Regularized Semiparametric Estimation for Ordinary Differential Equations

<div><p>Ordinary differential equations (ODEs) are widely used in modeling dynamic systems and have ample applications in the fields of physics, engineering, economics, and biological sciences. The ODE parameters often possess physiological meanings and can help scientists gain better understanding of the system. One key interest is thus to well estimate these parameters. Ideally, constant parameters are preferred due to their easy interpretation. In reality, however, constant parameters can be too restrictive such that even after incorporating error terms, there could still be unknown sources of disturbance that lead to poor agreement between observed data and the estimated ODE system. In this article, we address this issue and accommodate short-term interferences by allowing parameters to vary with time. We propose a new regularized estimation procedure on the time-varying parameters of an ODE system so that these parameters could change with time during transitions but remain constants within stable stages. We found, through simulation studies, that the proposed method performs well and tends to have less variation in comparison to the nonregularized approach. On the theoretical front, we derive finite-sample estimation error bounds for the proposed method. Applications of the proposed method to modeling the hare–lynx relationship and the measles incidence dynamic in Ontario, Canada lead to satisfactory and meaningful results. Supplementary materials for this article are available online.</p></div

Link prediction for egocentrically sampled networks

Link prediction in networks is typically accomplished by estimating or ranking the probabilities of edges for all pairs of nodes. In practice, especially for social networks, the data are often collected by egocentric sampling, which means selecting a subset of nodes and recording all of their edges. This sampling mechanism requires different prediction tools than the typical assumption of links missing at random. We propose a new computationally efficient link prediction algorithm for egocentrically sampled networks, estimating the underlying probability matrix by estimating its row space. We empirically evaluate the method on several synthetic and real-world networks and show that it provides accurate predictions for network links. Supplemental materials including the code for experiments are available online.</p

A Transfer Learning Approach for Predictive Modeling of Degenerate Biological Systems

<div><p>Modeling of a new domain can be challenging due to scarce data and high-dimensionality. Transfer learning aims to integrate data of the new domain with knowledge about some related old domains, to model the new domain better. This article studies transfer learning for degenerate biological systems. Degeneracy refers to the phenomenon that structurally different elements of the system perform the same/similar function or yield the same/similar output. Degeneracy exists in various biological systems and contributes to the heterogeneity, complexity, and robustness of the systems. Modeling of degenerate biological systems is challenging and models enabling transfer learning in such systems have been little studied. In this article, we propose a predictive model that integrates transfer learning and degeneracy under a Bayesian framework. Theoretical properties of the proposed model are studied. Finally, we present an application of modeling the predictive relationship between transcription factors and gene expression across multiple cell lines. The model achieves good prediction accuracy, and identifies known and possibly new degenerate mechanisms of the system. Supplementary materials for this article are available online.</p></div

An undirected artificial network.

<p>The numbers on the lines denote the weights of the links. Although the weight of link is greater than that of link , link is more important for node than link is, because link is the only path through which node can reach the remainder of the network.</p

Modeling Time-Varying Effects With Large-Scale Survival Data: An Efficient Quasi-Newton Approach

<p>Nonproportional hazards models often arise in biomedical studies, as evidenced by a recent national kidney transplant study. During the follow-up, the effects of baseline risk factors, such as patients’ comorbidity conditions collected at transplantation, may vary over time. To model such dynamic changes of covariate effects, time-varying survival models have emerged as powerful tools. However, traditional methods of fitting time-varying effects survival model rely on an expansion of the original dataset in a repeated measurement format, which, even with a moderate sample size, leads to an extremely large working dataset. Consequently, the computational burden increases quickly as the sample size grows, and analyses of a large dataset such as our motivating example defy any existing statistical methods and software. We propose a novel application of quasi-Newton iteration method to model time-varying effects in survival analysis. We show that the algorithm converges superlinearly and is computationally efficient for large-scale datasets. We apply the proposed methods, via a stratified procedure, to analyze the national kidney transplant data and study the impact of potential risk factors on post-transplant survival. Supplementary materials for this article are available online.</p

The distributions of the link salience, the link statistical importance and the disparity filtering importance.

<p>Link measurement refers to the values of the link salience, link statistical importance, and the disparity filtering importance that are given by the salience, GLANB and disparity methods separately. For the GLANB and disparity methods, the smaller values mean higher importance. For the salience method, the larger values mean higher importance.</p

The local control rate, disease-free survival (DFS), and overall survival (OS) of the cohort (Fig. 2A: local control rate, Fig. 2B: DFS, Fig. 2C: OS).

<p>The local control rate, disease-free survival (DFS), and overall survival (OS) of the cohort (Fig. 2A: local control rate, Fig. 2B: DFS, Fig. 2C: OS).</p

The distribution of links in link-shells.

<p>For the coauthor, fetion and email networks, we extract the top 10% important links, based on the GLANB, disparity filter and salience methods separately, to analyze their distributions in terms of link-shells. In addition, we also exclude the links that have degree of 1 to extract the remaining top 10% important links based on the salience method (salience-E) to analyze the distribution.</p

An undirected artificial network.

<p>The first number on the line is the value of the link weight, and the second number is the value of the link salience. Although the link gets the largest value 1 of the link salience, it is only important for node . The links and have the smallest value of the link salience, but they are in the core of the network.</p

Cumulative incidence of Grade 3+ acute complications to NCI CTC 3.0 (during ACT and CRT).

<p>Cumulative incidence of Grade 3+ acute complications to NCI CTC 3.0 (during ACT and CRT).</p