arXiv subjects

Matt Goldman

Publications and source records attributed to Matt Goldman.

7 recordsLinked to original sources

arXiv2022

Estimation and Inference on Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels under Weak Dependence

This paper provides estimation and inference methods for a conditional average treatment effects (CATE) characterized by a high-dimensional parameter in both homogeneous cross-sectional and unit-heterogeneous dynamic panel data settings. In our leading example, we model CATE by interacting the base treatment variable with explanatory variables. The first step of our procedure is orthogonalization, where we partial out the controls and unit effects from the outcome and the base treatment and take the cross-fitted residuals. This step uses a novel generic cross-fitting method we design for weakly dependent time series and panel data. This method "leaves out the neighbors" when fitting nuisance components, and we theoretically power it by using Strassen's coupling. As a result, we can rely on any modern machine learning method in the first step, provided it learns the residuals well enough. Second, we construct an orthogonal (or residual) learner of CATE -- the Lasso CATE -- that regresses the outcome residual on the vector of interactions of the residualized treatment with explanatory variables. If the complexity of CATE function is simpler than that of the first-stage regression, the orthogonal learner converges faster than the single-stage regression-based learner. Third, we perform simultaneous inference on parameters of the CATE function using debiasing. We also can use ordinary least squares in the last two steps when CATE is low-dimensional. In heterogeneous panel data settings, we model the unobserved unit heterogeneity as a weakly sparse deviation from Mundlak (1978)'s model of correlated unit effects as a linear function of time-invariant covariates and make use of L1-penalization to estimate these models. We demonstrate our methods by estimating price elasticities of groceries based on scanner data. We note that our results are new even for the cross-sectional (i.i.d) case.

stat.ML↗

arXiv2022

Machine Learning for Variance Reduction in Online Experiments

We consider the problem of variance reduction in randomized controlled trials, through the use of covariates correlated with the outcome but independent of the treatment. We propose a machine learning regression-adjusted treatment effect estimator, which we call MLRATE. MLRATE uses machine learning predictors of the outcome to reduce estimator variance. It employs cross-fitting to avoid overfitting biases, and we prove consistency and asymptotic normality under general conditions. MLRATE is robust to poor predictions from the machine learning step: if the predictions are uncorrelated with the outcomes, the estimator performs asymptotically no worse than the standard difference-in-means estimator, while if predictions are highly correlated with outcomes, the efficiency gains are large. In A/A tests, for a set of 48 outcome metrics commonly monitored in Facebook experiments the estimator has over 70% lower variance than the simple difference-in-means estimator, and about 19% lower variance than the common univariate procedure which adjusts only for pre-experiment values of the outcome.

stat.ML↗

arXiv2020

Network experimentation at scale

We describe our framework, deployed at Facebook, that accounts for interference between experimental units through cluster-randomized experiments. We document this system, including the design and estimation procedures, and detail insights we have gained from the many experiments that have used this system at scale. We introduce a cluster-based regression adjustment that substantially improves precision for estimating global treatment effects as well as testing for interference as part of our estimation procedure. With this regression adjustment, we find that imbalanced clusters can better account for interference than balanced clusters without sacrificing accuracy. In addition, we show how logging exposure to a treatment can be used for additional variance reduction. Interference is a widely acknowledged issue with online field experiments, yet there is less evidence from real-world experiments demonstrating interference in online settings. We fill this gap by describing two case studies that capture significant network effects and highlight the value of this experimentation framework.

cs.SI↗

arXiv2019

Matching on What Matters: A Pseudo-Metric Learning Approach to Matching Estimation in High Dimensions

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.

econ.EM↗

arXiv2018

Pricing Engine: Estimating Causal Impacts in Real World Business Settings

We introduce the Pricing Engine package to enable the use of Double ML estimation techniques in general panel data settings. Customization allows the user to specify first-stage models, first-stage featurization, second stage treatment selection and second stage causal-modeling. We also introduce a DynamicDML class that allows the user to generate dynamic treatment-aware forecasts at a range of leads and to understand how the forecasts will vary as a function of causally estimated treatment parameters. The Pricing Engine is built on Python 3.5 and can be run on an Azure ML Workbench environment with the addition of only a few Python packages. This note provides high-level discussion of the Double ML method, describes the packages intended use and includes an example Jupyter notebook demonstrating application to some publicly available data. Installation of the package and additional technical documentation is available at $\href{https://github.com/bquistorff/pricingengine}{github.com/bquistorff/pricingengine}$.

econ.EM↗

arXiv2017

Comparing distributions by multiple testing across quantiles or CDF values

When comparing two distributions, it is often helpful to learn at which quantiles or values there is a statistically significant difference. This provides more information than the binary "reject" or "do not reject" decision of a global goodness-of-fit test. Framing our question as multiple testing across the continuum of quantiles $τ\in(0,1)$ or values $r\in\mathbb{R}$, we show that the Kolmogorov--Smirnov test (interpreted as a multiple testing procedure) achieves strong control of the familywise error rate. However, its well-known flaw of low sensitivity in the tails remains. We provide an alternative method that retains such strong control of familywise error rate while also having even sensitivity, i.e., equal pointwise type I error rates at each of $n\to\infty$ order statistics across the distribution. Our one-sample method computes instantly, using our new formula that also instantly computes goodness-of-fit $p$-values and uniform confidence bands. To improve power, we also propose stepdown and pre-test procedures that maintain control of the asymptotic familywise error rate. One-sample and two-sample cases are considered, as well as extensions to regression discontinuity designs and conditional distributions. Simulations, empirical examples, and code are provided.

math.ST↗

arXiv2016

Fractional order statistic approximation for nonparametric conditional quantile inference

Using and extending fractional order statistic theory, we characterize the $O(n^{-1})$ coverage probability error of the previously proposed confidence intervals for population quantiles using $L$-statistics as endpoints in Hutson (1999). We derive an analytic expression for the $n^{-1}$ term, which may be used to calibrate the nominal coverage level to get $O\bigl(n^{-3/2}[\log(n)]^3\bigr)$ coverage error. Asymptotic power is shown to be optimal. Using kernel smoothing, we propose a related method for nonparametric inference on conditional quantiles. This new method compares favorably with asymptotic normality and bootstrap methods in theory and in simulations. Code is available from the second author's website for both unconditional and conditional methods, simulations, and empirical examples.

math.ST↗