This paper presents a novel nonlinear regression model for estimating heterogeneous treatment effects from observational data, geared specifically towards situations with small effect sizes, heterogeneous effects, and strong confounding. Standard nonlinear regression models, which may work quite well for prediction, have two notable weaknesses when used to estimate heterogeneous treatment effects. First, they can yield badly biased estimates of treatment effects when fit to data with strong confounding. The Bayesian causal forest model presented in this paper avoids this problem by directly incorporating an estimate of the propensity function in the specification of the response model, implicitly inducing a covariate-dependent prior on the regression function. Second, standard approaches to response surface modeling do not provide adequate control over the strength of regularization over effect heterogeneity. The Bayesian causal forest model permits treatment effect heterogeneity to be regularized separately from the prognostic effect of control variables, making it possible to informatively "shrink to homogeneity". We illustrate these benefits via the reanalysis of an observational study assessing the causal effects of smoking on medical expenditures as well as extensive simulation studies.

Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects

Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects

There is a lack of methodological results to design efficient Markov chain Monte Carlo ( MCMC) algorithms for statistical models with discrete-valued high-dimensional parameters. Motivated by this ...

Informed proposals for local MCMC in discrete spaces

Many modern clustering methods scale well to a large number of data points, N, but not to a large number of clusters, K. This paper introduces PERCH, a new non-greedy, incremental algorithm for hierarchical clustering that scales to both massive N and K---a problem setting we term extreme clustering. Our algorithm efficiently routes new data points to the leaves of an incrementally-built tree. Motivated by the desire for both accuracy and speed, our approach performs tree rotations for the sake of enhancing subtree purity and encouraging balancedness. We prove that, under a natural separability assumption, our non-greedy algorithm will produce trees with perfect dendrogram purity regardless of data arrival order. Our experiments demonstrate that PERCH constructs more accurate trees than other tree-building clustering algorithms and scales well with both N and K, achieving a higher quality clustering than the strongest flat clustering competitor in nearly half the time.

https://dl.acm.org/doi/pdf/10.1145/3097983.3098079

A Hierarchical Algorithm for Extreme Clustering

Storing data in synthetic DNA offers the possibility of improving information density and durability by several orders of magnitude compared to current storage technologies. However, DNA data storage requires a computationally intensive process to retrieve the data. In particular, a crucial step in the data retrieval pipeline involves clustering billions of strings with respect to edit distance. Datasets in this domain have many notable properties, such as containing a very large number of small clusters that are well-separated in the edit distance metric space. In this regime, existing algorithms are unsuitable because of either their long running time or low accuracy. To address this issue, we present a novel distributed algorithm for approximately computing the underlying clusters. Our algorithm converges efficiently on any dataset that satisfies certain separability properties, such as those coming from DNA data storage systems. We also prove that, under these assumptions, our algorithm is robust to outliers and high levels of noise. We provide empirical justification of the accuracy, scalability, and convergence of our algorithm on real and synthetic data. Compared to the state-of-the-art algorithm for clustering DNA sequences, our algorithm simultaneously achieves higher accuracy and a 1000x speedup on three real datasets.

/pdf/clustering-billions-of-reads-for-dna-data-storage-1dv6bkfqe8.pdf

Clustering Billions of Reads for DNA Data Storage

Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models However, for some applications, this assumption is inappropriate For example, when performing entity resolution, the size of each cluster should be unrelated to the size of the data set, and each cluster should contain a negligible fraction of the total number of data points These applications require models that yield clusters whose sizes grow sublinearly with the size of the data set We address this requirement by defining the microclustering property and introducing a new class of models that can exhibit this property We compare models within this class to two commonly used clustering models using four entity-resolution data sets

/pdf/flexible-models-for-microclustering-with-application-to-owa8aeuzvq.pdf

Flexible Models for Microclustering with Application to Entity Resolution

Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models. However, for some applications, this assumption is inappropriate. For example, when performing entity resolution, the size of each cluster should be unrelated to the size of the data set, and each cluster should contain a negligible fraction of the total number of data points. These applications require models that yield clusters whose sizes grow sublinearly with the size of the data set. We address this requirement by defining the microclustering property and introducing a new class of models that can exhibit this property. We compare models within this class to two commonly used clustering models using four entity-resolution data sets.

Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models. However, for some tasks, this assumption is undesirable. For example, when performing entity resolution, the size of each cluster is often unrelated to the size of the data set. Consequently, each cluster contains a negligible fraction of the total number of data points. Such tasks therefore require models that yield clusters whose sizes grow sublinearly with the size of the data set. We address this requirement by defining the \emph{microclustering property} and introducing a new model that exhibits this property. We compare this model to several commonly used clustering models by checking model fit using real and simulated data sets.

/pdf/microclustering-when-the-cluster-sizes-grow-sublinearly-with-13lkkpdebf.pdf

Microclustering: When the Cluster Sizes Grow Sublinearly with the Size of the Data Set

We develop a Gaussian-process mixture model for heterogeneous treatment effect estimation that leverages the use of transformed outcomes. The approach we will present attempts to improve point estimation and uncertainty quantification relative to past work that has used transformed variable related methods as well as traditional outcome modeling. Earlier work on modeling treatment effect heterogeneity using transformed outcomes has relied on tree based methods such as single regression trees and random forests. Under the umbrella of non-parametric models, outcome modeling has been performed using Bayesian additive regression trees and various flavors of weighted single trees. These approaches work well when large samples are available, but suffer in smaller samples where results are more sensitive to model misspecification - our method attempts to garner improvements in inference quality via a correctly specified model rooted in Bayesian non-parametrics. Furthermore, while we begin with a model that assumes that the treatment assignment mechanism is known, an extension where it is learnt from the data is presented for applications to observational studies. Our approach is applied to simulated and real data to demonstrate our theorized improvements in inference with respect to two causal estimands: the conditional average treatment effect and the average treatment effect. By leveraging our correctly specified model, we are able to more accurately estimate the treatment effects while reducing their variance.

Gaussian Process Mixtures for Estimating Heterogeneous Treatment Effects

Accurately monitoring the number of individuals inside a building is vital to limiting COVID-19 transmission. Low adoption of contact tracing apps due to privacy concerns has increased pervasiveness of passive digital tracking alternatives. Large arrays of WiFi access points can conveniently track mobile devices on university and industry campuses. The CrowdMap system employed by the University of Southern California enables such tracking by collecting aggregate statistics from connections to access points around campus. However, since these devices can be used to infer the movement of individuals, there is still a significant risk that even aggregate occupancy statistics will violate the location privacy of individuals. We examine the use of Differential Privacy in reporting statistics from this system as measured using point and range count queries. We propose discretization schemes to model the positions of users given only user connections to WiFi access points. Using this information we are able to release accurate counts of occupants in areas of campus buildings such as labs, hallways, and large discussion halls with minimized risk to individual users' privacy.

Abbas Zaidi

Papers

Flexible Models for Microclustering with Application to Entity Resolution

Flexible Models for Microclustering with Application to Entity Resolution

Microclustering: When the Cluster Sizes Grow Sublinearly with the Size of the Data Set

Gaussian Process Mixtures for Estimating Heterogeneous Treatment Effects

Differentially Private Occupancy Monitoring from WiFi Access Points