The Semantic Web emerged as an extension to the traditional Web, towards adding meaning to a distributed Web of structured and linked data. At its core, the concept of ontology provides the means to semantically describe and structure information and data and expose it to software and human agents in a machine and human-readable form. For software agents to be realized, it is crucial to develop powerful artificial intelligence and machine learning techniques, able to extract knowledge from information and data sources and represent it in the underlying ontology. This survey aims to provide insight into key aspects of ontology-based knowledge extraction, from various sources such as text, images, databases and human expertise, with emphasis on the task of feature selection. First, some of the most common classification and feature selection algorithms are briefly presented. Then, selected methodologies, which utilize ontologies to represent features and perform feature selection and classification, are described. The presented examples span diverse application domains, e.g., medicine, tourism, mechanical and civil engineering, and demonstrate the feasibility and applicability of such methods.

We consider the problem of recommending relevant content to users of an internet platform in the form of lists of items, called slates. We introduce a variational Bayesian Recurrent Neural Net recommender system that acts on time series of interactions between the internet platform and the user, and which scales to real world industrial situations. The recommender system is tested both online on real users, and on an offline dataset collected from a Norwegian web-based marketplace, FINN.no, that is made public for research. This is one of the first publicly available datasets which includes all the slates that are presented to users as well as which items (if any) in the slates were clicked on. Such a data set allows us to move beyond the common assumption that implicitly assumes that users are considering all possible items at each interaction. Instead we build our likelihood using the items that are actually in the slate, and evaluate the strengths and weaknesses of both approaches theoretically and in experiments. We also introduce a hierarchical prior for the item parameters based on group memberships. Both item parameters and user preferences are learned probabilistically. Furthermore, we combine our model with bandit strategies to ensure learning, and introduce `in-slate Thompson Sampling' which makes use of the slates to maximise explorative opportunities. We show experimentally that explorative recommender strategies perform on par or above their greedy counterparts. Even without making use of exploration to learn more effectively, click rates increase simply because of improved diversity in the recommended slates.

Data science is an interdisciplinary field. One of the building blocks of data science is statistics. Without a decent level of statistics knowledge, it would be highly difficult to understand or interpret the data. Statistics helps us explain the data. We use statistics to infer results about a population based on a sample drawn from that population.

The use of deep neural networks (DNNs) in safety-critical applications like mobile health and autonomous driving is challenging due to numerous model-inherent shortcomings. These shortcomings are diverse and range from a lack of generalization over insufficient interpretability to problems with malicious inputs. Cyber-physical systems employing DNNs are therefore likely to suffer from safety concerns. In recent years, a zoo of state-of-the-art techniques aiming to address these safety concerns has emerged. This work provides a structured and broad overview of them. We first identify categories of insufficiencies to then describe research activities aiming at their detection, quantification, or mitigation. Our paper addresses both machine learning experts and safety engineers: The former ones might profit from the broad range of machine learning topics covered and discussions on limitations of recent methods. The latter ones might gain insights into the specifics of modern ML methods. We moreover hope that our contribution fuels discussions on desiderata for ML systems and strategies on how to propel existing approaches accordingly.

Recurrent meta reinforcement learning (meta-RL) agents are agents that employ a recurrent neural network (RNN) for the purpose of "learning a learning algorithm". After being trained on a pre-specified task distribution, the learned weights of the agent's RNN are said to implement an efficient learning algorithm through their activity dynamics, which allows the agent to quickly solve new tasks sampled from the same distribution. However, due to the black-box nature of these agents, the way in which they work is not yet fully understood. In this study, we shed light on the internal working mechanisms of these agents by reformulating the meta-RL problem using the Partially Observable Markov Decision Process (POMDP) framework. We hypothesize that the learned activity dynamics is acting as belief states for such agents. Several illustrative experiments suggest that this hypothesis is true, and that recurrent meta-RL agents can be viewed as agents that learn to act optimally in partially observable environments consisting of multiple related tasks. This view helps in understanding their failure cases and some interesting model-based results reported in the literature.

We bring together topological data analysis, applied category theory, and machine learning to study multiparameter hierarchical clustering. We begin by introducing a procedure for flattening multiparameter hierarchical clusterings. We demonstrate that this procedure is a functor from a category of multiparameter hierarchical partitions to a category of binary integer programs. We also include empirical results demonstrating its effectiveness. Next, we introduce a Bayesian update algorithm for learning clustering parameters from data. We demonstrate that the composition of this algorithm with our flattening procedure satisfies a consistency property.

The posterior over Bayesian neural network (BNN) parameters is extremely high-dimensional and non-convex. For computational reasons, researchers approximate this posterior using inexpensive mini-batch methods such as mean-field variational inference or stochastic-gradient Markov chain Monte Carlo (SGMCMC). To investigate foundational questions in Bayesian deep learning, we instead use full-batch Hamiltonian Monte Carlo (HMC) on modern architectures. We show that (1) BNNs can achieve significant performance gains over standard training and deep ensembles; (2) a single long HMC chain can provide a comparable representation of the posterior to multiple shorter chains; (3) in contrast to recent studies, we find posterior tempering is not needed for near-optimal performance, with little evidence for a "cold posterior" effect, which we show is largely an artifact of data augmentation; (4) BMA performance is robust to the choice of prior scale, and relatively similar for diagonal Gaussian, mixture of Gaussian, and logistic priors; (5) Bayesian neural networks show surprisingly poor generalization under domain shift; (6) while cheaper alternatives such as deep ensembles and SGMCMC methods can provide good generalization, they provide distinct predictive distributions from HMC. Notably, deep ensemble predictive distributions are similarly close to HMC as standard SGLD, and closer than standard variational inference.

We address the problem of modeling constrained hospital resources in the midst of the COVID-19 pandemic in order to inform decision-makers of future demand and assess the societal value of possible interventions. For broad applicability, we focus on the common yet challenging scenario where patient-level data for a region of interest are not available. Instead, given daily admissions counts, we model aggregated counts of observed resource use, such as the number of patients in the general ward, in the intensive care unit, or on a ventilator. In order to explain how individual patient trajectories produce these counts, we propose an aggregate count explicit-duration hidden Markov model, nicknamed the ACED-HMM, with an interpretable, compact parameterization. We develop an Approximate Bayesian Computation approach that draws samples from the posterior distribution over the model's transition and duration parameters given aggregate counts from a specific location, thus adapting the model to a region or individual hospital site of interest. Samples from this posterior can then be used to produce future forecasts of any counts of interest. Using data from the United States and the United Kingdom, we show our mechanistic approach provides competitive probabilistic forecasts for the future even as the dynamics of the pandemic shift. Furthermore, we show how our model provides insight about recovery probabilities or length of stay distributions, and we suggest its potential to answer challenging what-if questions about the societal value of possible interventions.

"Deep Learning"/"Deep Neural Nets" is a technological marvel that is now increasingly deployed at the cutting-edge of artificial intelligence tasks. This dramatic success of deep learning in the last few years has been hinged on an enormous amount of heuristics and it has turned out to be a serious mathematical challenge to be able to rigorously explain them. In this thesis, submitted to the Department of Applied Mathematics and Statistics, Johns Hopkins University we take several steps towards building strong theoretical foundations for these new paradigms of deep-learning. In chapter 2 we show new circuit complexity theorems for deep neural functions and prove classification theorems about these function spaces which in turn lead to exact algorithms for empirical risk minimization for depth 2 ReLU nets. We also motivate a measure of complexity of neural functions to constructively establish the existence of high-complexity neural functions. In chapter 3 we give the first algorithm which can train a ReLU gate in the realizable setting in linear time in an almost distribution free set up. In chapter 4 we give rigorous proofs towards explaining the phenomenon of autoencoders being able to do sparse-coding. In chapter 5 we give the first-of-its-kind proofs of convergence for stochastic and deterministic versions of the widely used adaptive gradient deep-learning algorithms, RMSProp and ADAM. This chapter also includes a detailed empirical study on autoencoders of the hyper-parameter values at which modern algorithms have a significant advantage over classical acceleration based methods. In the last chapter 6 we give new and improved PAC-Bayesian bounds for the risk of stochastic neural nets. This chapter also includes an experimental investigation revealing new geometric properties of the paths in weight space that are traced out by the net during the training.

In this work, we deal with the problem of rating in sports, where the skills of the players/teams are inferred from the observed outcomes of the games. Our focus is on the online rating algorithms which estimate the skills after each new game by exploiting the probabilistic models of the relationship between the skills and the game outcome. We propose a Bayesian approach which may be seen as an approximate Kalman filter and which is generic in the sense that it can be used with any skills-outcome model and can be applied in the individual-as well as in the group-sports. We show how the well-know algorithms (such as the Elo, the Glicko, and the TrueSkill algorithms) may be seen as instances of the one-fits-all approach we propose. In order to clarify the conditions under which the gains of the Bayesian approach over the simpler solutions can actually materialize, we critically compare the known and the new algorithms by means of numerical examples using the synthetic as well as the empirical data. In this work we are interested in the rating algorithms that can be systematically derived from the probabilistic models which describe i) how the the skills affect the outcomes of the games, as well as ii) how the skills evolve in time, i.e., characterize the skills dynamics. Using the probabilistic models, the forecasting of the game outcomes is naturally derived from the rating.