Surprise-based learning allows agents to adapt quickly in non-stationary stochastic environments. Most existing approaches to surprise-based learning and change point detection assume either implicitly or explicitly a simple, hierarchical generative model of observation sequences that are characterized by stationary periods separated by sudden changes. In this work we show that exact Bayesian inference gives naturally rise to a surprise-modulated trade-off between forgetting and integrating the new observations with the current belief. We demonstrate that many existing approximate Bayesian approaches also show surprise-based modulation of learning rates, and we derive novel particle filters and variational filters with update rules that exhibit surprise-based modulation. Our derived filters have a constant scaling in observation sequence length and particularly simple update dynamics for any distribution in the exponential family. Empirical results show that these filters estimate parameters better than alternative approximate approaches and reach comparative levels of performance to computationally more expensive algorithms. The theoretical insight of casting various approaches under the same interpretation of surprise-based learning, as well as the proposed filters, may find useful applications in reinforcement learning in non-stationary environments and in the analysis of animal and human behavior.

Geodesic distance is the shortest path between two points in a Riemannian manifold. Manifold learning algorithms, such as Isomap, seek to learn a manifold that preserves geodesic distances. However, such methods operate on the ambient dimensionality, and are therefore fragile to noise dimensions. We developed an unsupervised random forest method (URerF) to approximately learn geodesic distances in linear and nonlinear manifolds with noise. URerF operates on low-dimensional sparse linear combinations of features, rather than the full observed dimensionality. To choose the optimal split in a computationally efficient fashion, we developed a fast Bayesian Information Criterion statistic for Gaussian mixture models. We introduce geodesic precision-recall curves which quantify performance relative to the true latent manifold. Empirical results on simulated and real data demonstrate that URerF is robust to high-dimensional noise, where as other methods, such as Isomap, UMAP, and FLANN, quickly deteriorate in such settings. In particular, URerF is able to estimate geodesic distances on a real connectome dataset better than other approaches.

Materials design can be cast as an optimization problem with the goal of achieving desired properties, by varying material composition, microstructure morphology, and processing conditions. Existence of both qualitative and quantitative material design variables leads to disjointed regions in property space, making the search for optimal design challenging. Limited availability of experimental data and the high cost of simulations magnify the challenge. This situation calls for design methodologies that can extract useful information from existing data and guide the search for optimal designs efficiently. To this end, we present a data-centric, mixed-variable Bayesian Optimization framework that integrates data from literature, experiments, and simulations for knowledge discovery and computational materials design. Our framework pivots around the Latent Variable Gaussian Process (LVGP), a novel Gaussian Process technique which projects qualitative variables on a continuous latent space for covariance formulation, as the surrogate model to quantify "lack of data" uncertainty. Expected improvement, an acquisition criterion that balances exploration and exploitation, helps navigate a complex, nonlinear design space to locate the optimum design. The proposed framework is tested through a case study which seeks to concurrently identify the optimal composition and morphology for insulating polymer nanocomposites. We also present an extension of mixed-variable Bayesian Optimization for multiple objectives to identify the Pareto Frontier within tens of iterations. These findings project Bayesian Optimization as a powerful tool for design of engineered material systems.

Assistive robots can potentially improve the quality of life and personal independence of elderly people by supporting everyday life activities. To guarantee a safe and intuitive interaction between human and robot, human intentions need to be recognized automatically. As humans communicate their intentions multimodally, the use of multiple modalities for intention recognition may not just increase the robustness against failure of individual modalities but especially reduce the uncertainty about the intention to be predicted. This is desirable as particularly in direct interaction between robots and potentially vulnerable humans a minimal uncertainty about the situation as well as knowledge about this actual uncertainty is necessary. Thus, in contrast to existing methods, in this work a new approach for multimodal intention recognition is introduced that focuses on uncertainty reduction through classifier fusion. For the four considered modalities speech, gestures, gaze directions and scene objects individual intention classifiers are trained, all of which output a probability distribution over all possible intentions. By combining these output distributions using the Bayesian method Independent Opinion Pool the uncertainty about the intention to be recognized can be decreased. The approach is evaluated in a collaborative human-robot interaction task with a 7-DoF robot arm. The results show that fused classifiers which combine multiple modalities outperform the respective individual base classifiers with respect to increased accuracy, robustness, and reduced uncertainty.

Canonical Correlation Analysis (CCA) is a classic technique for multi-view data analysis. To overcome the deficiency of linear correlation in practical multi-view learning tasks, various CCA variants were proposed to capture nonlinear dependency. However, it is non-trivial to have an in-principle understanding of these variants due to their inherent restrictive assumption on the data and latent code distributions. Although some works have studied probabilistic interpretation for CCA, these models still require the explicit form of the distributions to achieve a tractable solution for the inference. In this work, we study probabilistic interpretation for CCA based on implicit distributions. We present Conditional Mutual Information (CMI) as a new criterion for CCA to consider both linear and nonlinear dependency for arbitrarily distributed data. To eliminate direct estimation for CMI, in which explicit form of the distributions is still required, we derive an objective which can provide an estimation for CMI with efficient inference methods. To facilitate Bayesian inference of multi-view analysis, we propose Adversarial CCA (ACCA), which achieves consistent encoding for multi-view data with the consistent constraint imposed on the marginalization of the implicit posteriors. Such a model would achieve superiority in the alignment of the multi-view data with implicit distributions. It is interesting to note that most of the existing CCA variants can be connected with our proposed CCA model by assigning specific form for the posterior and likelihood distributions. Extensive experiments on nonlinear correlation analysis and cross-view generation on benchmark and real-world datasets demonstrate the superiority of our model.

Moral responsibility is a major concern in automated decision-making, with applications ranging from self-driving cars to kidney exchanges. From the viewpoint of automated systems, the urgent questions are: (a) How can models of moral scenarios and blameworthiness be extracted and learnt automatically from data? (b) How can judgements be computed tractably, given the split-second decision points faced by the system? By building on deep tractable probabilistic learning, we propose a learning regime for inducing models of such scenarios automatically from data and reasoning tractably from them. We report on experiments that compare our system with human judgement in three illustrative domains: lung cancer staging, teamwork management, and trolley problems.

Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic systems, the case for abstracting probabilistic models is not yet fully understood. In this paper, we provide a semantical framework for analyzing such abstractions from first principles. We develop the framework in a general way, allowing for expressive languages, including logic-based ones that admit relational and hierarchical constructs with stochastic primitives. We motivate a definition of consistency between a high-level model and its low-level counterpart, but also treat the case when the high-level model is missing critical information present in the low-level model. We prove properties of abstractions, both at the level of the parameter as well as the structure of the models. We conclude with some observations about how abstractions can be derived automatically.

In digital advertising, Click-Through Rate (CTR) and Conversion Rate (CVR) are very important metrics for evaluating ad performance. As a result, ad event prediction systems are vital and widely used for sponsored search and display advertising as well as Real-Time Bidding (RTB). In this work, we introduce an enhanced method for ad event prediction (i.e. clicks, conversions) by proposing a new efficient feature engineering approach. A large real-world event-based dataset of a running marketing campaign is used to evaluate the efficiency of the proposed prediction algorithm. The results illustrate the benefits of the proposed ad event prediction approach, which significantly outperforms the alternative ones.

We extend two kinds of causal models, structural equation models and simulation models, to infinite variable spaces. This enables a semantics for conditionals founded on a calculus of intervention, and axiomatization of causal reasoning for rich, expressive generative models---including those in which a causal representation exists only implicitly---in an open-universe setting. Further, we show that under suitable restrictions the two kinds of models are equivalent, perhaps surprisingly as their axiomatizations differ substantially in the general case. We give a series of complete axiomatizations in which the open-universe nature of the setting is seen to be essential.

How to better support police to prevent terrorist attacks continues to be a major political concern due to continued violence perpetrated by extremists [13, 2]. In contrast to the majority of terrorist incidents in the latter half of the twentieth century which were executed by known organised terrorist groups with substantial planning and sophistication, more recent attacks have often involved individuals or small groups targeting civilians in public places using basic equipment such as vehicles, guns and knives [13, 23]. Consequentially this entails less sophistication in materials, planning and execution. In terms of analysing how to understand and prevent terrorism, criminologist focus has shifted from "individual qualities (who we think terrorists'are') to ... what