Jin Zhu

Borui Tang, Jin Zhu, Junxian Zhu et al.

Analysis of high-dimensional data has led to increased interest in both single index models (SIMs) and the best-subset selection. SIMs provide an interpretable and flexible modeling framework for high-dimensional data, while the best-subset selection aims to find a sparse model from a large set of predictors. However, the best-subset selection in high-dimensional models is known to be computationally intractable. Existing proxy algorithms are appealing but do not yield the bestsubset solution. In this paper, we directly tackle the intractability by proposing a provably scalable algorithm for the best-subset selection in high-dimensional SIMs. We directly proved the subset selection consistency and oracle property for our algorithmic solution, distinguishing it from other state-of-the-art support recovery methods in SIMs. The algorithm comprises a generalized information criterion to determine the support size of the regression coefficients, eliminating the model selection tuning. Moreover, our method does not assume an error distribution or a specific link function and hence is flexible to apply. Extensive simulation results demonstrate that our method is not only computationally efficient but also able to exactly recover the best subset in various settings (e.g., linear regression, Poisson regression, heteroscedastic models).

Jin Zhu, Xueqin Wang, Liyuan Hu et al.

We introduce a new library named abess that implements a unified framework of best-subset selection for solving diverse machine learning problems, e.g., linear regression, classification, and principal component analysis. Particularly, the abess certifiably gets the optimal solution within polynomial times with high probability under the linear model. Our efficient implementation allows abess to attain the solution of best-subset selection problems as fast as or even 20x faster than existing competing variable (model) selection toolboxes. Furthermore, it supports common variants like best group subset selection and $\ell_2$ regularized best-subset selection. The core of the library is programmed in C++. For ease of use, a Python library is designed for conveniently integrating with scikit-learn, and it can be installed from the Python library Index. In addition, a user-friendly R library is available at the Comprehensive R Archive Network. The source code is available at: https://github.com/abess-team/abess.

Hongyi Zhou, Josiah P. Hanna, Jin Zhu et al.

This paper studies off-policy evaluation (OPE) in reinforcement learning with a focus on behavior policy estimation for importance sampling. Prior work has shown empirically that estimating a history-dependent behavior policy can lead to lower mean squared error (MSE) even when the true behavior policy is Markovian. However, the question of why the use of history should lower MSE remains open. In this paper, we theoretically demystify this paradox by deriving a bias-variance decomposition of the MSE of ordinary importance sampling (IS) estimators, demonstrating that history-dependent behavior policy estimation decreases their asymptotic variances while increasing their finite-sample biases. Additionally, as the estimated behavior policy conditions on a longer history, we show a consistent decrease in variance. We extend these findings to a range of other OPE estimators, including the sequential IS estimator, the doubly robust estimator and the marginalized IS estimator, with the behavior policy estimated either parametrically or non-parametrically.