Zijun Gao

Zijun Gao is a Ph.D. candidate in the Statistics Department at Stanford University advised by Professor Trevor Hastie. Prior to attending Stanford, she obtained a Bachelor of Science in Mathematics from Tsinghua University, China.

Her major research interest is causal inference with heterogeneity. Her works focus on developing efficient methodologies of estimating and validating heterogeneous causal effects with applications of large-scale healthcare databases. She also works on real-world data motivated topics such as conditional density estimation and batched bandit problem.

news

Feb 2, 2022	Our JMLR paper “LinCDE: Conditional Density Estimation via Lindsey’s Method” is now online!
Oct 9, 2021	R package `LinCDE` is released!
Sep 30, 2020	Zijun Gao receives Ric Weiland Graduate Fellowship!

selected publications

DINA

Estimating Heterogeneous Treatment Effects for General Responses

Gao, Zijun, and Hastie, Trevor

submitted to Journal of the Royal Statistical Society: Series B 2022

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Heterogeneous treatment effect models allow us to compare treatments at subgroup and individual levels, and are of increasing popularity in applications like personalized medicine, advertising, and education. In this talk, we first survey different causal estimands used in practice, which focus on estimating the difference in conditional means. We then propose DINA — the difference in natural parameters — to quantify heterogeneous treatment effect in exponential families and the Cox model. For binary outcomes and survival times, DINA is both convenient and more practical for modeling the influence of covariates on the treatment effect. Second, we introduce a meta-algorithm for DINA, which allows practitioners to use powerful off-the-shelf machine learning tools for the estimation of nuisance functions, and which is also statistically robust to errors in inaccurate nuisance function estimation. We demonstrate the efficacy of our method combined with various machine learning base-learners on simulated and real datasets.
LinCDE

Conditional Density Estimation via Lindsey’s Method

Gao, Zijun, and Hastie, Trevor

Journal of Machine Learning Research 2022

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Conditional density estimation is a fundamental problem in statistics, with scientific and practical applications in biology, economics, finance and environmental studies, to name a few. In this paper, we propose a conditional density estimator based on gradient boosting and Lindsey’s method (LinCDE). LinCDE admits flexible modeling of the density family and can capture distributional characteristics like modality and shape. In particular, when suitably parametrized, LinCDE will produce smooth and non-negative density estimates. Furthermore, like boosted regression trees, LinCDE does automatic feature selection. We demonstrate LinCDE’s efficacy through extensive simulations and several real data examples.
Assessment of heterogeneous treatment effect estimation accuracy via matching

Gao, Zijun, Hastie, Trevor, and Tibshirani, Robert

Statistics in Medicine 2021

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We study the assessment of the accuracy of heterogeneous treatment effect (HTE) estimation, where the HTE is not directly observable so standard computation of prediction errors is not applicable. To tackle the difficulty, we propose an assessment approach by constructing pseudo-observations of the HTE based on matching. Our contributions are three-fold: first, we introduce a novel matching distance derived from proximity scores in random forests; second, we formulate the matching problem as an average minimum-cost flow problem and provide an efficient algorithm; third, we propose a match-then-split principle for the assessment with cross-validation. We demonstrate the efficacy of the assessment approach on synthetic data and data generated from a real dataset.
Minimax optimal nonparametric estimation of heterogeneous treatment effects

Gao, Zijun, and Han, Yanjun

Conference on Neural Information Processing Systems (NeurIPS) (Spotlight) 2020

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A central goal of causal inference is to detect and estimate the treatment effects of a given treatment or intervention on an outcome variable of interest, where a member known as the heterogeneous treatment effect (HTE) is of growing popularity in recent practical applications such as the personalized medicine. In this paper, we model the HTE as a smooth nonparametric difference between two less smooth baseline functions, and determine the tight statistical limits of the nonparametric HTE estimation as a function of the covariate geometry. In particular, a two-stage nearest-neighbor-based estimator throwing away observations with poor matching quality is near minimax optimal. We also establish the tight dependence on the density ratio without the usual assumption that the covariate densities are bounded away from zero, where a key step is to employ a novel maximal inequality which could be of independent interest.
Batched multi-armed bandits problem

Gao, Zijun, Han, Yanjun, Ren, Zhimei, and Zhou, Zhengqing

Conference on Neural Information Processing Systems (NeurIPS) (Oral) 2019

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In this paper, we study the multi-armed bandit problem in the batched setting where the employed policy must split data into a small number of batches. While the minimax regret for the two-armed stochastic bandits has been completely characterized in \citeperchet2016batched, the effect of the number of arms on the regret for the multi-armed case is still open. Moreover, the question whether adaptively chosen batch sizes will help to reduce the regret also remains underexplored. In this paper, we propose the BaSE (batched successive elimination) policy to achieve the rate-optimal regrets (within logarithmic factors) for batched multi-armed bandits, with matching lower bounds even if the batch sizes are determined in an adaptive manner.