arXiv subjects

Jingang Miao

Publications and source records attributed to Jingang Miao.

3 recordsLinked to original sources

arXiv2022

Privacy-Preserving Inference on the Ratio of Two Gaussians Using Sums

The ratio of two Gaussians is useful in many contexts of statistical inference. We discuss statistically valid inference of the ratio under Differential Privacy (DP). We use the delta method to derive the asymptotic distribution of the ratio estimator and use the Gaussian mechanism to provide (epsilon, delta)-DP guarantees. Like many statistics, quantities involved in the inference of a ratio can be re-written as functions of sums, and sums are easy to work with for many reasons. In the context of DP, the sensitivity of a sum is easy to calculate. We focus on getting the correct coverage probability of 95\% confidence intervals (CIs) of the DP ratio estimator. Our simulations show that the no-correction method, which ignores the DP noise, gives CIs that are too narrow to provide proper coverage for small samples. In our specific simulation scenario, the coverage of 95% CIs can be as low as below 10%. We propose two methods to mitigate the under-coverage issue, one based on Monte Carlo simulation and the other based on analytical correction. We show that the CIs of our methods have much better coverage with reasonable privacy budgets. In addition, our methods can handle weighted data, when the weights are fixed and bounded.

stat.ME↗

arXiv2019

A Deep Probabilistic Model for Customer Lifetime Value Prediction

Accurate predictions of customers' future lifetime value (LTV) given their attributes and past purchase behavior enables a more customer-centric marketing strategy. Marketers can segment customers into various buckets based on the predicted LTV and, in turn, customize marketing messages or advertising copies to serve customers in different segments better. Furthermore, LTV predictions can directly inform marketing budget allocations and improve real-time targeting and bidding of ad impressions. One challenge of LTV modeling is that some customers never come back, and the distribution of LTV can be heavy-tailed. The commonly used mean squared error (MSE) loss does not accommodate the significant fraction of zero value LTV from one-time purchasers and can be sensitive to extremely large LTV's from top spenders. In this article, we model the distribution of LTV given associated features as a mixture of zero point mass and lognormal distribution, which we refer to as the zero-inflated lognormal (ZILN) distribution. This modeling approach allows us to capture the churn probability and account for the heavy-tailedness nature of LTV at the same time. It also yields straightforward uncertainty quantification of the point prediction. The ZILN loss can be used in both linear models and deep neural networks (DNN). For model evaluation, we recommend the normalized Gini coefficient to quantify model discrimination and decile charts to assess model calibration. Empirically, we demonstrate the predictive performance of our proposed model on two real-world public datasets.

stat.AP↗

arXiv2019

A Python Library For Empirical Calibration

Dealing with biased data samples is a common task across many statistical fields. In survey sampling, bias often occurs due to unrepresentative samples. In causal studies with observational data, the treated versus untreated group assignment is often correlated with covariates, i.e., not random. Empirical calibration is a generic weighting method that presents a unified view on correcting or reducing the data biases for the tasks mentioned above. We provide a Python library EC to compute the empirical calibration weights. The problem is formulated as convex optimization and solved efficiently in the dual form. Compared to existing software, EC is both more efficient and robust. EC also accommodates different optimization objectives, supports weight clipping, and allows inexact calibration, which improves usability. We demonstrate its usage across various experiments with both simulated and real-world data.

stat.CO↗