APPENDIX A. Visualizing the Wishart Distribution The Wishart distribution is a generalization to multiple dimensions of the chi-squared distribution, or in the case of non-integer degrees of freedom, of the gamma distribution. We show in fig.5 that for a 1-dimensional and equal to 1 Σ scale matrix, the Wishart distribution W 1( n, 1) is equivalent to the χ 2 ( n) distribution. Figure 5: Monodimensional Wishart Distribution and χ 2 (n) distribution comparison Save for this simple case, being the Wishart a distribution over matrices, it is a generally hard task to visualize it as a density function. Samples can be however drawn from it and the eigenvectors and eigenvalues of the resulting sampled matrix can be exploited to define an ellipse. An example of this technique is shown in fig.6.

The identification of cyberattacks which target information and communication systems has been a focus of the research community for years. Network intrusion detection is a complex problem which presents a diverse number of challenges. Many attacks currently remain undetected, while newer ones emerge due to the proliferation of connected devices and the evolution of communication technology. In this survey, we review the methods that have been applied to network data with the purpose of developing an intrusion detector, but contrary to previous reviews in the area, we analyze them from the perspective of the Knowledge Discovery in Databases (KDD) process. As such, we discuss the techniques used for the capture, preparation and transformation of the data, as well as, the data mining and evaluation methods. In addition, we also present the characteristics and motivations behind the use of each of these techniques and propose more adequate and up-to-date taxonomies and definitions for intrusion detectors based on the terminology used in the area of data mining and KDD. Special importance is given to the evaluation procedures followed to assess the different detectors, discussing their applicability in current real networks. Finally, as a result of this literature review, we investigate some open issues which will need to be considered for further research in the area of network security.

There is fast-growing literature on estimating heterogeneous treatment effects via random forests in observational studies. However, there are few approaches available for right-censored survival data. In clinical trials, right-censored survival data are frequently encountered. Quantifying the causal relationship between a treatment and the survival outcome is of great interest. Random forests provide a robust, nonparametric approach to statistical estimation. In addition, recent developments allow forest-based methods to quantify the uncertainty of the estimated heterogeneous treatment effects. We propose causal survival forests that directly target on estimating the treatment effect from an observational study. We establish consistency and asymptotic normality of the proposed estimators and provide an estimator of the asymptotic variance that enables valid confidence intervals of the estimated treatment effect. The performance of our approach is demonstrated via extensive simulations and data from an HIV study.

A bstract Continuous high frequency water quality monitoring is becoming a critical task to support water management. Despite the advancement s in sensor technologies, certain variables cannot be easily and/or economically monitored in - situ and in real time. In these cases, surrogate measures can be used to make estimations by means of data - driven models. In th is work, variables that are commonly measured in - situ are used as surrogates to estimate the concentration s of nutrients in a rural catchment and in an urban one, making use of machine learning models, specifically Random Forests . The results are compared with those of linear modelling using the same number of surrogates, obtaining a reduction in the Root Mean Squared Error (RMSE) of up to 60.1% . Th e profit from including up to seven surrogate sensors was computed, concluding that adding more than 4 and 5 sensors in each of the catchments respectively was not worthy in terms of error improvement. Keywords water monitoring, water quality, surrogate parameters, random forests, soft - sensors, machine learning 2 1. Introduction Waterb odies must maintain a good ecological and chemical status in order to protect human health, preserve water supply and safeguard natural ecosystems and biodiversity. The assessment of the ecological status of these waterbodies in a coherent and comprehensiv e way would benefit from improving water quality monitoring progra mmes (Voulvoulis et al., 2017) . To date, many substa nces like major nutrients (nitrogen (N) and phosphorus (P)) are mostly monitored by means of analytical discrete campaigns with low sampling frequenc y . Nutrient monitoring is of great importance to reduce the risk of eutrophication, a water quality problem that leads to numerous negative impacts like public health issues, fish mortality and unhealthy ecosystems, among others .

In the last decade, social networks became most popular medium for communication and interaction. As an example, micro-blogging service Twitter has more than 200 million registered users who exchange more than 65 million posts per day. Users express their thoughts, ideas, and even their intentions through these tweets. Most of the tweets are written informally and often in slang language, that contains misspelt and abbreviated words. This paper investigates the problem of selecting features that affect extracting user's intention from Twitter feeds based on text mining techniques. It starts by presenting the method we used to construct our own dataset from extracted Twitter feeds. Following that, we present two techniques of feature selection followed by classification. In the first technique, we use Information Gain as a one-phase feature selection, followed by supervised classification algorithms. In the second technique, we use a hybrid approach based on forward feature selection algorithm in which two feature selection techniques employed followed by classification algorithms. We examine these two techniques with four classification algorithms. We evaluate them using our own dataset, and we critically review the results.

Benjamin Franklin said that only two things are certain in life: death and taxes. That explains why my colleagues at STATWORX were less than excited when they told me about their plans for the weekend a few weeks back: doing their income tax declaration. Man, I thought, that sucks, I'd rather spend this time outdoors. And then an idea was born. What could taxes and the outdoors possibly have in common?

Label ranking is a prediction task which deals with learning a mapping between an instance and a ranking (i.e., order) of labels from a finite set, representing their relevance to the instance. Boosting is a well-known and reliable ensemble technique that was shown to often outperform other learning algorithms. While boosting algorithms were developed for a multitude of machine learning tasks, label ranking tasks were overlooked. In this paper, we propose a boosting algorithm which was specifically designed for label ranking tasks. Extensive evaluation of the proposed algorithm on 24 semi-synthetic and real-world label ranking datasets shows that it significantly outperforms existing state-of-the-art label ranking algorithms.

When creating text classification systems, one of the major bottlenecks is the annotation of training data. Active learning has been proposed to address this bottleneck using stopping methods to minimize the cost of data annotation. An important capability for improving the utility of stopping methods is to effectively forecast the performance of the text classification models. Forecasting can be done through the use of logarithmic models regressed on some portion of the data as learning is progressing. A critical unexplored question is what portion of the data is needed for accurate forecasting. There is a tension, where it is desirable to use less data so that the forecast can be made earlier, which is more useful, versus it being desirable to use more data, so that the forecast can be more accurate. We find that when using active learning it is even more important to generate forecasts earlier so as to make them more useful and not waste annotation effort. We investigate the difference in forecasting difficulty when using accuracy and F-measure as the text classification system performance metrics and we find that F-measure is more difficult to forecast. We conduct experiments on seven text classification datasets in different semantic domains with different characteristics and with three different base machine learning algorithms. We find that forecasting is easiest for decision tree learning, moderate for Support Vector Machines, and most difficult for neural networks.

The aim of this work is to propose a meta-algorithm for automatic classification in the presence of discrete binary classes. Classifier learning in the presence of overlapping class distributions is a challenging problem in machine learning. Overlapping classes are described by the presence of ambiguous areas in the feature space with a high density of points belonging to both classes. This often occurs in real-world datasets, one such example is numeric data denoting properties of particle decays derived from high-energy accelerators like the Large Hadron Collider (LHC). A significant body of research targeting the class overlap problem use ensemble classifiers to boost the performance of algorithms by using them iteratively in multiple stages or using multiple copies of the same model on different subsets of the input training data. The former is called boosting and the latter is called bagging. The algorithm proposed in this thesis targets a challenging classification problem in high energy physics - that of improving the statistical significance of the Higgs discovery. The underlying dataset used to train the algorithm is experimental data built from the official ATLAS full-detector simulation with Higgs events (signal) mixed with different background events (background) that closely mimic the statistical properties of the signal generating class overlap. The algorithm proposed is a variant of the classical boosted decision tree which is known to be one of the most successful analysis techniques in experimental physics. The algorithm utilizes a unified framework that combines two meta-learning techniques - bagging and boosting. The results show that this combination only works in the presence of a randomization trick in the base learners.

Tree-based machine learning models such as random forests, decision trees and gradient boosted trees are popular nonlinear predictive models, yet comparatively little attention has been paid to explaining their predictions. Here we improve the interpretability of tree-based models through three main contributions. We apply these tools to three medical machine learning problems and show how combining many high-quality local explanations allows us to represent global structure while retaining local faithfulness to the original model. These tools enable us to (1) identify high-magnitude but low-frequency nonlinear mortality risk factors in the US population, (2) highlight distinct population subgroups with shared risk characteristics, (3) identify nonlinear interaction effects among risk factors for chronic kidney disease and (4) monitor a machine learning model deployed in a hospital by identifying which features are degrading the model's performance over time. Given the popularity of tree-based machine learning models, these improvements to their interpretability have implications across a broad set of domains.