A framework for dependency estimation in heterogeneous data streams

Estimating dependencies from data is a fundamental task of Knowledge Discovery. Identifying the relevant variables leads to a better understanding of data and improves both the runtime and the outcomes of downstream Data Mining tasks. Dependency estimation from static numerical data has received much attention. However, real-world data often occurs as heterogeneous data streams: On the one hand, data is collected online and is virtually infinite. On the other hand, the various components of a stream may be of different types, e.g., numerical, ordinal or categorical. For this setting, we propose Monte Carlo Dependency Estimation (MCDE), a framework that quantifies multivariate dependency as the average statistical discrepancy between marginal and conditional distributions, via Monte Carlo simulations. MCDE handles heterogeneity by leveraging three statistical tests: the Mann–Whitney U, the Kolmogorov–Smirnov and the Chi-Squared test. We demonstrate that MCDE goes beyond the state of the art regarding dependency estimation by meeting a broad set of requirements. Finally, we show with a real-world use case that MCDE can discover useful patterns in heterogeneous data streams

Hypoglycemia detection in patients with type 1 diabetes using EEG signals

The main risk for patients with type 1 diabetes (T1D) is to fall into hypoglycemia. We have extended the quantitative detection of hypoglycemia from the altered EEG signal in T1D patients by analyzing all EEG channel data through different measures of signal complexity such as the fractal domain and entropy indices. Finally, they were classified through a neural network in order to detect hypoglycemia with a high percentage of precision using the results obtained from the complexity analysis

Estimating Dependency, Monitoring and Knowledge Discovery in High-Dimensional Data Streams

Data Mining – known as the process of extracting knowledge from massive data sets – leads to phenomenal impacts on our society, and now affects nearly every aspect of our lives: from the layout in our local grocery store, to the ads and product recommendations we receive, the availability of treatments for common diseases, the prevention of crime, or the efficiency of industrial production processes. However, Data Mining remains difficult when (1) data is high-dimensional, i.e., has many attributes, and when (2) data comes as a stream. Extracting knowledge from high-dimensional data streams is impractical because one must cope with two orthogonal sets of challenges. On the one hand, the effects of the so-called "curse of dimensionality" bog down the performance of statistical methods and yield to increasingly complex Data Mining problems. On the other hand, the statistical properties of data streams may evolve in unexpected ways, a phenomenon known in the community as "concept drift". Thus, one needs to update their knowledge about data over time, i.e., to monitor the stream. While previous work addresses high-dimensional data sets and data streams to some extent, the intersection of both has received much less attention. Nevertheless, extracting knowledge in this setting is advantageous for many industrial applications: identifying patterns from high-dimensional data streams in real-time may lead to larger production volumes, or reduce operational costs. The goal of this dissertation is to bridge this gap. We first focus on dependency estimation, a fundamental task of Data Mining. Typically, one estimates dependency by quantifying the strength of statistical relationships. We identify the requirements for dependency estimation in high-dimensional data streams and propose a new estimation framework, Monte Carlo Dependency Estimation (MCDE), that fulfils them all. We show that MCDE leads to efficient dependency monitoring. Then, we generalise the task of monitoring by introducing the Scaling Multi-Armed Bandit (S-MAB) algorithms, extending the Multi-Armed Bandit (MAB) model. We show that our algorithms can efficiently monitor statistics by leveraging user-specific criteria. Finally, we describe applications of our contributions to Knowledge Discovery. We propose an algorithm, Streaming Greedy Maximum Random Deviation (SGMRD), which exploits our new methods to extract patterns, e.g., outliers, in high-dimensional data streams. Also, we present a new approach, that we name kj-Nearest Neighbours (kj-NN), to detect outlying documents within massive text corpora. We support our algorithmic contributions with theoretical guarantees, as well as extensive experiments against both synthetic and real-world data. We demonstrate the benefits of our methods against real-world use cases. Overall, this dissertation establishes fundamental tools for Knowledge Discovery in high-dimensional data streams, which help with many applications in the industry, e.g., anomaly detection, or predictive maintenance. To facilitate the application of our results and future research, we publicly release our implementations, experiments, and benchmark data via open-source platforms

Measuring association with recursive rank binning

Pairwise measures of dependence are a common tool to map data in the early stages of analysis with several modern examples based on maximized partitions of the pairwise sample space. Following a short survey of modern measures of dependence, we introduce a new measure which recursively splits the ranks of a pair of variables to partition the sample space and computes the $\chi^2$ statistic on the resulting bins. Splitting logic is detailed for splits maximizing a score function and randomly selected splits. Simulations indicate that random splitting produces a statistic conservatively approximated by the $\chi^2$ distribution without a loss of power to detect numerous different data patterns compared to maximized binning. Though it seems to add no power to detect dependence, maximized recursive binning is shown to produce a natural visualization of the data and the measure. Applying maximized recursive rank binning to S&P 500 constituent data suggests the automatic detection of tail dependence.Comment: 59 pages, 22 figure

ASSESSING THE MODEL FIT OF MULTIDIMENSIONAL ITEM RESPONSE THEORY MODELS WITH POLYTOMOUS RESPONSES USING LIMITED-INFORMATION STATISTICS

Under item response theory, three types of limited information goodness-of-fit test statistics – M2, Mord, and C2 – have been proposed to assess model-data fit when data are sparse. However, the evaluation of the performance of these GOF statistics under multidimensional item response theory (MIRT) models with polytomous data is limited. The current study showed that M2 and C2 were well-calibrated under true model conditions and were powerful under misspecified model conditions. Mord were not well-calibrated when the number of response categories was more than three. RMSEA2 and RMSEAC2 are good tools to evaluate approximate fit. The second study aimed to evaluate the psychometric properties of the Religious Commitment Inventory-10 (RCI-10; Worthington et al., 2003) within the IRT framework and estimate C2 and its RMSEA to assess global model-fit. Results showed that the RCI-10 was best represented by a bifactor model. The scores from the RCI-10 could be scored as unidimensional notwithstanding the presence of multidimensionality. Two-factor correlational solution should not be used. Study two also showed that religious commitment is a risk factor of intimate partner violence, whereas spirituality was a protecting factor from the violence. More alcohol was related with more abusive behaviors. Implications of the two studies were discussed

CLADAG 2021 BOOK OF ABSTRACTS AND SHORT PAPERS

The book collects the short papers presented at the 13th Scientific Meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society (SIS). The meeting has been organized by the Department of Statistics, Computer Science and Applications of the University of Florence, under the auspices of the Italian Statistical Society and the International Federation of Classification Societies (IFCS). CLADAG is a member of the IFCS, a federation of national, regional, and linguistically-based classification societies. It is a non-profit, non-political scientific organization, whose aims are to further classification research

Image Analysis Applications of the Maximum Mean Discrepancy Distance Measure

The need to quantify distance between two groups of objects is prevalent throughout the signal processing world. The difference of group means computed using the Euclidean, or L2 distance, is one of the predominant distance measures used to compare feature vectors and groups of vectors, but many problems arise with it when high data dimensionality is present. Maximum mean discrepancy (MMD) is a recent unsupervised kernel-based pattern recognition method which may improve differentiation between two distinct populations over many commonly used methods such as the difference of means, when paired with the proper feature representations and kernels. MMD-based distance computation combines many powerful concepts from the machine learning literature, such as data distribution-leveraging similarity measures and kernel methods for machine learning. Due to this heritage, we posit that dissimilarity-based classification and changepoint detection using MMD can lead to enhanced separation between different populations. To test this hypothesis, we conduct studies comparing MMD and the difference of means in two subareas of image analysis and understanding: first, to detect scene changes in video in an unsupervised manner, and secondly, in the biomedical imaging field, using clinical ultrasound to assess tumor response to treatment. We leverage effective computer vision data descriptors, such as the bag-of-visual-words and sparse combinations of SIFT descriptors, and choose from an assessment of several similarity kernels (e.g. Histogram Intersection, Radial Basis Function) in order to engineer useful systems using MMD. Promising improvements over the difference of means, measured primarily using precision/recall for scene change detection, and k-nearest neighbour classification accuracy for tumor response assessment, are obtained in both applications.1 yea