Statistical and Information-Theoretic Methods for Data-Analysis

In this Thesis, we develop theory and methods for computational data analysis. The problems in data analysis are approached from three perspectives: statistical learning theory, the Bayesian framework, and the information-theoretic minimum description length (MDL) principle. Contributions in statistical learning theory address the possibility of generalization to unseen cases, and regression analysis with partially observed data with an application to mobile device positioning. In the second part of the Thesis, we discuss so called Bayesian network classifiers, and show that they are closely related to logistic regression models. In the final part, we apply the MDL principle to tracing the history of old manuscripts, and to noise reduction in digital signals.

Mining Sequential Data – in Search of Segmental Structures

Segmentation is a data mining technique yielding simplified representations of sequences of ordered points. A sequence is divided into some number of homogeneous blocks, and all points within a segment are described by a single value. The focus in this thesis is on piecewise-constant segments, where the most likely description for each segment and the most likely segmentation into some number of blocks can be computed efficiently. Representing sequences as segmentations is useful in, e.g., storage and indexing tasks in sequence databases, and segmentation can be used as a tool in learning about the structure of a given sequence. The discussion in this thesis begins with basic questions related to segmentation analysis, such as choosing the number of segments, and evaluating the obtained segmentations. Standard model selection techniques are shown to perform well for the sequence segmentation task. Segmentation evaluation is proposed with respect to a known segmentation structure. Applying segmentation on certain features of a sequence is shown to yield segmentations that are significantly close to the known underlying structure. Two extensions to the basic segmentation framework are introduced: unimodal segmentation and basis segmentation. The former is concerned with segmentations where the segment descriptions first increase and then decrease, and the latter with the interplay between different dimensions and segments in the sequence. These problems are formally defined and algorithms for solving them are provided and analyzed. Practical applications for segmentation techniques include time series and data stream analysis, text analysis, and biological sequence analysis. In this thesis segmentation applications are demonstrated in analyzing genomic sequences.

Computationally Efficient Methods for MDL-Optimal Density Estimation and Data Clustering

The Minimum Description Length (MDL) principle is a general, well-founded theoretical formalization of statistical modeling. The most important notion of MDL is the stochastic complexity, which can be interpreted as the shortest description length of a given sample of data relative to a model class. The exact definition of the stochastic complexity has gone through several evolutionary steps. The latest instantation is based on the so-called Normalized Maximum Likelihood (NML) distribution which has been shown to possess several important theoretical properties. However, the applications of this modern version of the MDL have been quite rare because of computational complexity problems, i.e., for discrete data, the definition of NML involves an exponential sum, and in the case of continuous data, a multi-dimensional integral usually infeasible to evaluate or even approximate accurately. In this doctoral dissertation, we present mathematical techniques for computing NML efficiently for some model families involving discrete data. We also show how these techniques can be used to apply MDL in two practical applications: histogram density estimation and clustering of multi-dimensional data.

Matrix Decomposition Methods for Data Mining : Computational Complexity and Algorithms

Matrix decompositions, where a given matrix is represented as a product of two other matrices, are regularly used in data mining. Most matrix decompositions have their roots in linear algebra, but the needs of data mining are not always those of linear algebra. In data mining one needs to have results that are interpretable -- and what is considered interpretable in data mining can be very different to what is considered interpretable in linear algebra. --- The purpose of this thesis is to study matrix decompositions that directly address the issue of interpretability. An example is a decomposition of binary matrices where the factor matrices are assumed to be binary and the matrix multiplication is Boolean. The restriction to binary factor matrices increases interpretability -- factor matrices are of the same type as the original matrix -- and allows the use of Boolean matrix multiplication, which is often more intuitive than normal matrix multiplication with binary matrices. Also several other decomposition methods are described, and the computational complexity of computing them is studied together with the hardness of approximating the related optimization problems. Based on these studies, algorithms for constructing the decompositions are proposed. Constructing the decompositions turns out to be computationally hard, and the proposed algorithms are mostly based on various heuristics. Nevertheless, the algorithms are shown to be capable of finding good results in empirical experiments conducted with both synthetic and real-world data.

Efficient search for statistically significant dependency rules in binary data

Analyzing statistical dependencies is a fundamental problem in all empirical science. Dependencies help us understand causes and effects, create new scientific theories, and invent cures to problems. Nowadays, large amounts of data is available, but efficient computational tools for analyzing the data are missing. In this research, we develop efficient algorithms for a commonly occurring search problem - searching for the statistically most significant dependency rules in binary data. We consider dependency rules of the form X->A or X->not A, where X is a set of positive-valued attributes and A is a single attribute. Such rules describe which factors either increase or decrease the probability of the consequent A. A classical example are genetic and environmental factors, which can either cause or prevent a disease. The emphasis in this research is that the discovered dependencies should be genuine - i.e. they should also hold in future data. This is an important distinction from the traditional association rules, which - in spite of their name and a similar appearance to dependency rules - do not necessarily represent statistical dependencies at all or represent only spurious connections, which occur by chance. Therefore, the principal objective is to search for the rules with statistical significance measures. Another important objective is to search for only non-redundant rules, which express the real causes of dependence, without any occasional extra factors. The extra factors do not add any new information on the dependence, but can only blur it and make it less accurate in future data. The problem is computationally very demanding, because the number of all possible rules increases exponentially with the number of attributes. In addition, neither the statistical dependency nor the statistical significance are monotonic properties, which means that the traditional pruning techniques do not work. As a solution, we first derive the mathematical basis for pruning the search space with any well-behaving statistical significance measures. The mathematical theory is complemented by a new algorithmic invention, which enables an efficient search without any heuristic restrictions. The resulting algorithm can be used to search for both positive and negative dependencies with any commonly used statistical measures, like Fisher's exact test, the chi-squared measure, mutual information, and z scores. According to our experiments, the algorithm is well-scalable, especially with Fisher's exact test. It can easily handle even the densest data sets with 10000-20000 attributes. Still, the results are globally optimal, which is a remarkable improvement over the existing solutions. In practice, this means that the user does not have to worry whether the dependencies hold in future data or if the data still contains better, but undiscovered dependencies.

Mining Cell Transition Data

Cell transition data is obtained from a cellular phone that switches its current serving cell tower. The data consists of a sequence of transition events, which are pairs of cell identifiers and transition times. The focus of this thesis is applying data mining methods to such data, developing new algorithms, and extracting knowledge that will be a solid foundation on which to build location-aware applications. In addition to a thorough exploration of the features of the data, the tools and methods developed in this thesis provide solutions to three distinct research problems. First, we develop clustering algorithms that produce a reliable mapping between cell transitions and physical locations observed by users of mobile devices. The main clustering algorithm operates in online fashion, and we consider also a number of offline clustering methods for comparison. Second, we define the concept of significant locations, known as bases, and give an online algorithm for determining them. Finally, we consider the task of predicting the movement of the user, based on historical data. We develop a prediction algorithm that considers paths of movement in their entirety, instead of just the most recent movement history. All of the presented methods are evaluated with a significant body of real cell transition data, collected from about one hundred different individuals. The algorithms developed in this thesis are designed to be implemented on a mobile device, and require no extra hardware sensors or network infrastructure. By not relying on external services and keeping the user information as much as possible on the user s own personal device, we avoid privacy issues and let the users control the disclosure of their location information.

Shifting centres: Pedagogical relations in the Era of Big Data

This paper presents a cautious argument for re-thinking both the nature and the centrality of the one-to-one teacher/student relationship in contemporary pedagogy. A case is made that learning in and for our times requires us to broaden our understanding of pedagogical relations beyond the singularity of the teacher/student binary and to promote the connected teacher as better placed to lead learning for these times. The argument proceeds in three parts: first, a characterization of our times as defined increasingly by the digital knowledge explosion of Big Data; second, a re-thinking of the nature of pedagogical relationships in the context of Big Data; and third, an account of the ways in which leaders can support their teachers to become more effective in leading learning by being more closely connected to their professional colleagues.

Bycatch and strandings programs as ecological indicators for data-limited cetaceans

An integrated approach of using strandings and bycatch data may provide an indicator of long-term trends for data-limited cetaceans. Strandings programs can give a faithful representation of the species composition of cetacean assemblages, while standardised bycatch rates can provide a measure of relative abundance. Comparing the two datasets may also facilitate managing impacts by understanding which species, sex or sizes are the most vulnerable to interactions with fisheries gear. Here we apply this approach to two long-term datasets in East Australia, bycatch in the Queensland Shark Control Program (QSCP, 1992–2012) and strandings in the Queensland Marine Wildlife Strandings and Mortality Program (StrandNet, 1996–2012). Short-beaked common dolphins, Delphinus delphis, were markedly more frequent in bycatch than in the strandings dataset, suggesting that they are more prone to being incidentally caught than other cetacean species in the region. The reverse was true for humpback whales, Megaptera novaeangliae, bottlenose dolphins, Tursiops spp.; and species predominantly found in offshore waters. QSCP bycatch was strongly skewed towards females for short-beaked common dolphins, and towards smaller sizes for Australian humpback dolphins, Sousa sahulensis. Overall, both datasets demonstrated similar seasonality and a similar long-term increase from 1996 until 2008. Analysis on a species-by-species basis was then used to explore potential explanations for long-term trends, which ranged from a recovering stock (humpback whales) to a shift in habitat use (short-beaked common dolphins).

Using Big Data to manage safety-related risk in the upstream oil and gas industry: A research agenda

Despite considerable effort and a broad range of new approaches to safety management over the years, the upstream oil & gas industry has been frustrated by the sector’s stubbornly high rate of injuries and fatalities. This short communication points out, however, that the industry may be in a position to make considerable progress by applying “Big Data” analytical tools to the large volumes of safety-related data that have been collected by these organizations. Toward making this case, we examine existing safety-related information management practices in the upstream oil & gas industry, and specifically note that data in this sector often tends to be highly customized, difficult to analyze using conventional quantitative tools, and frequently ignored. We then contend that the application of new Big Data kinds of analytical techniques could potentially reveal patterns and trends that have been hidden or unknown thus far, and argue that these tools could help the upstream oil & gas sector to improve its injury and fatality statistics. Finally, we offer a research agenda toward accelerating the rate at which Big Data and new analytical capabilities could play a material role in helping the industry to improve its health and safety performance.

A data fusion approach of multiple maintenance data sources for real-world reliability modelling

A central tenet in the theory of reliability modelling is the quantification of the probability of asset failure. In general, reliability depends on asset age and the maintenance policy applied. Usually, failure and maintenance times are the primary inputs to reliability models. However, for many organisations, different aspects of these data are often recorded in different databases (e.g. work order notifications, event logs, condition monitoring data, and process control data). These recorded data cannot be interpreted individually, since they typically do not have all the information necessary to ascertain failure and preventive maintenance times. This paper presents a methodology for the extraction of failure and preventive maintenance times using commonly-available, real-world data sources. A text-mining approach is employed to extract keywords indicative of the source of the maintenance event. Using these keywords, a Naïve Bayes classifier is then applied to attribute each machine stoppage to one of two classes: failure or preventive. The accuracy of the algorithm is assessed and the classified failure time data are then presented. The applicability of the methodology is demonstrated on a maintenance data set from an Australian electricity company.