Abstract--Predictive uncertainty is crucial for many computer vision tasks, from image classification to autonomous driving systems. Hamiltonian Monte Carlo (HMC) is an inference method for sampling complex posterior distributions. On the other hand, Dropout regularization has been proposed as an approximate model averaging technique that tends to improve generalization in large scale models such as deep neural networks. Although, HMC provides convergence guarantees for most standard Bayesian models, it does not handle discrete parameters arising from Dropout regularization. In this paper, we present a robust methodology for predictive uncertainty in large scale classification problems, based on Dropout and Stochastic Gradient Hamiltonian Monte Carlo. Even though Dropout induces a non-smooth energy function with no such convergence guarantees, the resulting discretization of the Hamiltonian proves empirical success. The proposed method allows to effectively estimate predictive accuracy and to provide better generalization for difficult test examples.

Ensemble learning is a powerful approach to construct a strong learner from multiple base learners. The most popular way to aggregate an ensemble of classifiers is majority voting, which assigns a sample to the class that most base classifiers vote for. However, improved performance can be obtained by assigning weights to the base classifiers according to their accuracy. This paper proposes an agreement rate initialized maximum likelihood estimator (ARIMLE) to optimally fuse the base classifiers. ARIMLE first uses a simplified agreement rate method to estimate the classification accuracy of each base classifier from the unlabeled samples, then employs the accuracies to initialize a maximum likelihood estimator (MLE), and finally uses the expectation-maximization algorithm to refine the MLE. Extensive experiments on visually evoked potential classification in a brain-computer interface application show that ARIMLE outperforms majority voting, and also achieves better or comparable performance with several other state-of-the-art classifier combination approaches.

There are many important regression problems in real-world brain-computer interface (BCI) applications, e.g., driver drowsiness estimation from EEG signals. This paper considers offline analysis: given a pool of unlabeled EEG epochs recorded during driving, how do we optimally select a small number of them to label so that an accurate regression model can be built from them to label the rest? Active learning is a promising solution to this problem, but interestingly, to our best knowledge, it has not been used for regression problems in BCI so far. This paper proposes a novel enhanced batch-mode active learning (EBMAL) approach for regression, which improves upon a baseline active learning algorithm by increasing the reliability, representativeness and diversity of the selected samples to achieve better regression performance. We validate its effectiveness using driver drowsiness estimation from EEG signals. However, EBMAL is a general approach that can also be applied to many other offline regression problems beyond BCI.

Active learning (AL) [33], a subfield of machine learning, considers the following problem: if the learning algorithm can choose the training data, then which training samples should it choose to maximize the learning performance, under a fixed budget, e.g., the maximum number of labeled training samples? As an example, consider emotion estimation in affective computing [28]. Emotions can be represented as continuous numbers in the 2D space of arousal and valence [30], or in the 3D space of arousal, valence, and dominance [26]. However, emotions are very subjective, subtle, and uncertain. So, usually multiple human assessors are needed to obtain the groundtruth emotion values for each affective sample (video, audio, image, physiological signal, etc). For example, 14-16 assessors were used to evaluate each video clip in the DEAP dataset [21], six to 17 assessors for each utterance in the VAM (Vera am Mittag in German, Vera at Noon in English) spontaneous speech corpus [16], and at least 110 assessors for each sound in the IADS-2 (International Affective Digitized Sounds 2nd Edition) dataset [4]. This is very time-consuming and labor-intensive. How should we optimally select the affective samples to label so that an accurate regression model can be built with the minimum cost (i.e., the minimum number of labeled samples)?

As research on hate speech becomes more and more relevant every day, most of it is still focused on hate speech detection. By attempting to replicate a hate speech detection experiment performed on an existing Twitter corpus annotated for hate speech, we highlight some issues that arise from doing research in the field of hate speech, which is essentially still in its infancy. We take a critical look at the training corpus in order to understand its biases, while also using it to venture beyond hate speech detection and investigate whether it can be used to shed light on other facets of research, such as popularity of hate tweets.

Linear regression is one of the essential tools in statistical analysis. In this course, we'll walk through step-by-step how to conduct many important analyses using SPSS. Although you will learn the basics of what these statistics are, we'll avoid complicated mathematical discussions and go right to what you need to know to conduct these analyses. Linear regression is basically a tool that allows you to test relationships between many variables at the same time, control for variables' effects, and create simple statistical models that allow you to make predictions. In this course, we'll cover the following key topics: You'll not only learn how to conduct these analyses, we'll also go over how to interpret the statistical results and how to graph the results using SPSS and a special Excel template I've created for you.

While the term "machine learning" generally relates to understanding structures or patterns in data, it can also refer to a very diverse set of activities and techniques. Most of us have experienced machine learning in our everyday lives with natural language processing (Alexa, Siri), image recognition (Facebook, Pinterest), purchase recommendations (Amazon) and search optimization (Google). These approaches generally use many different types of algorithms (e.g., neural networks, decision trees, clustering, support vector machines, etc.) Industrial operations, on the other hand, need more specialized approaches that can provide actionable insights to reduce downtime as well as improve throughput, operator safety, and product quality. Whether you call it Industry 4.0 or Industrial IoT or Digital Operations, the increased access to operational data, combined with the spread of computing, connectivity, and storage, has created the perfect environment for transforming industrial operations. The real opportunity is in unlocking the value of this data.

Linear models, as their name implies, relates an outcome to a set of predictors of interest using linear assumptions. Regression models, a subset of linear models, are the most important statistical analysis tool in a data scientist's toolkit. This course covers regression analysis, least squares and inference using regression models. Special cases of the regression model, ANOVA and ANCOVA will be covered as well. Analysis of residuals and variability will be investigated.

Python, a multi-paradigm programming language, has become the language of choice for data scientists for data analysis, visualization, and machine learning. This course takes you through the various different concepts that get you acquainted and working with the different aspects of Machine Learning. You'll start by diving into classical statistical analysis, where you will learn to compute descriptive statistics with Pandas. From there, you will be introduced to supervised learning, where you will explore the principles of machine learning and train different machine learning models. After that, you'll work with algorithms for regression analysis, and employ different types of regression, such as ridge and lasso regression, and spline interpolation using SciPy.

About this course: With every smartphone and computer now boasting multiple processors, the use of functional ideas to facilitate parallel programming is becoming increasingly widespread. In this course, you'll learn the fundamentals of parallel programming, from task parallelism to data parallelism. In particular, you'll see how many familiar ideas from functional programming map perfectly to to the data parallel paradigm. We'll start the nuts and bolts how to effectively parallelize familiar collections operations, and we'll build up to parallel collections, a production-ready data parallel collections library available in the Scala standard library. Throughout, we'll apply these concepts through several hands-on examples that analyze real-world data, such as popular algorithms like k-means clustering.