This introduction aims to provide readers an intuitive understanding of Gaussian processes regression. Gaussian processes regression (GPR) models have been widely used in machine learning applications because their representation flexibility and inherently uncertainty measures over predictions. The paper starts with explaining mathematical basics that Gaussian processes built on including multivariate normal distribution, kernels, non-parametric models, joint and conditional probability. The Gaussian processes regression is then described in an accessible way by balancing showing unnecessary mathematical derivation steps and missing key conclusive results. An illustrative implementation of a standard Gaussian processes regression algorithm is provided. Beyond the standard Gaussian processes regression, existing software packages to implement state-of-the-art Gaussian processes algorithms are reviewed. Lastly, more advanced Gaussian processes regression models are specified. The paper is written in an accessible way, thus undergraduate science and engineering background will find no difficulties in following the content.

Understanding and quantifying uncertainty in black box Neural Networks (NNs) is critical when deployed in real-world settings such as healthcare. Recent works using Bayesian and non-Bayesian methods have shown how a unified predictive uncertainty can be modelled for NNs. Decomposing this uncertainty to disentangle the granular sources of heteroscedasticity in data provides rich information about its underlying causes. We propose a conceptually simple non-Bayesian approach, deep split ensemble, to disentangle the predictive uncertainties using a multivariate Gaussian mixture model. The NNs are trained with clusters of input features, for uncertainty estimates per cluster. We evaluate our approach on a series of benchmark regression datasets, while also comparing with unified uncertainty methods. Extensive analyses using dataset shits and empirical rule highlight our inherently well-calibrated models. Our work further demonstrates its applicability in a multi-modal setting using a benchmark Alzheimer's dataset and also shows how deep split ensembles can highlight hidden modality-specific biases. The minimal changes required to NNs and the training procedure, and the high flexibility to group features into clusters makes it readily deployable and useful. The source code is available at https://github.com/wazeerzulfikar/deep-split-ensembles

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known computational burden of Markov Chain Monte Carlo approach for Bayesian regression, we developed a multilevel Gibbs sampler for Bayesian regression of linear mixed models. The level hierarchy of data matrices is created by clustering the features and/or samples of data matrices. Additionally, the use of correlated samples is investigated for variance reduction to improve the convergence of the Markov Chain. Testing on a diverse set of data sets, speed-up is achieved for almost all of them without significant loss in predictive performance.

The communication between data-generating devices is partially responsible for a growing portion of the world's power consumption. Thus reducing communication is vital, both, from an economical and an ecological perspective. For machine learning, on-device learning avoids sending raw data, which can reduce communication substantially. Furthermore, not centralizing the data protects privacy-sensitive data. However, most learning algorithms require hardware with high computation power and thus high energy consumption. In contrast, ultra-low-power processors, like FPGAs or micro-controllers, allow for energy-efficient learning of local models. Combined with communication-efficient distributed learning strategies, this reduces the overall energy consumption and enables applications that were yet impossible due to limited energy on local devices. The major challenge is then, that the low-power processors typically only have integer processing capabilities. This paper investigates an approach to communication-efficient on-device learning of integer exponential families that can be executed on low-power processors, is privacy-preserving, and effectively minimizes communication. The empirical evaluation shows that the approach can reach a model quality comparable to a centrally learned regular model with an order of magnitude less communication. Comparing the overall energy consumption, this reduces the required energy for solving the machine learning task by a significant amount.

Hate speech is an important problem in the management of user-generated content. In order to remove offensive content or ban misbehaving users, content moderators need reliable hate speech detectors. Recently, deep neural networks based on transformer architecture, such as (multilingual) BERT model, achieve superior performance in many natural language classification tasks, including hate speech detection. So far, these methods have not been able to quantify their output in terms of reliability. We propose a Bayesian method using Monte Carlo Dropout within the attention layers of the transformer models to provide well-calibrated reliability estimates. We evaluate and visualize the introduced approach on hate speech detection problems in several languages. From the experiments performed it was observed that our approach significantly improve the hate speech detection that can not be trusted. Our approach not only improves classification performance of the state-of-the-art multilingual BERT model, but the computed reliability scores also significantly reduce the workload in the inspection of offending cases and in reannotation campaigns. The provided visualization helps to understand the borderline outcomes.

Scientists and engineers are often interested in learning the number of subpopulations (or components) present in a data set. A common suggestion is to use a finite mixture model (FMM) with a prior on the number of components. Past work has shown the resulting FMM component-count posterior is consistent; that is, the posterior concentrates on the true generating number of components. But existing results crucially depend on the assumption that the component likelihoods are perfectly specified. In practice, this assumption is unrealistic, and empirical evidence suggests that the FMM posterior on the number of components is sensitive to the likelihood choice. In this paper, we add rigor to data-analysis folk wisdom by proving that under even the slightest model misspecification, the FMM component-count posterior diverges: the posterior probability of any particular finite number of latent components converges to 0 in the limit of infinite data. We illustrate practical consequences of our theory on simulated and real data sets.

Created by Philipp Muellauer Preview this Udemy Course - GET COUPON CODE Welcome to the Complete Data Science and Machine Learning Bootcamp, the only course you need to learn Python and get into data science. At over 40 hours, this Python course is without a doubt the most comprehensive data science and machine learning course available online. Even if you have zero programming experience, this course will take you from beginner to mastery. Here's why: The course is a taught by the lead instructor at the App Brewery, London's leading in-person programming bootcamp. In the course, you'll be learning the latest tools and technologies that are used by data scientists at Google, Amazon, or Netflix.

This work presents a mathematical treatment of the relation between Self-Organizing Maps (SOMs) and Gaussian Mixture Models (GMMs). We show that energy-based SOM models can be interpreted as performing gradient descent, minimizing an approximation to the GMM log-likelihood that is particularly valid for high data dimensionalities. The SOM-like decrease of the neighborhood radius can be understood as an annealing procedure ensuring that gradient descent does not get stuck in undesirable local minima. This link allows to treat SOMs as generative probabilistic models, giving a formal justification for using SOMs, e.g., to detect outliers, or for sampling.

Properly calibrated human trust is essential for successful interaction between humans and automation. However, while human trust calibration can be improved by increased automation transparency, too much transparency can overwhelm human workload. To address this tradeoff, we present a probabilistic framework using a partially observable Markov decision process (POMDP) for modeling the coupled trust-workload dynamics of human behavior in an action-automation context. We specifically consider hands-off Level 2 driving automation in a city environment involving multiple intersections where the human chooses whether or not to rely on the automation. We consider automation reliability, automation transparency, and scene complexity, along with human reliance and eye-gaze behavior, to model the dynamics of human trust and workload. We demonstrate that our model framework can appropriately vary automation transparency based on real-time human trust and workload belief estimates to achieve trust calibration.

As per the records of theWorld Health Organization, the first formally reported incidence of Zika virus occurred in Brazil in May 2015. The disease then rapidly spread to other countries in Americas and East Asia, affecting more than 1,000,000 people. Zika virus is primarily transmitted through bites of infected mosquitoes of the species Aedes (Aedes aegypti and Aedes albopictus). The abundance of mosquitoes and, as a result, the prevalence of Zika virus infections are common in areas which have high precipitation, high temperature, and high population density.Nonlinear spatio-temporal dependency of such data and lack of historical public health records make prediction of the virus spread particularly challenging. In this article, we enhance Zika forecasting by introducing the concepts of topological data analysis and, specifically, persistent homology of atmospheric variables, into the virus spread modeling. The topological summaries allow for capturing higher order dependencies among atmospheric variables that otherwise might be unassessable via conventional spatio-temporal modeling approaches based on geographical proximity assessed via Euclidean distance. We introduce a new concept of cumulative Betti numbers and then integrate the cumulative Betti numbers as topological descriptors into three predictive machine learning models: random forest, generalized boosted regression, and deep neural network. Furthermore, to better quantify for various sources of uncertainties, we combine the resulting individual model forecasts into an ensemble of the Zika spread predictions using Bayesian model averaging. The proposed methodology is illustrated in application to forecasting of the Zika space-time spread in Brazil in the year 2018.