Distributed Monitoring of the R(sup 2) Statistic for Linear Regression

The problem of monitoring a multivariate linear regression model is relevant in studying the evolving relationship between a set of input variables (features) and one or more dependent target variables. This problem becomes challenging for large scale data in a distributed computing environment when only a subset of instances is available at individual nodes and the local data changes frequently. Data centralization and periodic model recomputation can add high overhead to tasks like anomaly detection in such dynamic settings. Therefore, the goal is to develop techniques for monitoring and updating the model over the union of all nodes data in a communication-efficient fashion. Correctness guarantees on such techniques are also often highly desirable, especially in safety-critical application scenarios. In this paper we develop DReMo a distributed algorithm with very low resource overhead, for monitoring the quality of a regression model in terms of its coefficient of determination (R2 statistic). When the nodes collectively determine that R2 has dropped below a fixed threshold, the linear regression model is recomputed via a network-wide convergecast and the updated model is broadcast back to all nodes. We show empirically, using both synthetic and real data, that our proposed method is highly communication-efficient and scalable, and also provide theoretical guarantees on correctness

Detecting Abnormal Machine Characteristics in Cloud Infrastructures

In the cloud computing environment resources are accessed as services rather than as a product. Monitoring this system for performance is crucial because of typical pay-peruse packages bought by the users for their jobs. With the huge number of machines currently in the cloud system, it is often extremely difficult for system administrators to keep track of all machines using distributed monitoring programs such as Ganglia1 which lacks system health assessment and summarization capabilities. To overcome this problem, we propose a technique for automated anomaly detection using machine performance data in the cloud. Our algorithm is entirely distributed and runs locally on each computing machine on the cloud in order to rank the machines in order of their anomalous behavior for given jobs. There is no need to centralize any of the performance data for the analysis and at the end of the analysis, our algorithm generates error reports, thereby allowing the system administrators to take corrective actions. Experiments performed on real data sets collected for different jobs validate the fact that our algorithm has a low overhead for tracking anomalous machines in a cloud infrastructure

nu-Anomica: A Fast Support Vector Based Novelty Detection Technique

In this paper we propose nu-Anomica, a novel anomaly detection technique that can be trained on huge data sets with much reduced running time compared to the benchmark one-class Support Vector Machines algorithm. In -Anomica, the idea is to train the machine such that it can provide a close approximation to the exact decision plane using fewer training points and without losing much of the generalization performance of the classical approach. We have tested the proposed algorithm on a variety of continuous data sets under different conditions. We show that under all test conditions the developed procedure closely preserves the accuracy of standard one-class Support Vector Machines while reducing both the training time and the test time by 5 - 20 times

Fast and Flexible Multivariate Time Series Subsequence Search

Multivariate Time-Series (MTS) are ubiquitous, and are generated in areas as disparate as sensor recordings in aerospace systems, music and video streams, medical monitoring, and financial systems. Domain experts are often interested in searching for interesting multivariate patterns from these MTS databases which often contain several gigabytes of data. Surprisingly, research on MTS search is very limited. Most of the existing work only supports queries with the same length of data, or queries on a fixed set of variables. In this paper, we propose an efficient and flexible subsequence search framework for massive MTS databases, that, for the first time, enables querying on any subset of variables with arbitrary time delays between them. We propose two algorithms to solve this problem (1) a List Based Search (LBS) algorithm which uses sorted lists for indexing, and (2) a R*-tree Based Search (RBS) which uses Minimum Bounding Rectangles (MBR) to organize the subsequences. Both algorithms guarantee that all matching patterns within the specified thresholds will be returned (no false dismissals). The very few false alarms can be removed by a post-processing step. Since our framework is also capable of Univariate Time-Series (UTS) subsequence search, we first demonstrate the efficiency of our algorithms on several UTS datasets previously used in the literature. We follow this up with experiments using two large MTS databases from the aviation domain, each containing several millions of observations. Both these tests show that our algorithms have very high prune rates (>99%) thus needing actual disk access for only less than 1% of the observations. To the best of our knowledge, MTS subsequence search has never been attempted on datasets of the size we have used in this paper

Fast Multivariate Search on Large Aviation Datasets

Multivariate Time-Series (MTS) are ubiquitous, and are generated in areas as disparate as sensor recordings in aerospace systems, music and video streams, medical monitoring, and financial systems. Domain experts are often interested in searching for interesting multivariate patterns from these MTS databases which can contain up to several gigabytes of data. Surprisingly, research on MTS search is very limited. Most existing work only supports queries with the same length of data, or queries on a fixed set of variables. In this paper, we propose an efficient and flexible subsequence search framework for massive MTS databases, that, for the first time, enables querying on any subset of variables with arbitrary time delays between them. We propose two provably correct algorithms to solve this problem (1) an R-tree Based Search (RBS) which uses Minimum Bounding Rectangles (MBR) to organize the subsequences, and (2) a List Based Search (LBS) algorithm which uses sorted lists for indexing. We demonstrate the performance of these algorithms using two large MTS databases from the aviation domain, each containing several millions of observations Both these tests show that our algorithms have very high prune rates (>95%) thus needing actua

Efficient Local Algorithms for Distributed Data Mining in Large Scale Peer to Peer Environments: A Deterministic Approach

Peer-to-peer (P2P) systems such as Gnutella, Napster, e-Mule, Kazaa, and Freenet are increasingly becoming popular for many applications that go beyond downloading music files without paying for it. Examples include P2P systems for network storage, web caching, searching and indexing of relevant documents and distributed network-threat analysis. These environments are rich in data and this data, if mined, can provide valuable source of information. Mining the web cache of users, for example, may often give information about their browsing patterns leading to efficient searching, resource utilization, query routing and more. However, most of the off-the-shelf data analysis techniques are designed for centralized applications where the entire data is stored in a single location. These techniques do not work in a highly decentralized, distributed environment such as a P2P network. We need distributed data mining algorithms that are fundamentally local, scalable, decentralized, asynchronous and anytime to solve this problem. This research proposes em>DeFraL

An efficient local Algorithm for Distributed Multivariate Regression in Peer-to-Peer Networks Abstract

This paper offers a local distributed algorithm for multivariate regression in large peer-to-peer environments. The algorithm is designed for distributed inferencing, data compaction, data modeling and classification tasks in many emerging peer-to-peer applications for bioinformatics, astronomy, social networking, sensor networks and web mining. Computing a global regression model from data available at the different peer-nodes using a traditional centralized algorithm for regression can be very costly and impractical because of the large number of data sources, the asynchronous nature of the peer-to-peer networks, and dynamic nature of the data/network. This paper proposes a two-step approach to deal with this problem. First, it offers an efficient local distributed algorithm that monitors the “quality ” of the current regression model. If the model is outdated, it uses this algorithm as a feedback mechanism for rebuilding the model. The local nature of the monitoring algorithm guarantees low monitoring cost. Experimental results presented in this paper strongly support the theoretical claims.