Anomaly detection is a very pervasive problem applicable to a variety of domains including network intrusion, fraud detection, and system failures. It is a crucial task in many applications because failure to detect anomalous activity could result in highly undesirable outcomes. For example, (i) detection of anomalous medical claims is important to identify fraud; (ii) detection of fraudulent credit card transactions is necessary to help prevent identity theft; and (iii) detection of abnormal network traffic is necessary to identify hacking. Many techniques have been developed for anomaly detection. These methods can be broadly classified into two categories: (i) rule-based systems, and (ii) statistical datadriven approaches. The rule-based systems are based on domain expertise and look for specific types of anomalies while the data-driven approaches look to identify anomalies by identifying statistically rare patterns. Examples of datadriven methods include parametric methods that assume a known family for the nominal (non-anomalous) distribution and nonparametric methods such as those using unsupervised or semi-supervised support vector machines (SVMs) [1], [2] or based on minimum volume set estimation [3], [4], [5]. The advantage of data-driven approaches over rule-based methods is that they can identify novel types of anomalies that are unknown to the domain expert.

Convolutional neural networks (CNNs) are similar to "ordinary" neural networks in the sense that they are made up of hidden layers consisting of neurons with "learnable" parameters. These neurons receive inputs, performs a dot product, and then follows it with a non-linearity. The whole network expresses the mapping between raw image pixels and their class scores. Conventionally, the Softmax function is the classifier used at the last layer of this network. However, there have been studies (Alalshekmubarak and Smith, 2013; Agarap, 2017; Tang, 2013) conducted to challenge this norm. The cited studies introduce the usage of linear support vector machine (SVM) in an artificial neural network architecture. This project is yet another take on the subject, and is inspired by (Tang, 2013). Empirical data has shown that the CNN-SVM model was able to achieve a test accuracy of ~99.04% using the MNIST dataset (LeCun, Cortes, and Burges, 2010). On the other hand, the CNN-Softmax was able to achieve a test accuracy of ~99.23% using the same dataset. Both models were also tested on the recently-published Fashion-MNIST dataset (Xiao, Rasul, and Vollgraf, 2017), which is suppose to be a more difficult image classification dataset than MNIST (Zalandoresearch, 2017). This proved to be the case as CNN-SVM reached a test accuracy of ~90.72%, while the CNN-Softmax reached a test accuracy of ~91.86%. The said results may be improved if data preprocessing techniques were employed on the datasets, and if the base CNN model was a relatively more sophisticated than the one used in this study.

Support Vector Machines: SVMs are one of the several examples of supervised ML algorithms dealing with classification. They can be used for either regression or classification, in situations where the training dataset teaches the algorithm about specific classes, so that it can then classify the newly included data. What sets them apart from other algorithms is that they are able to separate classes quicker and with lesser overfitting than several other classification algorithms. A few of the biggest pain points that have been resolved using SVMs are display advertising, image-based gender detection and image classification with large feature sets. These are moderate in their accuracy, as well as their training times, mostly because it assumes linear approximation.

This paper proposes the adaptation of Support Vector Data Description (SVDD) to the multiple kernel case (MK-SVDD), based on SimpleMKL. It also introduces a variant called Slim-MK-SVDD that is able to produce a tighter frontier around the data. For the sake of comparison, the equivalent methods are also developed for One-Class SVM, known to be very similar to SVDD for certain shapes of kernels. Those algorithms are illustrated in the context of 3D-shapes filtering and outliers detection. For the 3D-shapes problem, the objective is to be able to select a sub-category of 3D-shapes, each sub-category being learned with our algorithm in order to create a filter. For outliers detection, we apply the proposed algorithms for unsupervised outliers detection as well as for the supervised case.

There are multiple ways to classify data with machine learning. You could run a logistic regression, use decision trees, or build a neural network to accomplish the task. In 1963, Vladimir Vapnik and Alexey Chervonenkis developed another classification tool, the support vector machine. Vapnik refined this classification method in the 1990's and extended uses for SVMs. Support vector machines have become a great tool for the data scientist.

Support vector machines (SVM) and other kernel techniques represent a family of powerful statistical classification methods with high accuracy and broad applicability. Because they use all or a significant portion of the training data, however, they can be slow, especially for large problems. Piecewise linear classifiers are similarly versatile, yet have the additional advantages of simplicity, ease of interpretation and, if the number of component linear classifiers is not too large, speed. Here we show how a simple, piecewise linear classifier can be trained from a kernel-based classifier in order to improve the classification speed. The method works by finding the root of the difference in conditional probabilities between pairs of opposite classes to build up a representation of the decision boundary. When tested on 17 different datasets, it succeeded in improving the classification speed of a SVM for 9 of them by factors as high as 88 times or more. The method is best suited to problems with continuum features data and smooth probability functions. Because the component linear classifiers are built up individually from an existing classifier, rather than through a simultaneous optimization procedure, the classifier is also fast to train.

There are 2 aspects of this research that are worth highlighting: (1) we showed that micro-structural extra-hippocampal abnormalities are consistent enough across medial temporal lobe epilepsy (TLE) patients that they can be used to predict TLE, and (2) we obtained regularization values for the models trained on this sparse data in an unusual but effective manner. Our input data consisted of 3 different diffusion imaging modalities: mean diffusivity (MD), fractional anisotropy (FA), and mean kurtosis (MK). Predictive models trained with MK proved to be the most accurate: .82 Also, the highest coefficients of these linear models were located within the inferior medial aspect of the temporal lobes. These locations have complex fiber anatomy with many crossings. Diffusion kurtosis imaging (DKI) is more apt than diffusion tensor imaging (DTI) at capturing fiber crossings due to the presence of non-Gaussian water diffusion.

The adoption of automated, data-driven decision making in an ever expanding range of applications has raised concerns about its potential unfairness towards certain social groups. In this context, a number of recent studies have focused on defining, detecting, and removing unfairness from data-driven decision systems. However, the existing notions of fairness, based on parity (equality) in treatment or outcomes for different social groups, tend to be quite stringent, limiting the overall decision making accuracy. In this paper, we draw inspiration from the fair-division and envy-freeness literature in economics and game theory and propose preference-based notions of fairness -- given the choice between various sets of decision treatments or outcomes, any group of users would collectively prefer its treatment or outcomes, regardless of the (dis)parity as compared to the other groups. Then, we introduce tractable proxies to design margin-based classifiers that satisfy these preference-based notions of fairness. Finally, we experiment with a variety of synthetic and real-world datasets and show that preference-based fairness allows for greater decision accuracy than parity-based fairness.

It is often argued that the algorithm used for machine learning is less important than the amount of data used to train the algorithm (e.g., Domingos, 2012; "More data beats a cleverer algorithm"). In a monumental study, Fernández-Delgado and colleagues tested 179 machine learning categorizers on 121 data sets. They found that a large majority of them, were essentially identical in their accuracy. In fact, 121 of them (that's a coincidence) were within 5 percentage points of one another averaging all of the data sets. The following two graphs show the same data organized either by family (color and order) or by accuracy (order) and family (color). Each family relies on the same core classifiers but may use different parameters or different transformations of the data.

Complex statistics in Machine Learning worry a lot of developers. Knowing statistics helps you build strong Machine Learning models that are optimized for a given problem statement. Understand the real-world examples that discuss the statistical side of Machine Learning and familiarize yourself with it. We will use libraries such as scikit-learn, e1071, randomForest, c50, xgboost, and so on.We will discuss the application of frequently used algorithms on various domain problems, using both Python and R programming.It focuses on the various tree-based machine learning models used by industry practitioners.We will also discuss k-nearest neighbors, Naive Bayes, Support Vector Machine and recommendation engine.By the end of the course, you will have mastered the required statistics for Machine Learning Algorithm and will be able to apply your new skills to any sort of industry problem.