Zhi Geng

Yan Zeng, Shenglan Nie, Feng Xie et al.

Imitation learning from demonstrations usually suffers from the confounding effects of unmeasured variables (i.e., unmeasured confounders) on the states and actions. If ignoring them, a biased estimation of the policy would be entailed. To break up this confounding gap, in this paper, we take the best of the strong power of instrumental variables (IV) and propose a Confounded Causal Imitation Learning (C2L) model. This model accommodates confounders that influence actions across multiple timesteps, rather than being restricted to immediate temporal dependencies. We develop a two-stage imitation learning framework for valid IV identification and policy optimization. In particular, in the first stage, we construct a testing criterion based on the defined pseudo-variable, with which we achieve identifying a valid IV for the C2L models. Such a criterion entails the sufficient and necessary identifiability conditions for IV validity. In the second stage, with the identified IV, we propose two candidate policy learning approaches: one is based on a simulator, while the other is offline. Extensive experiments verified the effectiveness of identifying the valid IV as well as learning the policy.

Yinan Lin, Wen Zhou, Zhi Geng et al.

In traditional logistic regression models, the link function is often assumed to be linear and continuous in predictors. Here, we consider a threshold model that all continuous features are discretized into ordinal levels, which further determine the binary responses. Both the threshold points and regression coefficients are unknown and to be estimated. For high dimensional data, we propose a fusion penalized logistic threshold regression (FILTER) model, where a fused lasso penalty is employed to control the total variation and shrink the coefficients to zero as a method of variable selection. Under mild conditions on the estimate of unknown threshold points, we establish the non-asymptotic error bound for coefficient estimation and the model selection consistency. With a careful characterization of the error propagation, we have also shown that the tree-based method, such as CART, fulfill the threshold estimation conditions. We find the FILTER model is well suited in the problem of early detection and prediction for chronic disease like diabetes, using physical examination data. The finite sample behavior of our proposed method are also explored and compared with extensive Monte Carlo studies, which supports our theoretical discoveries.