Matrix factorization (MF) plays an important role in a wide range of machine learning and data mining models. MF is commonly used to obtain item embeddings and feature representations due to its ability to capture correlations and higher-order statistical dependencies across dimensions. In many applications, the categories of items exhibit a hierarchical tree structure. For instance, human diseases can be divided into coarse categories, e.g., bacterial, and viral. These categories can be further divided into finer categories, e.g., viral infections can be respiratory, gastrointestinal, and exanthematous viral diseases. In e-commerce, products, movies, books, etc., are grouped into hierarchical categories, e.g., clothing items are divided by gender, then by type (formal, casual, etc.). While the tree structure and the categories of the different items may be known in some applications, they have to be learned together with the embeddings in many others. In this work, we propose eTREE, a model that incorporates the (usually ignored) tree structure to enhance the quality of the embeddings. We leverage the special uniqueness properties of Nonnegative MF (NMF) to prove identifiability of eTREE. The proposed model not only exploits the tree structure prior, but also learns the hierarchical clustering in an unsupervised data-driven fashion. We derive an efficient algorithmic solution and a scalable implementation of eTREE that exploits parallel computing, computation caching, and warm start strategies. We showcase the effectiveness of eTREE on real data from various application domains: healthcare, recommender systems, and education. We also demonstrate the meaningfulness of the tree obtained from eTREE by means of domain experts interpretation.

Leveraging large amounts of longitudinal electronic health records (EHR) data has shown great potentials for predicting progression of various diseases. In this work, we proposed a deep learning algorithm based on a customized Long Short-Term Memory (LSTM) model with built-in temporal sequence learning mechanism, named as Order-Aware Medical SeQuence Learning (OA-MedSQL). The model can predict various clinical outcomes from EHR sequences with competitive accuracies, meanwhile automatically distills patient medical journeys into clinically meaningful and relevant temporal sequences. The extraction of milestone temporal sequences is mainly facilitated by enforcing an order to the neurons of the LSTM model when updating their cell states at each time step. We have evaluated the proposed approach on a real-world EHR dataset that focuses on the task of predicting first-line treatment initiation for Waldenström Macroglobulinemia (WM) patients. OA-MedSQL can achieve comparable or better performance than several competitive baseline methods. Furthermore, OA-MedSQL offers a native way to extract milestone temporal sequences that are both explanatory of patient journeys and predictive of clinical outcomes.

Estimating and surveillance volumes of patients are of great importance for public health and resource allocation. In many situations, the change of these volumes is correlated with many factors, e.g., seasonal environmental variables, medicine sales, and patient medical claims. It is often of interest to predict patient volumes and to that end, discovering causalities can improve the prediction accuracy. Correlations do not imply causations and they can be spurious, which in turn may entail deterioration of prediction performance if the prediction is based on them. By contrast, in this paper, we propose an approach for prediction based on causalities discovered by Gaussian processes. Our interest is in estimating volumes of patients that suffer from allergy and where the model and the results are highly interpretable. In selecting features, instead of only using correlation, we take causal information into account. Specifically, we adopt the Gaussian processes-based convergent cross mapping framework for causal discovery which is proven to be more reliable than the Granger causality when time series are coupled. Moreover, we introduce a novel method for selecting the history or look-back length of features from the perspective of a dynamical system in a principled manner. The quasi-periodicities that commonly exist in observations of volumes of patients and environment variables can readily be accommodated. Further, the proposed method performs well even in cases when the data are scarce. Also, the approach can be modified without much difficulty to forecast other types of patient volumes. We validate the method with synthetic and real-world datasets.

Convergent cross mapping (CCM) is designed for causal discovery between coupled time series for which Granger's method for detecting causality is shown to be unreliable. The theoretical foundation of CCM is based on state space reconstruction, and therefore, for the accuracy of its results, the quality of the reconstruction is crucial. However, in the CCM framework, the reconstruction of an attractor manifold is usually implemented by direct delay embedding, where the reconstruction parameters are often selected by grid search methods. In this paper, we propose a more reliable and principled approach, which is based on Gaussian processes (GPs) that improves the attractor reconstruction. We validated the approach with the well-studied Lorenz attractor with and without observation noise. The experimental results indicate that our method is more robust to noise and that it consistently provides a reliable attractor manifold reconstruction. The proposed method was then tested on a real-world dataset, and the results suggested that the CCM equipped with an improved attractor manifold not only determined correctly the causal relationship but also improved the convergence, which is critical for causal discovery.

Opinion dynamics and its understanding in social networks is an emerging field of research in recent years. Existing work mainly considers direct exchanges of opinions among agents under certain conditions. This paper addresses a problem where the agents of a network make and exchange decisions repeatedly in a multi-hypothesis scenario and learn from the neighbors' decisions. Two models are proposed where the agents of the network use quasi-Bayesian learning to extract information about the true hypothesis from the neighbors' decisions. Theoretical analysis is provided about the conditions of a setting when agents become stubborn, that is, when they do not change their opinions anymore. We have run computer simulations to demonstrate the asymptotical properties of the proposed models. With our simulations we also show that, under one of the models, the agents of the network reach a consensus, and under the other, they form clusters.

Opinion dynamics in social networks has been widely studied in recent years, mostly by considering exchanges of opinions among neighboring agents. This paper addresses a scenario where the agents make decisions repeatedly on two hypotheses and where agents only exchange decisions. Motivated by the Bayesian models in the literature of human cognition, we model this learning procedure by the Bayes' rule. The social belief of each agent is defined to be the posterior of one of the hypotheses conditioned on the information it obtained from the society. We show that under certain conditions, once the social belief evolves to some region, the agent will refuse to change its belief. We demonstrate the asymptotical properties of the proposed model by computer simulations.

In this paper, we consider the problem of social learning in a network of agents where the agents make decisions onK hypotheses sequentially and broadcast their decisions to others. Each agent in the system has a private observation that is generated by one of the hypotheses. All the observations are independently generated from the same hypothesis. We study a setting where the agents randomly choose to make decisions prudently or non-prudently. A prudent decision is based on the private observation of the agent and all the previous decisions, whereas a non-prudent decision relies only on the private observation of the agent. We present a Bayesian learning method for the agents that exploits the information from other decisions. We analyze the asymptotical property of this system. A proof is presented that with the proposed decision policy, the posterior probability of the true hypothesis converges to one in probability. Simulation results are also provided.

In this paper, we consider the problem of social learning when decisions by agents in a network are made randomly. The agents receive private signals and use them for decision making on binary hypotheses under which the signals are generated. The agents make the decisions sequentially one at a time. All the agents know the decisions of the previous agents. We study a setting where the agents instead of making deterministic decisions by maximizing personal expected utility, they act randomly according to their private beliefs. We propose a method by which the agents learn from the previous agents' random decisions using the Bayesian theory. We define the concept of social belief about the truthfulness of the two hypotheses and analyze its convergence. We provide performance and convergence analysis of the proposed method as well as simulation results that include comparisons with a deterministic decision making system.

In this paper, we study the problem of distributed hypothesis testing in cooperative networks of agents. All agents are trying to reach consensus on the state of nature by their private signals and the binary actions of their neighbors. This is a challenging problem because the exchanged information of the agents is highly compressed. We propose a gossip-type method where every agent's decision converges in probability to the optimal decision held by a fictitious fusion center. We prove the asymptotical property of the proposed method and provide simulation results that demonstrate the communication cost and convergence time of the method.