Curriculum Guidelines for Undergraduate Programs in Data Science

The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in Data Science. The group consisted of 25 undergraduate faculty from a variety of institutions in the U.S., primarily from the disciplines of mathematics, statistics and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in Data Science

Sequential pattern mining with uncertain data

In recent years, a number of emerging applications, such as sensor monitoring systems, RFID networks and location based services, have led to the proliferation of uncertain data. However, traditional data mining algorithms are usually inapplicable in uncertain data because of its probabilistic nature. Uncertainty has to be carefully handled; otherwise, it might significantly downgrade the quality of underlying data mining applications. Therefore, we extend traditional data mining algorithms into their uncertain versions so that they still can produce accurate results. In particular, we use a motivating example of sequential pattern mining to illustrate how to incorporate uncertain information in the process of data mining. We use possible world semantics to interpret two typical types of uncertainty: the tuple-level existential uncertainty and the attribute-level temporal uncertainty. In an uncertain database, it is probabilistic that a pattern is frequent or not; thus, we define the concept of probabilistic frequent sequential patterns. And various algorithms are designed to mine probabilistic frequent patterns efficiently in uncertain databases. We also implement our algorithms on distributed computing platforms, such as MapReduce and Spark, so that they can be applied in large scale databases. Our work also includes uncertainty computation in supervised machine learning algorithms. We develop an artificial neural network to classify numeric uncertain data; and a Naive Bayesian classifier is designed for classifying categorical uncertain data streams. We also propose a discretization algorithm to pre-process numerical uncertain data, since many classifiers work with categoric data only. And experimental results in both synthetic and real-world uncertain datasets demonstrate that our methods are effective and efficient

Low-latency, query-driven analytics over voluminous multidimensional, spatiotemporal datasets

2017 Summer.Includes bibliographical references.Ubiquitous data collection from sources such as remote sensing equipment, networked observational devices, location-based services, and sales tracking has led to the accumulation of voluminous datasets; IDC projects that by 2020 we will generate 40 zettabytes of data per year, while Gartner and ABI estimate 20-35 billion new devices will be connected to the Internet in the same time frame. The storage and processing requirements of these datasets far exceed the capabilities of modern computing hardware, which has led to the development of distributed storage frameworks that can scale out by assimilating more computing resources as necessary. While challenging in its own right, storing and managing voluminous datasets is only the precursor to a broader field of study: extracting knowledge, insights, and relationships from the underlying datasets. The basic building block of this knowledge discovery process is analytic queries, encompassing both query instrumentation and evaluation. This dissertation is centered around query-driven exploratory and predictive analytics over voluminous, multidimensional datasets. Both of these types of analysis represent a higher-level abstraction over classical query models; rather than indexing every discrete value for subsequent retrieval, our framework autonomously learns the relationships and interactions between dimensions in the dataset (including time series and geospatial aspects), and makes the information readily available to users. This functionality includes statistical synopses, correlation analysis, hypothesis testing, probabilistic structures, and predictive models that not only enable the discovery of nuanced relationships between dimensions, but also allow future events and trends to be predicted. This requires specialized data structures and partitioning algorithms, along with adaptive reductions in the search space and management of the inherent trade-off between timeliness and accuracy. The algorithms presented in this dissertation were evaluated empirically on real-world geospatial time-series datasets in a production environment, and are broadly applicable across other storage frameworks

Divide and Recombine for Large and Complex Data: Model Likelihood Functions using MCMC and TRMM Big Data Analysis

Divide & Recombine (D&R) is a powerful and practical statistical framework for the analysis of large and complex data. In D&R, big data are divided into subsets, each analytic method is applied to subsets with no communication among subsets, and the outputs are recombined to form a result of the analytic method for the entire data. This enables deep analysis and practical computational performance. The aim of this thesis is to provide an innovative D&R procedure to model likelihood of the generalized linear model for large data sets using Markov chain Monte Carlo (MCMC) methods and to present an analysis of Tropical Rainfall Measuring Mission (TRMM) data utilizing the DeltaRho D&R computational environment. The first chapter briefly introduces DeltaRho computation environment, followed by the introduction of univariate and multivariate skew-normal distribution and the derivation of parameter estimation using sample moments. Then a very basic introduction to MCMC sampling is provided as the MCMC sampling method could be used to characterize the posterior distribution in Chapter 3. Finally, the chapter is closed by a nonparametric procedure for decomposing a seasonal time series into seasonal, trend and remainder components – STL. In the second chapter, an innovate D&R procedure is proposed to compute likelihood functions of data-model (DM) parameters for big data. The likelihood-model (LM) is a parametric probability density function of the DM parameters. The density parameters are estimated by fitting the density to MCMC draws from each subset DM likelihood function, and then the fitted densities are recombined. The procedure is illustrated using normal and skew-normal LMs for the logistic regression DM on simulated data. Also, a novel diagnostic method is developed to measure the degree of the similarity between fitted density and the true likelihood function, with a real data application illustrated in the later section. In the last chapter, the focus is to present an analysis of TRMM big data utilizing the DeltaRho D&R computational environment. First, the exploratory data analysis is conducted to investigate the spatial patterns of precipitation and the seasonal behaviors of rain rates at different time scales. Then, spatio-temporal logistic models are constructed to explain the variation of 3-hr precipitation occurrence in automation for 460,800 locations, followed by model diagnostics and model inference. Furthermore, more advanced predictive models– two-stage logistic regression model, spatial-temporal autologistic regression model, and neighbor recurrent logistic regression model– are developed to forecast the probability of 3-hr precipitation occurrence at all locations. Finally, the chapter is ended with the application of spatio-temporal logistic models on daily heavy rainfall data

Monitoring data streams

Stream monitoring is concerned with analyzing data that is represented in the form of infinite streams. This field has gained prominence in recent years, as streaming data is generated in increasing volume and dimension in a variety of areas. It finds application in connection with monitoring industrial sensors, "smart" technology like smart houses and smart cars, wearable devices used for medical and physiological monitoring, but also in environmental surveillance or finance. However, stream monitoring is a challenging task due to the diverse and changing nature of the streaming data, its high volume and high dimensionality with thousands of sensors producing streams with millions of measurements over short time spans. Automated, scalable and efficient analysis of these streams can help to keep track of important events, highlight relevant aspects and provide better insights into the monitored system. In this thesis, we propose techniques adapted to these tasks in supervised and unsupervised settings, in particular Stream Classification and Stream Dependency Monitoring. After a motivating introduction, we introduce concepts related to streaming data and discuss technological frameworks that have emerged to deal with streaming data in the second chapter of this thesis. We introduce the notion of information theoretical entropy as a useful basis for data monitoring in the third chapter. In the second part of the thesis, we present Probabilistic Hoeffding Trees, a novel approach towards stream classification. We will show how probabilistic learning greatly improves the flexibility of decision trees and their ability to adapt to changes in data streams. The general technique is applicable to a variety of classification models and fast to compute without significantly greater memory cost compared to regular Hoeffding Trees. We show that our technique achieves better or on-par results to current state-of-the-art tree classification models on a variety of large, synthetic and real life data sets. In the third part of the thesis, we concentrate on unsupervised monitoring of data streams. We will use mutual information as entropic measure to identify the most important relationships in a monitored system. By using the powerful concept of mutual information we can, first, capture relevant aspects in a great variety of data sources with different underlying concepts and possible relationships and, second, analyze theoretical and computational complexity. We present the MID and DIMID algorithms. They perform extremely efficient on high dimensional data streams and provide accurate results, outperforming state-of-the-art algorithms for dependency monitoring. In the fourth part of this thesis, we introduce delayed relationships as a further feature in the dependency analysis. In reality, the phenomena monitored by e.g. some type of sensor might depend on another, but measurable effects can be delayed. This delay might be due to technical reasons, i.e. different stream processing speeds, or because the effects actually appear delayed over time. We present Loglag, the first algorithm that monitors dependency with respect to an optimal delay. It utilizes several approximation techniques to achieve competitive resource requirements. We demonstrate its scalability and accuracy on real world data, and also give theoretical guarantees to its accuracy

Music similarity analysis using the big data framework spark

A parameterizable recommender system based on the Big Data processing framework Spark is introduced, which takes multiple tonal properties of music into account and is capable of recommending music based on a user's personal preferences. The implemented system is fully scalable; more songs can be added to the dataset, the cluster size can be increased, and the possibility to add different kinds of audio features and more state-of-the-art similarity measurements is given. This thesis also deals with the extraction of the required audio features in parallel on a computer cluster. The extracted features are then processed by the Spark based recommender system, and song recommendations for a dataset consisting of approximately 114000 songs are retrieved in less than 12 seconds on a 16 node Spark cluster, combining eight different audio feature types and similarity measurements.Ein parametrisierbares Empfehlungssystem, basierend auf dem Big Data Framework Spark, wird präsentiert. Dieses berücksichtigt verschiedene klangliche Eigenschaften der Musik und erstellt Musikempfehlungen basierend auf den persönlichen Vorlieben eines Nutzers. Das implementierte Empfehlungssystem ist voll skalierbar. Mehr Lieder können dem Datensatz hinzugefügt werden, mehr Rechner können in das Computercluster eingebunden werden und die Möglichkeit andere Audiofeatures und aktuellere Ähnlichkeitsmaße hizuzufügen und zu verwenden, ist ebenfalls gegeben. Des Weiteren behandelt die Arbeit die parallele Berechnung der benötigten Audiofeatures auf einem Computercluster. Die Features werden von dem auf Spark basierenden Empfehlungssystem verarbeitet und Empfehlungen für einen Datensatz bestehend aus ca. 114000 Liedern können unter Berücksichtigung von acht verschiedenen Arten von Audiofeatures und Abstandsmaßen innerhalb von zwölf Sekunden auf einem Computercluster mit 16 Knoten berechnet werden

Performance and Reliability Evaluation of Apache Kafka Messaging System

Streaming data is now flowing across various devices and applications around us. This type of data means any unbounded, ever growing, infinite data set which is continuously generated by all kinds of sources. Examples include sensor data transmitted among different Internet of Things (IoT) devices, user activity records collected on websites and payment requests sent from mobile devices. In many application scenarios, streaming data needs to be processed in real-time because its value can be futile over time. A variety of stream processing systems have been developed in the last decade and are evolving to address rising challenges. A typical stream processing system consists of multiple processing nodes in the topology of a DAG (directed acyclic graph). To build real-time streaming data pipelines across those nodes, message middleware technology is widely applied. As a distributed messaging system with high durability and scalability, Apache Kafka has become very popular among modern companies. It ingests streaming data from upstream applications and store the data in its distributed cluster, which provides a fault-tolerant data source for stream processors. Therefore, Kafka plays a critical role to ensure the completeness, correctness and timeliness of streaming data delivery. However, it is impossible to meet all the user requirements in real-time cases with a simple and fixed data delivery strategy. In this thesis, we address the challenge of choosing a proper configuration to guarantee both performance and reliability of Kafka for complex streaming application scenarios. We investigate the features that have an impact on the performance and reliability metrics. We propose a queueing based prediction model to predict the performance metrics, including producer throughput and packet latency of Kafka. We define two reliability metrics, the probability of message loss and the probability of message duplication. We create an ANN model to predict these metrics given unstable network metrics like network delay and packet loss rate. To collect sufficient training data we build a Docker-based Kafka testbed with a fault injection module. We use a new quality-of-service metric, timely throughput to help us choosing proper batch size in Kafka. Based on this metric, we propose a dynamic configuration method, which reactively guarantees both performance and reliability of Kafka under complex operation conditions