Robust and Heterogenous Odds Ratio: Estimating Price Sensitivity for Unbought Items

Problem definition: Mining for heterogeneous responses to an intervention is a crucial step for data-driven operations, for instance to personalize treatment or pricing. We investigate how to estimate price sensitivity from transaction-level data. In causal inference terms, we estimate heterogeneous treatment effects when (a) the response to treatment (here, whether a customer buys a product) is binary, and (b) treatment assignments are partially observed (here, full information is only available for purchased items). Methodology/Results: We propose a recursive partitioning procedure to estimate heterogeneous odds ratio, a widely used measure of treatment effect in medicine and social sciences. We integrate an adversarial imputation step to allow for robust inference even in presence of partially observed treatment assignments. We validate our methodology on synthetic data and apply it to three case studies from political science, medicine, and revenue management. Managerial Implications: Our robust heterogeneous odds ratio estimation method is a simple and intuitive tool to quantify heterogeneity in patients or customers and personalize interventions, while lifting a central limitation in many revenue management data

Generic machine learning inference on heterogenous treatment effects in randomized experiments

We propose strategies to estimate and make inference on key features of heterogeneous effects in randomized experiments. These key features include best linear predictors of the effects using machine learning proxies, average effects sorted by impact groups, and average characteristics of most and least impacted units. The approach is valid in high dimensional settings, where the effects are proxied by machine learning methods. We post-process these proxies into the estimates of the key features. Our approach is generic, it can be used in conjunction with penalized methods, deep and shallow neural networks, canonical and new random forests, boosted trees, and ensemble methods. Our approach is agnostic and does not make unrealistic or hard-to-check assumptions; we don’t require conditions for consistency of the ML methods. Estimation and inference relies on repeated data splitting to avoid overfitting and achieve validity. For inference, we take medians of p-values and medians of confidence intervals, resulting from many different data splits, and then adjust their nominal level to guarantee uniform validity. This variational inference method is shown to be uniformly valid and quantifies the uncertainty coming from both parameter estimation and data splitting. The inference method could be of substantial independent interest in many machine learning applications. An empirical application to the impact of micro-credit on economic development illustrates the use of the approach in randomized experiments. An additional application to the impact of the gender discrimination on wages illustrates the potential use of the approach in observational studies, where machine learning methods can be used to condition flexibly on very high-dimensional controls.https://arxiv.org/abs/1712.04802First author draf

2D score based estimation of heterogeneous treatment effects

Statisticians show growing interest in estimating and analyzing heterogeneity in causal effects in observational studies. However, there usually exists a trade-off between accuracy and interpretability for developing a desirable estimator for treatment effects, especially in the case when there are a large number of features in estimation. To make efforts to address the issue, we propose a score-based framework for estimating the Conditional Average Treatment Effect (CATE) function in this paper. The framework integrates two components: (i) leverage the joint use of propensity and prognostic scores in a matching algorithm to obtain a proxy of the heterogeneous treatment effects for each observation, (ii) utilize non-parametric regression trees to construct an estimator for the CATE function conditioning on the two scores. The method naturally stratifies treatment effects into subgroups over a 2d grid whose axis are the propensity and prognostic scores. We conduct benchmark experiments on multiple simulated data and demonstrate clear advantages of the proposed estimator over state of the art methods. We also evaluate empirical performance in real-life settings, using two observational data from a clinical trial and a complex social survey, and interpret policy implications following the numerical results

Generic Machine Learning Inference on Heterogenous Treatment Effects in Randomized Experiments

We propose strategies to estimate and make inference on key features of heterogeneous effects in randomized experiments. These key features include best linear predictors of the effects using machine learning proxies, average effects sorted by impact groups, and average characteristics of most and least impacted units. The approach is valid in high dimensional settings, where the effects are proxied by machine learning methods. We post-process these proxies into the estimates of the key features. Our approach is generic, it can be used in conjunction with penalized methods, deep and shallow neural networks, canonical and new random forests, boosted trees, and ensemble methods. It does not rely on strong assumptions. In particular, we don't require conditions for consistency of the machine learning methods. Estimation and inference relies on repeated data splitting to avoid overfitting and achieve validity. For inference, we take medians of p-values and medians of confidence intervals, resulting from many different data splits, and then adjust their nominal level to guarantee uniform validity. This variational inference method is shown to be uniformly valid and quantifies the uncertainty coming from both parameter estimation and data splitting. We illustrate the use of the approach with two randomized experiments in development on the effects of microcredit and nudges to stimulate immunization demand.Comment: 53 pages, 6 figures, 15 table

On Interpreting Eddy Covariance In Small Area Agricultural Situations With Contrasting Site Management.

This dissertation examined the carbon sequestration potential of a low C:N soil amendment and its incorporation into the soil over a rolling agricultural field. A segmented planar fit was developed to assess and correct the systematic errors the topography introduces on the carbon dioxide fluxes. The carbon dioxide fluxes were then be partitioned into gross primary productivity and soil respiration to understand the influence of the contrasting management practices, using flux variance partitioning. Concomitant with the partitioning, high resolution temporal and spatial scale remote sensing images were interpolated and standardized to conduct hypothesis testing for treatment effects

Robust and Heterogenous Odds Ratio: Estimating Price Sensitivity for Unbought Items

Problem definition: Mining for heterogeneous responses to an intervention is a crucial step for data-driven operations, for instance to personalize treatment or pricing. We investigate how to estimate price sensitivity from transaction-level data. In causal inference terms, we estimate heterogeneous treatment effects when (a) the response to treatment (here, whether a customer buys a product) is binary, and (b) treatment assignments are partially observed (here, full information is only available for purchased items). Methodology/Results: We propose a recursive partitioning procedure to estimate heterogeneous odds ratio, a widely used measure of treatment effect in medicine and social sciences. We integrate an adversarial imputation step to allow for robust estimation even in presence of partially observed treatment assignments. We validate our methodology on synthetic data and apply it to three case studies from political science, medicine, and revenue management. Managerial Implications: Our robust heterogeneous odds ratio estimation method is a simple and intuitive tool to quantify heterogeneity in patients or customers and personalize interventions, while lifting a central limitation in many revenue management data