory and practice. Secondly, we briefly introduce several typical image matching-based applications for a comprehensive understanding of the significance of image matching. In addition, we also provide a comprehensive and objective comparison of these classical and latest techniques through extensive experiments on representative datasets. Finally, we conclude with the current status of image matching technologies and deliver insightful discussions and prospects for future works. This survey can serve as a reference for (but not limited to) researchers and engineers in image matching and related fields.
Journal Article
Dynamic Matching in School Choice: Efficient Seat Reassignment After Late Cancellations
In the school choice market, where scarce public school seats are assigned to students, a key operational issue is how to reassign seats that are vacated after an initial round of centralized assignment. Practical solutions to the reassignment problem must be simple to implement, truthful, and efficient while also alleviating costly student movement between schools. We propose and axiomatically justify a class of reassignment mechanisms, the permuted lottery deferred acceptance (PLDA) mechanisms. Our mechanisms generalize the commonly used deferred acceptance (DA) school choice mechanism to a two-round setting and retain its desirable incentive and efficiency properties. School choice systems typically run DA with a lottery number assigned to each student to break ties in school priorities. We show that under natural conditions on demand, the second-round tie-breaking lottery can be correlated arbitrarily with that of the first round without affecting allocative welfare and that
reversing
the lottery order between rounds minimizes reassignment among all PLDA mechanisms. Empirical investigations based on data from New York City high school admissions support our theoretical findings.
This paper was accepted by Gad Allon, operations management.
Journal Article
Higher Market Thickness Reduces Matching Rate in Online Platforms: Evidence from a Quasiexperiment
Market thickness is a key parameter that can make or break a platform’s business model. Thicker markets can offer more opportunities for participants to meet and higher chances that a potential match exists. However, they can also be vulnerable to potential search frictions. In this paper, using data from an online peer-to-peer holiday property rental platform, we aim to identify and measure the causal impact of market thickness on matching rates. In particular, we exploit an exogenous shock to market size caused by a one-time migration of listings from other platforms, which gives rise to a quasiexperimental design. We find that increased market thickness actually leads to lower matching rates. Keeping search technology and other factors constant, doubling market size leads to a 15.4% reduction in traveler confirmation rate and a 15.9% reduction in host occupancy rate. As a result, the platform lost 5.6% of potential matches because of the increased market size. We attribute the effect to increased search friction: travelers’ search intensity increases by 18.3% when market size doubles. This effect is especially prominent when the matching needs to take place within a limited time. Our results offer insights for future empirical and theoretical research on matching markets. They also highlight that is important for platform owners to watch out for increased search frictions as markets grow and invest in search technologies to facilitate more efficient search.
This paper was accepted by Charles Corbett, operations management.
Journal Article
THE IMPLEMENTATION DUALITY
Conjugate duality relationships are pervasive in matching and implementation problems and provide much of the structure essential for characterizing stable matches and implementable allocations in models with quasilinear (or transferable) utility. In the absence of quasilinearity, a more abstract duality relationship, known as a Galois connection, takes the role of (generalized) conjugate duality. While weaker, this duality relationship still induces substantial structure. We show that this structure can be used to extend existing results for, and gain new insights into, adverse-selection principalagent problems and two-sided matching problems without quasilinearity.
Journal Article
On some hard and some tractable cases of the maximum acyclic matching problem
Three well-studied types of subgraph-restricted matchings are induced matchings, uniquely restricted matchings, and acyclic matchings. While it is hard to determine the maximum size of a matching of each of these types, whether some given graph has a maximum matching that is induced or has a maximum matching that is uniquely restricted, can both be decided efficiently. In contrast to that we show that deciding whether a given bipartite graph of maximum degree at most four has a maximum matching that is acyclic is NP-complete. Furthermore, we show that maximum weight acyclic matchings can be determined efficiently for \\[P_4\\]-free graphs and \\[2P_3\\]-free graphs, and we characterize the graphs for which every maximum matching is acyclic.
Journal Article
Stable Matching with Proportionality Constraints
School choice programs seek to give students the option to choose their school but also close an opportunity gap. To be fair in the assignment of students, it is usually argued that the assignment of students to schools should be stable. This second concern is usually expressed in terms of proportions. As an example, in 1989, the city of White Plains, New York, required each school to have the same proportions of Blacks, Hispanics, and “others,” a term that includes Whites and Asians. Satisfying both these concerns at the same time is difficult. Prior work replaces the proportions by numbers related to the capacity of school, but this assumes each school is operating at full capacity, which is often not the case. In this paper, we treat such proportionality constraints as soft but provide ex post guarantees on how well the constraints are satisfied while preserving stability.
The problem of finding stable matches that meet distributional concerns is usually formulated by imposing side constraints whose “right-hand sides” are absolute numbers specified before the preferences or number of agents on the “proposing” side are known. In many cases, it is more natural to express the relevant constraints as proportions. We treat such constraints as soft but provide ex post guarantees on how well the constraints are satisfied while preserving stability. Our technique requires an extension of Scarf’s lemma, which is of independent interest.
Journal Article
Using NSGA-III for optimising biomedical ontology alignment
To support semantic inter-operability between the biomedical information systems, it is necessary to determine the correspondences between the heterogeneous biomedical concepts, which is commonly known as biomedical ontology matching. Biomedical concepts are usually complex and ambiguous, which makes matching biomedical ontologies a challenge. Since none of the similarity measures can distinguish the heterogeneous biomedical concepts in any context independently, usually several similarity measures are applied together to determine the biomedical concepts mappings. However, the ignorance of the effects brought about by different biomedical concept mapping's preference on the similarity measures significantly reduces the alignment's quality. In this study, a non-dominated sorting genetic algorithm (NSGA)-III-based biomedical ontology matching technique is proposed to effectively match the biomedical ontologies, which first utilises an ontology partitioning technique to transform the large-scale biomedical ontology matching problem into several ontology segment-matching problems, and then uses NSGA-III to determine the optimal alignment without tuning the aggregating weights. The experiment is conducted on the anatomy track and large biomedic ontologies track which are provided by the Ontology Alignment Evaluation Initiative (OAEI), and the comparisons with OAEI's participants show the effectiveness of the authors' approach.
Journal Article
Ignorance Is Almost Bliss: Near-Optimal Stochastic Matching with Few Queries
We study the stochastic matching problem with the goal of finding a maximum matching in a graph whose edges are unknown but can be accessed via queries. This is a special case of stochastic
k
-cycle packing, in which the problem is to find a maximum packing of cycles, each of which exists with some probability. We provide polynomial-time
adaptive
and
nonadaptive
algorithms that provably yield a near-optimal solution, using a number of edge queries that is linear in the number of vertices. We are especially interested in kidney exchange, with which pairs of patients with end-stage renal failure and their willing but incompatible donors participate in a mechanism that performs
compatibility tests
between patients and donors and swaps the donors of some patients so that a large number of patients receive compatible kidneys. Because of the significant cost of performing compatibility tests, currently, kidney exchange programs perform at most one compatibility test per patient. Our theoretical results applied to kidney exchange show that, by increasing the number of compatibility tests performed per patient from one to a larger constant, we effectively get the full benefit of exhaustive testing at a fraction of the cost. We show, on both generated and real data from the UNOS nationwide kidney exchange, that even a small number of nonadaptive edge queries per vertex results in large gains in expected successful matches.
Journal Article