More Like this

1. Simultaneous Change Point Inference and Structure Recovery for High Dimensional Gaussian Graphical Models

   Liu, B.; Zhang, X.; Liu, Y. (October 2021, Journal of machine learning research)

   In this article, we investigate the problem of simultaneous change point inference and structure recovery in the context of high dimensional Gaussian graphical models with possible abrupt changes. In particular, motivated by neighborhood selection, we incorporate a threshold variable and an unknown threshold parameter into a joint sparse regression model which combines p l1-regularized node-wise regression problems together. The change point estimator and the corresponding estimated coefficients of precision matrices are obtained together. Based on that, a classifier is introduced to distinguish whether a change point exists. To recover the graphical structure correctly, a data-driven thresholding procedure is proposed. In theory, under some sparsity conditions and regularity assumptions, our method can correctly choose a homogeneous or heterogeneous model with high accuracy. Furthermore, in the latter case with a change point, we establish estimation consistency of the change point estimator, by allowing the number of nodes being much larger than the sample size. Moreover, it is shown that, in terms of structure recovery of Gaussian graphical models, the proposed thresholding procedure achieves model selection consistency and controls the number of false positives. The validity of our proposed method is justified via extensive numerical studies. Finally, we apply our proposed method to the S&P 500 dataset to show its empirical usefulness. 

   more » « less
2. Regression Adjustments for Estimating the Global Treatment Effect in Experiments with Interference

   https://doi.org/10.1515/jci-2018-0026  

   Chin, Alex (May 2019, Journal of Causal Inference)

   Abstract Standard estimators of the global average treatment effect can be biased in the presence of interference. This paper proposes regression adjustment estimators for removing bias due to interference in Bernoulli randomized experiments. We use a fitted model to predict the counterfactual outcomes of global control and global treatment. Our work differs from standard regression adjustments in that the adjustment variables are constructed from functions of the treatment assignment vector, and that we allow the researcher to use a collection of any functions correlated with the response, turning the problem of detecting interference into a feature engineering problem. We characterize the distribution of the proposed estimator in a linear model setting and connect the results to the standard theory of regression adjustments under SUTVA. We then propose an estimator that allows for flexible machine learning estimators to be used for fitting a nonlinear interference functional form. We propose conducting statistical inference via bootstrap and resampling methods, which allow us to sidestep the complicated dependences implied by interference and instead rely on empirical covariance structures. Such variance estimation relies on an exogeneity assumption akin to the standard unconfoundedness assumption invoked in observational studies. In simulation experiments, our methods are better at debiasing estimates than existing inverse propensity weighted estimators based on neighborhood exposure modeling. We use our method to reanalyze an experiment concerning weather insurance adoption conducted on a collection of villages in rural China. 

   more » « less
3. Exploiting neighborhood interference with low-order interactions under unit randomized design

   https://doi.org/10.1515/jci-2022-0051  

   Cortez-Rodriguez, Mayleen; Eichhorn, Matthew; Yu, Christina Lee (January 2023, Journal of Causal Inference)

   Abstract Network interference, where the outcome of an individual is affected by the treatment assignment of those in their social network, is pervasive in real-world settings. However, it poses a challenge to estimating causal effects. We consider the task of estimating the total treatment effect (TTE), or the difference between the average outcomes of the population when everyone is treated versus when no one is, under network interference. Under a Bernoulli randomized design, we provide an unbiased estimator for the TTE when network interference effects are constrained to low-order interactions among neighbors of an individual. We make no assumptions on the graph other than bounded degree, allowing for well-connected networks that may not be easily clustered. We derive a bound on the variance of our estimator and show in simulated experiments that it performs well compared with standard estimators for the TTE. We also derive a minimax lower bound on the mean squared error of our estimator, which suggests that the difficulty of estimation can be characterized by the degree of interactions in the potential outcomes model. We also prove that our estimator is asymptotically normal under boundedness conditions on the network degree and potential outcomes model. Central to our contribution is a new framework for balancing model flexibility and statistical complexity as captured by this low-order interactions structure. 

   more » « less
4. Minimizing Interference and Selection Bias in Network Experiment Design

   Fatemi, Z.; Zheleva, E. (January 2020, 14th International AAAI Conference on Web and Social Media)

   null (Ed.)

   Current approaches to A/B testing in networks focus on limiting interference, the concern that treatment effects can ”spill over” from treatment nodes to control nodes and lead to biased causal effect estimation. Prominent methods for network experiment design rely on two-stage randomization, in which sparsely-connected clusters are identified and cluster randomization dictates the node assignment to treatment and control. Here, we show that cluster randomization does not ensure sufficient node randomization and it can lead to selection bias in which treatment and control nodes represent different populations of users. To address this problem, we propose a principled framework for network experiment design which jointly minimizes interference and selection bias. We introduce the concepts of edge spillover probability and cluster matching and demonstrate their importance for designing network A/B testing. Our experiments on a number of real-world datasets show that our proposed framework leads to significantly lower error in causal effect estimation than existing solutions. 

   more » « less
5. Nearly Optimal Learning Using Sparse Deep ReLU Networks in Regularized Empirical Risk Minimization With Lipschitz Loss

   https://doi.org/10.1162/neco_a_01742  

   Huang, Ke; Liu, Mingming; Ma, Shujie (March 2025, Neural Computation)

   Abstract We propose a sparse deep ReLU network (SDRN) estimator of the regression function obtained from regularized empirical risk minimization with a Lipschitz loss function. Our framework can be applied to a variety of regression and classification problems. We establish novel nonasymptotic excess risk bounds for our SDRN estimator when the regression function belongs to a Sobolev space with mixed derivatives. We obtain a new, nearly optimal, risk rate in the sense that the SDRN estimator can achieve nearly the same optimal minimax convergence rate as one-dimensional nonparametric regression with the dimension involved in a logarithm term only when the feature dimension is fixed. The estimator has a slightly slower rate when the dimension grows with the sample size. We show that the depth of the SDRN estimator grows with the sample size in logarithmic order, and the total number of nodes and weights grows in polynomial order of the sample size to have the nearly optimal risk rate. The proposed SDRN can go deeper with fewer parameters to well estimate the regression and overcome the overfitting problem encountered by conventional feedforward neural networks. 

   more » « less