In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the underlying dynamics. In these settings, parametric ODE model cannot be formulated. Here, we overcome this issue by introducing a novel paradigm of nonparametric ODE modelling that can learn the underlying dynamics of arbitrary continuous-time systems without prior knowledge. We propose to learn non-linear, unknown differential functions from state observations using Gaussian process vector fields within the exact ODE formalism. We demonstrate the model's capabilities to infer dynamics from sparse data and to simulate the system forward into future.

This paper presents a generic Bayesian framework that enables any deep learning model to actively learn from targeted crowds. Our framework inherits from recent advances in Bayesian deep learning, and extends existing work by considering the targeted crowdsourcing approach, where multiple annotators with unknown expertise contribute an uncontrolled amount (often limited) of annotations. Our framework leverages the low-rank structure in annotations to learn individual annotator expertise, which then helps to infer the true labels from noisy and sparse annotations. It provides a unified Bayesian model to simultaneously infer the true labels and train the deep learning model in order to reach an optimal learning efficacy. Finally, our framework exploits the uncertainty of the deep learning model during prediction as well as the annotators' estimated expertise to minimize the number of required annotations and annotators for optimally training the deep learning model. We evaluate the effectiveness of our framework for intent classification in Alexa (Amazon's personal assistant), using both synthetic and real-world datasets. Experiments show that our framework can accurately learn annotator expertise, infer true labels, and effectively reduce the amount of annotations in model training as compared to state-of-the-art approaches. We further discuss the potential of our proposed framework in bridging machine learning and crowdsourcing towards improved human-in-the-loop systems.

Probabilistic graphical models offer a powerful framework to account for the dependence structure between variables, which is represented as a graph. However, the dependence between variables may render inference tasks intractable. In this paper we review techniques exploiting the graph structure for exact inference, borrowed from optimisation and computer science. They are built on the principle of variable elimination whose complexity is dictated in an intricate way by the order in which variables are eliminated. The so-called treewidth of the graph characterises this algorithmic complexity: low-treewidth graphs can be processed efficiently. The first message that we illustrate is therefore the idea that for inference in graphical model, the number of variables is not the limiting factor, and it is worth checking for the treewidth before turning to approximate methods. We show how algorithms providing an upper bound of the treewidth can be exploited to derive a 'good' elimination order enabling to perform exact inference. The second message is that when the treewidth is too large, algorithms for approximate inference linked to the principle of variable elimination, such as loopy belief propagation and variational approaches, can lead to accurate results while being much less time consuming than Monte-Carlo approaches. We illustrate the techniques reviewed in this article on benchmarks of inference problems in genetic linkage analysis and computer vision, as well as on hidden variables restoration in coupled Hidden Markov Models.

Although materially beneficial corporate deployments of AI are beginning to proliferate, the AI activities of the majority still amount to a few isolated pilot projects conceived in an ad-hoc basis. Organisations without a clear AI strategy – and that's most – run the risk of falling behind as other better organised industry players move forward. That said, while individual AI solutions can be transformative within the scope of their application, that's not as clear-cut an argument for front-to-back change as, say, the digital transformation of a high street retailer. Developing an AI strategy requires an exercise of careful discrimination – acknowledging the present limitations of AI as well as its strengths in order to identify where one can, cannot, or even should not exploit it. This article is about the'what' of an AI strategy rather than the equally important'how'.

Interpreting black box classifiers, such as deep networks, allows an analyst to validate a classifier before it is deployed in a high-stakes setting. A natural idea is to visualize the deep network's representations, so as to "see what the network sees". In this paper, we demonstrate that standard dimension reduction methods in this setting can yield uninformative or even misleading visualizations. Instead, we present DarkSight, which visually summarizes the predictions of a classifier in a way inspired by notion of dark knowledge. DarkSight embeds the data points into a low-dimensional space such that it is easy to compress the deep classifier into a simpler one, essentially combining model compression and dimension reduction. We compare DarkSight against t-SNE both qualitatively and quantitatively, demonstrating that DarkSight visualizations are more informative. Our method additionally yields a new confidence measure based on dark knowledge by quantifying how unusual a given vector of predictions is.

Robust Reinforcement Learning aims to derive an optimal behavior that accounts for model uncertainty in dynamical systems. However, previous studies have shown that by considering the worst case scenario, robust policies can be overly conservative. Our \textit{soft-robust} framework is an attempt to overcome this issue. In this paper, we present a novel Soft-Robust Actor-Critic algorithm (SR-AC). It learns an optimal policy with respect to a distribution over an uncertainty set and stays robust to model uncertainty but avoids the conservativeness of robust strategies. We show convergence of the SR-AC and test the efficiency of our approach on different domains by comparing it against regular learning methods and their robust formulations.

We consider the problem of structure learning for binary Bayesian networks. Our approach is to recover the true parents and children for each node first and then combine the results to recover the skeleton. We do not assume any specific probability distribution for the nodes. Rather, we show that if the probability distribution satisfies certain conditions then we can exactly recover the parents and children of a node by performing l1-regularized linear regression with sufficient number of samples. The sample complexity of our proposed approach depends logarithmically on the number of nodes in the Bayesian network. Furthermore, our method runs in polynomial time.

Environmental monitoring allows authorities to understand the impact of potentially harmful phenomena, such as air pollution, excessive noise, and radiation. Recently, there has been considerable interest in participatory sensing as a paradigm for such large-scale data collection because it is cost-effective and able to capture more fine-grained data than traditional approaches that use stationary sensors scattered in cities. In this approach, ordinary citizens (non-expert contributors) collect environmental data using low-cost mobile devices. However, these participants are generally self-interested actors that have their own goals and make local decisions about when and where to take measurements. This can lead to highly inefficient outcomes, where observations are either taken redundantly or do not provide sufficient information about key areas of interest. To address these challenges, it is necessary to guide and to coordinate participants, so they take measurements when it is most informative. To this end, we develop a computationally-efficient coordination algorithm (adaptive Best-Match) that suggests to users when and where to take measurements. Our algorithm exploits probabilistic knowledge of human mobility patterns, but explicitly considers the uncertainty of these patterns and the potential unwillingness of people to take measurements when requested to do so. In particular, our algorithm uses a local search technique, clustering and random simulations to map participants to measurements that need to be taken in space and time. We empirically evaluate our algorithm on a real-world human mobility and air quality dataset and show that it outperforms the current state of the art by up to 24% in terms of utility gained.

The widespread growth of high-dimensional biological data in particular has spurred a renewed interest in the use of graphical models to aid in the discovery of novel biological mechanisms (Bühlmann, Kalisch, and Meier 2014). While the past decade has witnessed tremendous developments towards understanding undirected graphical models (Meinshausen and Bühlmann 2006; Ravikumar, Wainwright, and Lafferty 2010; Yang, Ravikumar, Allen, and Liu 2015), there has been less progress towards understanding directed graphical models--also known as Bayesian networks (BNs) or structural equation models (SEM)--for high-dimensional data with p n. A BN is represented by a directed acyclic graph (DAG), whose structure contains a richer and different set of conditional independence relations than an undirected graph. Moreover, DAGs are commonly used 2 Learning Large-Scale Bayesian Networks with the sparsebn Package in causal inference where the direction of an edge encodes causality. Consequently, there have been continuing efforts in structure learning of directed graphs from data.

Threshold tests have recently been proposed as a useful method for detecting bias in lending, hiring, and policing decisions. For example, in the case of credit extensions, these tests aim to estimate the bar for granting loans to white and minority applicants, with a higher inferred threshold for minorities indicative of discrimination. This technique, however, requires fitting a complex Bayesian latent variable model for which inference is often computationally challenging. Here we develop a method for fitting threshold tests that is two orders of magnitude faster than the existing approach, reducing computation from hours to minutes. To achieve these performance gains, we introduce and analyze a flexible family of probability distributions on the interval [0, 1] -- which we call discriminant distributions -- that is computationally efficient to work with. We demonstrate our technique by analyzing 2.7 million police stops of pedestrians in New York City.