Partially Observed Dynamic Tensor Response Regression.

In modern data science, dynamic tensor data prevail in numerous applications. An important task is to characterize the relationship between dynamic tensor datasets and external covariates. However, the tensor data are often only partially observed, rendering many existing methods inapplicable. In this article, we develop a regression model with a partially observed dynamic tensor as the response and external covariates as the predictor. We introduce the low-rankness, sparsity, and fusion structures on the regression coefficient tensor, and consider a loss function projected over the observed entries. We develop an efficient nonconvex alternating updating algorithm, and derive the finite-sample error bound of the actual estimator from each step of our optimization algorithm. Unobserved entries in the tensor response have imposed serious challenges. As a result, our proposal differs considerably in terms of estimation algorithm, regularity conditions, as well as theoretical properties, compared to the existing tensor completion or tensor response regression solutions. We illustrate the efficacy of our proposed method using simulations and two real applications, including a neuroimaging dementia study and a digital advertising study.

Generalized Connectivity Matrix Response Regression with Applications in Brain Connectivity Studies.

Multiple-subject network data are fast emerging in recent years, where a separate connectivity matrix is measured over a common set of nodes for each individual subject, along with subject covariates information. In this article, we propose a new generalized matrix response regression model, where the observed network is treated as a matrix-valued response and the subject covariates as predictors. The new model characterizes the population-level connectivity pattern through a low-rank intercept matrix, and the effect of subject covariates through a sparse slope tensor. We develop an efficient alternating gradient descent algorithm for parameter estimation, and establish the non-asymptotic error bound for the actual estimator from the algorithm, which quantifies the interplay between the computational and statistical errors. We further show the strong consistency for graph community recovery, as well as the edge selection consistency. We demonstrate the efficacy of our method through simulations and two brain connectivity studies.

Provable Convex Co-clustering of Tensors.

Cluster analysis is a fundamental tool for pattern discovery of complex heterogeneous data. Prevalent clustering methods mainly focus on vector or matrix-variate data and are not applicable to general-order tensors, which arise frequently in modern scientific and business applications. Moreover, there is a gap between statistical guarantees and computational efficiency for existing tensor clustering solutions due to the nature of their non-convex formulations. In this work, we bridge this gap by developing a provable convex formulation of tensor co-clustering. Our convex co-clustering (CoCo) estimator enjoys stability guarantees and its computational and storage costs are polynomial in the size of the data. We further establish a non-asymptotic error bound for the CoCo estimator, which reveals a surprising "blessing of dimensionality" phenomenon that does not exist in vector or matrix-variate cluster analysis. Our theoretical findings are supported by extensive simulated studies. Finally, we apply the CoCo estimator to the cluster analysis of advertisement click tensor data from a major online company. Our clustering results provide meaningful business insights to improve advertising effectiveness.

Mixed-Effect Time-Varying Network Model and Application in Brain Connectivity Analysis.

Time-varying networks are fast emerging in a wide range of scientific and business applications. Most existing dynamic network models are limited to a single-subject and discrete-time setting. In this article, we propose a mixed-effect network model that characterizes the continuous time-varying behavior of the network at the population level, meanwhile taking into account both the individual subject variability as well as the prior module information. We develop a multistep optimization procedure for a constrained likelihood estimation and derive the associated asymptotic properties. We demonstrate the effectiveness of our method through both simulations and an application to a study of brain development in youth. Supplementary materials for this article are available online.

Tensor Graphical Model: Non-Convex Optimization and Statistical Inference.

We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. A critical challenge in the estimation and inference of this model is the fact that its penalized maximum likelihood estimation involves minimizing a non-convex objective function. To address it, this paper makes two contributions: (i) In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with an optimal statistical rate of convergence. (ii) We propose a de-biased statistical inference procedure for testing hypotheses on the true support of the sparse precision matrices, and employ it for testing a growing number of hypothesis with false discovery rate (FDR) control. The asymptotic normality of our test statistic and the consistency of FDR control procedure are established. Our theoretical results are backed up by thorough numerical studies and our real applications on neuroimaging studies of Autism spectrum disorder and users' advertising click analysis bring new scientific findings and business insights. The proposed methods are encoded into a publicly available R package Tlasso.

Simultaneous Clustering and Estimation of Heterogeneous Graphical Models.

We consider joint estimation of multiple graphical models arising from heterogeneous and high-dimensional observations. Unlike most previous approaches which assume that the cluster structure is given in advance, an appealing feature of our method is to learn cluster structure while estimating heterogeneous graphical models. This is achieved via a high dimensional version of Expectation Conditional Maximization (ECM) algorithm (Meng and Rubin, 1993). A joint graphical lasso penalty is imposed on the conditional maximization step to extract both homogeneity and heterogeneity components across all clusters. Our algorithm is computationally efficient due to fast sparse learning routines and can be implemented without unsupervised learning knowledge. The superior performance of our method is demonstrated by extensive experiments and its application to a Glioblastoma cancer dataset reveals some new insights in understanding the Glioblastoma cancer. In theory, a non-asymptotic error bound is established for the output directly from our high dimensional ECM algorithm, and it consists of two quantities: statistical error (statistical accuracy) and optimization error (computational complexity). Such a result gives a theoretical guideline in terminating our ECM iterations.

Evidence for preoperative aspirin improving major outcomes in patients with chronic kidney disease undergoing cardiac surgery: a cohort study.

BACKGROUND: Effects of aspirin on patients with chronic kidney disease (CKD) remains unclear. This study aimed to examine the effect of preoperative aspirin use on postoperative renal function and 30-day mortality in patients with CKD undergoing cardiac surgery. METHODS: A retrospective cohort study was performed on consecutive patients (n = 5175) receiving cardiac surgery in 2 tertiary hospitals. Of all patients, 3585 met the inclusion criteria and underwent the analysis to determine the association of preoperative aspirin with incidence of acute kidney injury (AKI) and death based on estimated glomerular filtration rate (eGFR). RESULTS: Of 3585 patients, 31.5% had CKD (eGFR < 60 mL/min/1.73 m2) at baseline and 27.6% had AKI postoperatively. The baseline eGFR had a nonlinear relationship with the incidence and stages of AKI. As eGFR decreased to 15 to 30 from more than or equal to 90 mL/min/1.73 m2, AKI and 30-day mortality increased to 50.5% from 23.5% and to 11.9% from 2.6%, respectively (P < 0.001). However, preoperative aspirin use was associated with a significant decrease in postoperative AKI and 30-day mortality in patients with CKD undergoing cardiac surgery, in particular, the survival benefit associated with aspirin was greater in patients with CKD (vs normal kidney function): 30-day mortality was reduced by 23.3%, 58.2%, or 70.0% for patients with baseline eGFR more than or equal to 90, 30 to 59, or 15 to 30 mL/min/1.73 m2, respectively (P trend < 0.001). CONCLUSIONS: For patients with CKD undergoing cardiac surgery, preoperative aspirin therapy was associated with renal protection and mortality decline. The magnitude of the survival benefit was greater in patients with CKD than normal kidney function.

Preoperative aspirin use and outcomes in cardiac surgery patients.

BACKGROUND: The effects of preoperative aspirin use on outcomes of cardiac surgery patients remain uncertain. This study was aimed to evaluate the effect of preoperative aspirin use on major outcomes in cardiac surgery patients. METHODS: An observational cohort study was performed on consecutive patients (n = 4256) undergoing cardiac surgery in 2 tertiary hospitals. Of all patients, 2868 patients met the inclusion criteria and were divided into 2 groups: those taking (n = 1923) or not taking (n = 945) aspirin within 5 days preceding surgery. RESULTS: Patients in the aspirin group presented significantly more with comorbidities including hypertension, diabetes, peripheral arterial disease, previous myocardial infarction, angina, cerebrovascular disease, older age, and male gender. With propensity scores adjusted and multivariate logistic regression, however, the results of this study showed that preoperative aspirin therapy (vs nonaspirin) significantly reduced the risk of 30-day mortality (3.5% vs 6.5%, OR: 0.611, 95% CI: 0.391-0.956, P = 0.031), postoperative renal failure (3.7% vs 7.1%, OR: 0.384, 95% CI: 0.254-0.579, P < 0.001), dialysis required (1.9% vs 3.6%, OR: 0.441, 95% CI: 0.254-0.579, P < 0.001), intensive care unit stay (mean 107.2 vs 136.1 h, P < 0.001) and a composite outcome-major adverse cardiocerebral events (8.7% vs 10.8%, OR: 0.662, 95% CI:: 0.482-0.909, P = 0.011) in the patients undergoing cardiac surgery. However, readmissions did not show a significant difference between the 2 groups (14.5% vs 12.8%, P = 0.944). CONCLUSIONS: Preoperative aspirin therapy is associated with a significant decrease in the risk of major cardiocerebral complications, renal failure, intensive care unit stay and 30-day mortality but does not increase the risk of readmissions in patients undergoing cardiac surgery.