Stochastic networks are a plausible representation of the relational information among entities in dynamic systems such as living cells or social communities. While there is a rich literature in estimating a static or temporally invariant network from observation data, little has been done toward estimating time-varying networks from time series of entity attributes. In this paper we present two new machine learning methods for estimating time-varying networks, which both build on a temporally smoothed $l_1$-regularized logistic regression formalism that can be cast as a standard convex-optimization problem and solved efficiently using generic solvers scalable to large networks. We report promising results on recovering simulated time-varying networks. For real data sets, we reverse engineer the latent sequence of temporally rewiring political networks between Senators from the US Senate voting records and the latent evolving regulatory networks underlying 588 genes across the life cycle of Drosophila melanogaster from the microarray time course.
We explore time-varying networks for high-dimensional locally stationary time series, using the large VAR model framework with both the transition and (error) precision matrices evolving smoothly over time. Two types of time-varying graphs are investigated: one containing directed edges of Granger causality linkages, and the other containing undirected edges of partial correlation linkages. Under the sparse structural assumption, we propose a penalised local linear method with time-varying weighted group LASSO to jointly estimate the transition matrices and identify their significant entries, …
Time series of individual subjects have become a common data type in psychological research. These data allow one to estimate models of within-subject dynamics, and thereby avoid the notorious problem of making within-subjects inferences from between-subjects data, and naturally address heterogeneity between subjects. A popular model for these data is the Vector Autoregressive (VAR) model, in which each variable is predicted as a linear function of all variables at previous time points. A key assumption of this model is that its parameters are constant (or stationary) across time. However, in …
Examples of cyclic (periodic) behavior in geophysical data abound. In many cases the primary period is known, such as in daily measurements of rain, temperature, and sea level. However, many time series of measurements contain cycles of unknown or varying length. We consider the problem of estimating the unknown period in a time series.We review the basic methods, compare their performance through a simulation studyusing observed sea level data, apply them to an astronomical data set, and discuss generalizations of the methods.
The estimation of time-varying networks for functional Magnetic Resonance Imaging (fMRI) data sets is of increasing importance and interest. In this work, we formulate the problem in a high-dimensional time series framework and introduce a data-driven method, namely Network Change Points Detection (NCPD), which detects change points in the network structure of a multivariate time series, with each component of the time series represented by a node in the network. NCPD is applied to various simulated data and a resting-state fMRI data set. This new methodology also allows us to identify common …
Sparsistent Estimation of Time-Varying Discrete Markov Random Fields
网络模型已经流行用于建模和表示观察变量之间的复杂关系和依赖关系。当数据来自动态随机过程时，单个静态网络模型不能充分捕获瞬时依赖性，例如生物体整个发育周期的基因调控依赖性。Kolar et al（2010 b）提出了一种基于核平滑l1惩罚逻辑斯谛回归的方法，用于从时间序列观测数据中收集的节点观测估计时变网络。在本文中，我们建立的条件下，所提出的方法一致地恢复时变网络的结构。这项工作补充了以往的经验研究结果，提供了良好的理论保证，建议的估计程序。为了完整性，我们在本文中包括数值模拟。
Yale School of Medicine（耶鲁大学医学院）；Yale University（耶鲁大学）
We propose a method for estimating more reproducible functional networks that are more strongly associated with dynamic task activity by using recurrent neural networks with long short term memory (LSTMs). The LSTM model is trained in an unsupervised manner to learn to generate the functional magnetic resonance imaging (fMRI) time-series data in regions of interest. The learned functional networks can then be used for further analysis, e.g., correlation analysis to determine functional networks that are strongly associated with an fMRI task paradigm. We test our approach and compare to other m…
This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To simultaneously handle these two types of time-varying features, a two-step approach is proposed: multiple change point locations are first identified based on comparing the difference between the localized averages on sample covariance matrices, and then graph supports are recovered based on a kernelized time-varying constrained $L_1$-minimization for inverse matr…
Estimating the individual treatment effect (ITE) from observational data is meaningful and practical in healthcare. Existing work mainly relies on the strong ignorability assumption that no hidden confounders exist, which may lead to bias in estimating causal effects. Some studies consider the hidden confounders are designed for static environment and not easily adaptable to a dynamic setting. In fact, most observational data (e.g., electronic medical records) is naturally dynamic and consists of sequential information. In this paper, we propose Deep Sequential Weighting (DSW) for estimating I…
Estimating dynamic treatment regimes (DTRs) from retrospective observational data is challenging as some degree of unmeasured confounding is often expected. In this work, we develop a framework of estimating properly defined "optimal" DTRs with a time-varying instrumental variable (IV) when unmeasured covariates confound the treatment and outcome, rendering the potential outcome distributions only partially identified. We derive a novel Bellman equation under partial identification, use it to define a generic class of estimands (termed IV-optimal DTRs), and study the associated estimation prob…
In this paper, we study time-varying graphical models based on data measured over a temporal grid. Such models are motivated by the needs to describe and understand evolving interacting relationships among a set of random variables in many real applications, for instance the study of how stocks interact with each other and how such interactions change over time. We propose a new model, LOcal Group Graphical Lasso Estimation (loggle), under the assumption that the graph topology changes gradually over time. Specifically, loggle uses a novel local group-lasso type penalty to efficiently incorpor…
Neuroscientists have enjoyed much success in understanding brain functions by constructing brain connectivity networks using data collected under highly controlled experimental settings. However, these experimental settings bear little resemblance to our real-life experience in day-to-day interactions with the surroundings. To address this issue, neuroscientists have been measuring brain activity under natural viewing experiments in which the subjects are given continuous stimuli, such as watching a movie or listening to a story. The main challenge with this approach is that the measured signa…
Estimating counterfactual outcomes over time from observational data is relevant for many applications (e.g., personalized medicine). Yet, state-of-the-art methods build upon simple long short-term memory (LSTM) networks, thus rendering inferences for complex, long-range dependencies challenging. In this paper, we develop a novel Causal Transformer for estimating counterfactual outcomes over time. Our model is specifically designed to capture complex, long-range dependencies among time-varying confounders. For this, we combine three transformer subnetworks with separate inputs for time-varying…
LMU Munich（慕尼黑大学）；Munich Center for Machine Learning（慕尼黑机器学习中心）；ETH Zurich（苏黎世联邦理工学院）
In medical practice, treatments are selected based on the expected causal effects on patient outcomes. Here, the gold standard for estimating causal effects are randomized controlled trials; however, such trials are costly and sometimes even unethical. Instead, medical practice is increasingly interested in estimating causal effects among patient (sub)groups from electronic health records, that is, observational data. In this paper, we aim at estimating the average causal effect (ACE) from observational data (patient trajectories) that are collected over time. For this, we propose DeepACE: an …
University of Oxford（牛津大学）；The Alan Turing Institute（艾伦·图灵研究所）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；University of Cambridge（剑桥大学）
Identifying when to give treatments to patients and how to select among multiple treatments over time are important medical problems with a few existing solutions. In this paper, we introduce the Counterfactual Recurrent Network (CRN), a novel sequence-to-sequence model that leverages the increasingly available patient observational data to estimate treatment effects over time and answer such medical questions. To handle the bias from time-varying confounders, covariates affecting the treatment assignment policy in the observational data, CRN uses domain adversarial training to build balancing…
We develop new algorithms for estimating heterogeneous treatment effects, combining recent developments in transfer learning for neural networks with insights from the causal inference literature. By taking advantage of transfer learning, we are able to efficiently use different data sources that are related to the same underlying causal mechanisms. We compare our algorithms with those in the extant literature using extensive simulation studies based on large-scale voter persuasion experiments and the MNIST database. Our methods can perform an order of magnitude better than existing benchmarks…
The estimation of probabilities of network edges from the observed adjacency matrix has important applications to predicting missing links and network denoising. It has usually been addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong assumptions on the network structure. Here we propose a novel computationally efficient method, based on neighborhood smoothing to estimate the expectation of the adjacency matrix directly, without making the structural assumptions that graphon estimation requires. The neighborhoo…
Nutanix Technologies India Pvt Ltd（Nutanix 印度私人有限公司）；IBM T J Watson Research Center, USA（美国 IBM T J 沃森研究中心）
India runs the fourth largest railway transport network size carrying over 8 billion passengers per year. However, the travel experience of passengers is frequently marked by delays, i.e., late arrival of trains at stations, causing inconvenience. In a first, we study the systemic delays in train arrivals using n-order Markov frameworks and experiment with two regression based models. Using train running-status data collected for two years, we report on an efficient algorithm for estimating delays at railway stations with near accurate results. This work can help railways to manage their resou…
Memorial Sloan Kettering Cancer Center（纪念斯隆凯特琳癌症中心）
We present a Bayesian hierarchical multi-view mixture model termed Symphony that simultaneously learns clusters of cells representing cell types and their underlying gene regulatory networks by integrating data from two views: single-cell gene expression data and paired epigenetic data, which is informative of gene-gene interactions. This model improves interpretation of clusters as cell types with similar expression patterns as well as regulatory networks driving expression, by explaining gene-gene covariances with the biological machinery regulating gene expression. We show the theoretical a…
Community detection is a fundamental problem in network analysis with many methods available to estimate communities. Most of these methods assume that the number of communities is known, which is often not the case in practice. We study a simple and very fast method for estimating the number of communities based on the spectral properties of certain graph operators, such as the non-backtracking matrix and the Bethe Hessian matrix. We show that the method performs well under several models and a wide range of parameters, and is guaranteed to be consistent under several asymptotic regimes. We c…
Several methods of estimating the mutual information of random variables have been developed in recent years. They can prove valuable for novel approaches to learning statistically independent features. In this paper, we use one of these methods, a mutual information neural estimation (MINE) network, to present a proof-of-concept of how a neural network can perform linear ICA. We minimize the mutual information, as estimated by a MINE network, between the output units of a differentiable encoder network. This is done by simple alternate optimization of the two networks. The method is shown to …
KTH Royal Institute of Technology（瑞典皇家理工学院）；INRIA Grenoble Rhone-Alpes（法国国家信息与自动化研究所格勒诺布尔罗纳-阿尔卑斯分部）；University of Tokyo（东京大学）；Cold Spring Harbor Laboratory（冷泉港实验室）
We design a self size-estimating feed-forward network (SSFN) using a joint optimization approach for estimation of number of layers, number of nodes and learning of weight matrices. The learning algorithm has a low computational complexity, preferably within few minutes using a laptop. In addition the algorithm has a limited need for human intervention to tune parameters. SSFN grows from a small-size network to a large-size network, guaranteeing a monotonically non-increasing cost with addition of nodes and layers. The learning approach uses judicious a combination of `lossless flow property' …
Estimating counterfactual treatment outcomes over time in complex multiagent scenarios
Graduate School of Informatics at Nagoya University（名古屋大学信息学研究科）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Graduate School of Informatics at Kyoto University（京都大学信息学研究科）；Graduate School of Engineering at the University of Tokyo（东京大学工学研究科）；Graduate School of Information Science and Technology at Osaka University（大阪大学信息科学与技术研究科）
Aggregate network properties such as cluster cohesion and the number of bridge nodes can be used to glean insights about a network's community structure, spread of influence and the resilience of the network to faults. Efficiently computing network properties when the network is fully observed has received significant attention (Wasserman and Faust 1994; Cook and Holder 2006), however the problem of computing aggregate network properties when there is missing data attributes has received little attention. Computing these properties for networks with missing attributes involves performing infer…
Most real-world networks are too large to be measured or studied directly and there is substantial interest in estimating global network properties from smaller sub-samples. One of the most important global properties is the number of vertices/nodes in the network. Estimating the number of vertices in a large network is a major challenge in computer science, epidemiology, demography, and intelligence analysis. In this paper we consider a population random graph G = (V;E) from the stochastic block model (SBM) with K communities/blocks. A sample is obtained by randomly choosing a subset W and le…
