High performance computing (HPC) facilities consist of a large number of interconnected computing units (or nodes) that execute highly complex scientific simulations to support scientific research. Monitoring such facilities, in real-time, is essential to ensure that the system operates at peak efficiency. Such systems are typically monitored using a variety of measurement and log data which capture the state of the various components within the system at regular intervals of time. As modern HPC systems grow in capacity and complexity, the data produced by current resource monitoring tools is at a scale that it is no longer feasible to be visually monitored by analysts. We propose a method that transforms the multi-dimensional output of resource monitoring tools to a low dimensional representation that facilitates the understanding of the behavior of a High Performance Computing (HPC) system. The proposed method automatically extracts the low-dimensional signal in the data which can be used to track the system efficiency and identify performance anomalies. The method models the resource usage data as a three dimensional tensor (capturing resource usage of all compute nodes for difference resources over time). A dynamic matrix factorization algorithm, called dynamicMF, is proposed to extract a low-dimensional temporal signal for each node, which is subsequently fed into an anomaly detector. Results on resource usage data collected from the Lonestar 4 system at the Texas Advanced Computing Center show that the identified anomalies are correlated with actual anomalous events reported in the system log messages.
The idea of dynamic matrix factorization has been used in designing the recommendation system. In particular, dynamic Poisson factorization (dPF) model works effectively when we assume each observation follows a Poisson distribution @cite_12 . In this model, because of their probabilistic setting, variational inference has been used to perform inference. After that, they use the block coordinate approach to solve the optimization problem yield as a result of variational inference. Although our model is similar to dPF in the design of shared components and local components, our model is different from dPF in several ways: (1) we do not assume the temporal relationship between consecutive timestep as in dPF, (2) because of our non-probabilistic formulation, we can avoid the problem of non-conjugacy in dPF and use more effective gradient-based optimization such as Adam algorithm instead of using block coordinate optimization with L-BFGS (a more computationally intensive optimization method) as a building block.
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Models for recommender systems use latent factors to explain the preferences and behaviors of users with respect to a set of items (e.g., movies, books, academic papers). Typically, the latent factors are assumed to be static and, given these factors, the observed pref- erences and behaviors of users are assumed to be generated without order. These assumptions limit the explorative and predictive capabilities of such models, since users' interests and item popularity may evolve over time. To address this, we propose dPF, a dynamic matrix factorization model based on the recent Poisson factorization model for recommendations. dPF models the time evolving latent factors with a Kalman filter and the actions with Poisson distributions. We derive a scalable variational inference algorithm to infer the latent factors. Finally, we demonstrate dPF on 10 years of user click data from arXiv.org, one of the largest repository of scientific papers and a formidable source of information about the behavior of scientists. Empirically we show performance improvement over both static and, more recently proposed, dynamic recommendation models. We also provide a thorough exploration of the inferred posteriors over the latent variables. Poisson factorization is a probabilistic model of users and items for recommendation systems, where the so-called implicit consumer data is modeled by a factorized Poisson distribution. There are many variants of Poisson factorization methods who show state-of-the-art performance on real-world recommendation tasks. However, most of them do not explicitly take into account the temporal behavior and the recurrent activities of users which is essential to recommend the right item to the right user at the right time. In this paper, we introduce Recurrent Poisson Factorization (RPF) framework that generalizes the classical PF methods by utilizing a Poisson process for modeling the implicit feedback. RPF treats time as a natural constituent of the model and brings to the table a rich family of time-sensitive factorization models. To elaborate, we instantiate several variants of RPF who are capable of handling dynamic user preferences and item specification (DRPF), modeling the social-aspect of product adoption (SRPF), and capturing the consumption heterogeneity among users and items (HRPF). We also develop a variational algorithm for approximate posterior inference that scales up to massive data sets. Furthermore, we demonstrate RPF's superior performance over many state-of-the-art methods on synthetic dataset, and large scale real-world datasets on music streaming logs, and user-item interactions in M-Commerce platforms. We develop a Bayesian nonparametric Poisson factorization model for recommendation systems. Poisson factorization implicitly models each user’s limited budget of attention (or money) that allows consumption of only a small subset of the available items. In our Bayesian nonparametric variant, the number of latent components is theoretically unbounded and eectively estimated when computing a posterior with observed user behavior data. To approximate the posterior, we develop an ecient variational inference algorithm. It adapts the dimensionality of the latent components to the data, only requires iteration over the user item pairs that have been rated, and has computational complexity on the same order as for a parametric model with xed dimensionality. We studied our model and algorithm with large realworld data sets of user-movie preferences. Our model eases the computational burden of searching for the number of latent components and gives better predictive performance than its parametric counterpart. We develop and analyze a broad family of stochastic randomized algorithms for inverting a matrix. We also develop specialized variants maintaining symmetry or positive definiteness of the iterates. All methods in the family converge globally and linearly (i.e., the error decays exponentially), with explicit rates. In special cases, we obtain stochastic block variants of several quasi-Newton updates, including bad Broyden (BB), good Broyden (GB), Powell-symmetric-Broyden (PSB), Davidon-Fletcher-Powell (DFP) and Broyden-Fletcher-Goldfarb-Shanno (BFGS). Ours are the first stochastic versions of these updates shown to converge to an inverse of a fixed matrix. Through a dual viewpoint we uncover a fundamental link between quasi-Newton updates and approximate inverse preconditioning. Further, we develop an adaptive variant of randomized block BFGS, where we modify the distribution underlying the stochasticity of the method throughout the iterative process to achieve faster convergence. By inverting several matrices from varied applications, we demonstrate that AdaRBFGS is highly competitive when compared to the well established Newton-Schulz and minimal residual methods. In particular, on large-scale problems our method outperforms the standard methods by orders of magnitude. Development of efficient methods for estimating the inverse of very large matrices is a much needed tool for preconditioning and variable metric optimization methods in the advent of the big data era.