Estimating the probabilities of connections between vertices in a random network using an observed adjacency matrix is an important task for network data analysis. Many existing estimation methods are based on certain assumptions on network structure, which limit their applicability in practice. Without making strong assumptions, we develop an iterative connecting probability estimation method based on neighborhood averaging. Starting at a random initial point or an existing estimate, our method iteratively updates the pairwise vertex distances, the sets of similar vertices, and connecting probabilities to improve the precision of the estimate. We propose a two-stage neighborhood selection procedure to achieve the trade-off between smoothness of the estimate and the ability to discover local structure. The tuning parameters can be selected by cross-validation. We establish desirable theoretical properties for our method, and further justify its superior performance by comparing with existing methods in simulation and real data analysis.

Estimating individual treatment effect (ITE) is a challenging problem in causal inference, due to the missing counterfactuals and the selection bias. Existing ITE estimation methods mainly focus on balancing the distributions of control and treated groups, but ignore the local similarity information that is helpful. In this paper, we propose a local similarity preserved individual treatment effect (SITE) estimation method based on deep representation learning. SITE preserves local similarity and balances data distributions simultaneously, by focusing on several hard samples in each mini-batch. Experimental results on synthetic and three real-world datasets demonstrate the advantages of the proposed SITE method, compared with the state-of-the-art ITE estimation methods.

We study the problem of system identification and adaptive control in partially observable linear dynamical systems. Adaptive and closed-loop system identification is a challenging problem due to correlations introduced in data collection. In this paper, we present the first model estimation method with finite-time guarantees in both open and closed-loop system identification. Deploying this estimation method, we propose adaptive control online learning (AdapOn), an efficient reinforcement learning algorithm that adaptively learns the system dynamics and continuously updates its controller through online learning steps. AdapOn estimates the model dynamics by occasionally solving a linear regression problem through interactions with the environment. Using policy re-parameterization and the estimated model, AdapOn constructs counterfactual loss functions to be used for updating the controller through online gradient descent. Over time, AdapOn improves its model estimates and obtains more accurate gradient updates to improve the controller. We show that AdapOn achieves a regret upper bound of $\text{polylog}\left(T\right)$, after $T$ time steps of agent-environment interaction. To the best of our knowledge, AdapOn is the first algorithm that achieves $\text{polylog}\left(T\right)$ regret in adaptive control of \textit{unknown} partially observable linear dynamical systems which includes linear quadratic Gaussian (LQG) control.

Estimating the probabilities of connections between vertices in a random network using an observed adjacency matrix is an important task for network data analysis. Many existing estimation methods are based on certain assumptions on network structure, which limit their applicability in practice. Without making strong assumptions, we develop an iterative connecting probability estimation method based on neighborhood averaging. Starting at a random initial point or an existing estimate, our method iteratively updates the pairwise vertex distances, the sets of similar vertices, and connecting probabilities to improve the precision of the estimate. We propose a two-stage neighborhood selection procedure to achieve the trade-off between smoothness of the estimate and the ability to discover local structure. The tuning parameters can be selected by cross-validation. We establish desirable theoretical properties for our method, and further justify its superior performance by comparing with existing methods in simulation and real data analysis.

Estimating individual treatment effect (ITE) is a challenging problem in causal inference, due to the missing counterfactuals and the selection bias. Existing ITE estimation methods mainly focus on balancing the distributions of control and treated groups, but ignore the local similarity information that is helpful. In this paper, we propose a local similarity preserved individual treatment effect (SITE) estimation method based on deep representation learning. SITE preserves local similarity and balances data distributions simultaneously, by focusing on several hard samples in each mini-batch. Experimental results on synthetic and three real-world datasets demonstrate the advantages of the proposed SITE method, compared with the state-of-the-art ITE estimation methods.

We formally introduce the notion of optimal ROC curve over a general model space.

We study the problem of system identification and adaptive control in partially observable linear dynamical systems.

Since its inception, the neural estimation of mutual information (MI) has demonstrated the empirical success of modeling expected dependency between high-dimensional random variables.

We develop a direct debiased machine learning framework comprising Neyman targeted estimation and generalized Riesz regression. Our framework unifies Riesz regression for automatic debiased machine learning, covariate balancing, targeted maximum likelihood estimation (TMLE), and density-ratio estimation. In many problems involving causal effects or structural models, the parameters of interest depend on regression functions. Plugging regression functions estimated by machine learning methods into the identifying equations can yield poor performance because of first-stage bias. To reduce such bias, debiased machine learning employs Neyman orthogonal estimating equations. Debiased machine learning typically requires estimation of the Riesz representer and the regression function. For this problem, we develop a direct debiased machine learning framework with an end-to-end algorithm. We formulate estimation of the nuisance parameters, the regression function and the Riesz representer, as minimizing the discrepancy between Neyman orthogonal scores computed with known and unknown nuisance parameters, which we refer to as Neyman targeted estimation. Neyman targeted estimation includes Riesz representer estimation, and we measure discrepancies using the Bregman divergence. The Bregman divergence encompasses various loss functions as special cases, where the squared loss yields Riesz regression and the Kullback-Leibler divergence yields entropy balancing. We refer to this Riesz representer estimation as generalized Riesz regression. Neyman targeted estimation also yields TMLE as a special case for regression function estimation. Furthermore, for specific pairs of models and Riesz representer estimation methods, we can automatically obtain the covariate balancing property without explicitly solving the covariate balancing objective.