The purpose of deep learning is to learn a representation of high dimensional and noisy data using a sequence of differentiable functions, i.e., geometric transformations, that can perhaps be used for supervised learning tasks among other tasks. It has had great success in discriminative models while generative models have not fared perhaps quite as well due to the limitations of explicit maximum likelihood estimation (MLE). Adversarial learning as presented in the Generative Adversarial Network (GAN) aims to overcome these problems by using implicit MLE. We will use the MNIST computer vision dataset and a synthetic financial transactions dataset for an insurance task for these experiments using GANs. GANs are a remarkably different method of learning compared to explicit MLE. Our purpose will be to show that the representation learnt by a GAN can be used for supervised learning tasks such as image recognition and insurance loss risk prediction.

Hypernetworks are neural networks that transform a random input vector into weights for a specified target neural network. We formulate the hypernetwork training objective as a compromise between accuracy and diversity, where the diversity takes into account trivial symmetry transformations of the target network. We show that this formulation naturally arises as a relaxation of an optimistic probability distribution objective for the generated networks, and we explain how it is related to variational inference. We use multi-layered perceptrons to form the mapping from the low dimensional input random vector to the high dimensional weight space, and demonstrate how to reduce the number of parameters in this mapping by weight sharing. We perform experiments on a four layer convolutional target network which classifies MNIST images, and show that the generated weights are diverse and have interesting distributions.

The area of online machine learning in big data streams covers algorithms that are (1) distributed and (2) work from data streams with only a limited possibility to store past data. The first requirement mostly concerns software architectures and efficient algorithms. The second one also imposes nontrivial theoretical restrictions on the modeling methods: In the data stream model, older data is no longer available to revise earlier suboptimal modeling decisions as the fresh data arrives. In this article, we provide an overview of distributed software architectures and libraries as well as machine learning models for online learning. We highlight the most important ideas for classification, regression, recommendation, and unsupervised modeling from streaming data, and we show how they are implemented in various distributed data stream processing systems. This article is a reference material and not a survey. We do not attempt to be comprehensive in describing all existing methods and solutions; rather, we give pointers to the most important resources in the field. All related sub-fields, online algorithms, online learning, and distributed data processing are hugely dominant in current research and development with conceptually new research results and software components emerging at the time of writing. In this article, we refer to several survey results, both for distributed data processing and for online machine learning. Compared to past surveys, our article is different because we discuss recommender systems in extended detail.

In order to design and operate the process it is important to know which variables have the strongest influence on performance. To estimate this we compared each state with the length and diameter of the resulting fibers, performing second order polynomial fit using samples over all 9 experiments, and noting the value of the resulting correlation coefficients R. The correlations between process parameters and the Length and Diameter is contained in Supplementary Table S.1. The angle and position have very little influence on the characteristics of the produced fibers. Polymer flow has a moderate influence (0.37) on length, but only a weak influence on diameter. Thus the most significant influence on overall performance is solvent speed followed by channel width.

Machine learning models are vulnerable to Adversarial Examples: minor perturbations to input samples intended to deliberately cause misclassification. Current defenses against adversarial examples, especially for Deep Neural Networks (DNN), are primarily derived from empirical developments, and their security guarantees are often only justified retroactively. Many defenses therefore rely on hidden assumptions that are subsequently subverted by increasingly elaborate attacks. This is not surprising: deep learning notoriously lacks a comprehensive mathematical framework to provide meaningful guarantees. In this paper, we leverage Gaussian Processes to investigate adversarial examples in the framework of Bayesian inference. Across different models and datasets, we find deviating levels of uncertainty reflect the perturbation introduced to benign samples by state-of-the-art attacks, including novel white-box attacks on Gaussian Processes. Our experiments demonstrate that even unoptimized uncertainty thresholds already reject adversarial examples in many scenarios.

We extend variational autoencoders (VAEs) to collaborative filtering for implicit feedback. This non-linear probabilistic model enables us to go beyond the limited modeling capacity of linear factor models which still largely dominate collaborative filtering research.We introduce a generative model with multinomial likelihood and use Bayesian inference for parameter estimation. Despite widespread use in language modeling and economics, the multinomial likelihood receives less attention in the recommender systems literature. We introduce a different regularization parameter for the learning objective, which proves to be crucial for achieving competitive performance. Remarkably, there is an efficient way to tune the parameter using annealing. The resulting model and learning algorithm has information-theoretic connections to maximum entropy discrimination and the information bottleneck principle. Empirically, we show that the proposed approach significantly outperforms several state-of-the-art baselines, including two recently-proposed neural network approaches, on several real-world datasets. We also provide extended experiments comparing the multinomial likelihood with other commonly used likelihood functions in the latent factor collaborative filtering literature and show favorable results. Finally, we identify the pros and cons of employing a principled Bayesian inference approach and characterize settings where it provides the most significant improvements.

Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance), with numerous successful applications. The representation is constructed as the expectation of the feature map defined by a kernel. As a mean, its classical empirical estimator, however, can be arbitrary severely affected even by a single outlier in case of unbounded features. To the best of our knowledge, unfortunately even the consistency of the existing few techniques trying to alleviate this serious sensitivity bottleneck is unknown. In this paper, we show how the recently emerged principle of median-of-means can be used to design minimax-optimal estimators for kernel mean embedding and MMD, with finite-sample strong outlier-robustness guarantees.

We propose a new Bayesian model for flexible nonlinear regression and classification using tree ensembles. The model is based on the RuleFit approach in Friedman and Popescu (2008) where rules from decision trees and linear terms are used in a L1-regularized regression. We modify RuleFit by replacing the L1-regularization by a horseshoe prior, which is well known to give aggressive shrinkage of noise predictor while leaving the important signal essentially untouched. This is especially important when a large number of rules are used as predictors as many of them only contribute noise. Our horseshoe prior has an additional hierarchical layer that applies more shrinkage a priori to rules with a large number of splits, and to rules that are only satisfied by a few observations. The aggressive noise shrinkage of our prior also makes it possible to complement the rules from boosting in Friedman and Popescu (2008) with an additional set of trees from random forest, which brings a desirable diversity to the ensemble. We sample from the posterior distribution using a very efficient and easily implemented Gibbs sampler. The new model is shown to outperform state-of-the-art methods like RuleFit, BART and random forest on 16 datasets. The model and its interpretation is demonstrated on the well known Boston housing data, and on gene expression data for cancer classification. The posterior sampling, prediction and graphical tools for interpreting the model results are implemented in a publicly available R package.

A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard updating in an augmented credal network, equivalent to a set of consistent Bayesian networks. A characterization of the computational complexity for this task is derived together with an efficient exact procedure for a subclass of instances. In the case of multiple uncertain evidences over the same variable, the proposed procedure can provide a set-valued version of the geometric approach to opinion pooling.

Noisy observations coupled with nonlinear dynamics pose one of the biggest challenges in robot motion planning. By decomposing the nonlinear dynamics into a discrete set of local dynamics models, hybrid dynamics provide a natural way to model nonlinear dynamics, especially in systems with sudden "jumps" in the dynamics, due to factors such as contacts. We propose a hierarchical POMDP planner that develops locally optimal motion plans for hybrid dynamics models. The hierarchical planner first develops a high-level motion plan to sequence the local dynamics models to be visited. The high-level plan is then converted into a detailed cost-optimized continuous state plan. This hierarchical planning approach results in a decomposition of the POMDP planning problem into smaller sub-parts that can be solved with significantly lower computational costs. The ability to sequence the visitation of local dynamics models also provides a powerful way to leverage the hybrid dynamics to reduce state uncertainty. We evaluate the proposed planner for two navigation and localization tasks in simulated domains, as well as an assembly task with a real robotic manipulator.