Objective: A median of 14.4% of patient undergone at least one adverse event during surgery and a third of them are preventable. The occurrence of adverse events forces surgeons to implement corrective strategies and, thus, deviate from the standard surgical process. Therefore, it is clear that the automatic identification of adverse events is a major challenge for patient safety. In this paper, we have proposed a method enabling us to identify such deviations. We have focused on identifying surgeons' deviations from standard surgical processes due to surgical events rather than anatomic specificities. This is particularly challenging, given the high variability in typical surgical procedure workflows. Methods: We have introduced a new approach designed to automatically detect and distinguish surgical process deviations based on multi-dimensional non-linear temporal scaling with a hidden semi-Markov model using manual annotation of surgical processes. The approach was then evaluated using cross-validation. Results: The best results have over 90% accuracy. Recall and precision were superior at 70%. We have provided a detailed analysis of the incorrectly-detected observations. Conclusion: Multi-dimensional non-linear temporal scaling with a hidden semi-Markov model provides promising results for detecting deviations. Our error analysis of the incorrectly-detected observations offers different leads in order to further improve our method. Significance: Our method demonstrated the feasibility of automatically detecting surgical deviations that could be implemented for both skill analysis and developing situation awareness-based computer-assisted surgical systems.

Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In this paper, we first show that for a set of important graph families it is possible to convert the structural constraints of structure into eigenvalue constraints of the graph Laplacian matrix. Then we introduce a unified graph learning framework, lying at the integration of the spectral properties of the Laplacian matrix with Gaussian graphical modeling that is capable of learning structures of a large class of graph families. The proposed algorithms are provably convergent and practically amenable for large-scale semi-supervised and unsupervised graph-based learning tasks. Extensive numerical experiments with both synthetic and real data sets demonstrate the effectiveness of the proposed methods. An R package containing code for all the experimental results is available at https://cran.r-project.org/package=spectralGraphTopology.

Imitation learning seeks to learn an expert policy from sampled demonstrations. However, in the real world, it is often difficult to find a perfect expert and avoiding dangerous behaviors becomes relevant for safety reasons. We present the idea of \textit{learning to avoid}, an objective opposite to imitation learning in some sense, where an agent learns to avoid a demonstrator policy given an environment. We define avoidance learning as the process of optimizing the agent's reward while avoiding dangerous behaviors given by a demonstrator. In this work we develop a framework of avoidance learning by defining a suitable objective function for these problems which involves the \emph{distance} of state occupancy distributions of the expert and demonstrator policies. We use density estimates for state occupancy measures and use the aforementioned distance as the reward bonus for avoiding the demonstrator. We validate our theory with experiments using a wide range of partially observable environments. Experimental results show that we are able to improve sample efficiency during training compared to state of the art policy optimization and safety methods.

To coordinate with other systems, agents must be able to determine what the systems are currently doing and predict what they will be doing in the future---plan and goal recognition. There are many methods for plan and goal recognition, but they assume a passive observer that continually monitors the target system. Real-world domains, where information gathering has a cost (e.g., moving a camera or a robot, or time taken away from another task), will often require a more active observer. We propose to combine goal recognition with other observer tasks in order to obtain \emph{active goal recognition} (AGR). We discuss this problem and provide a model and preliminary experimental results for one form of this composite problem. As expected, the results show that optimal behavior in AGR problems balance information gathering with other actions (e.g., task completion) such as to achieve all tasks jointly and efficiently. We hope that our formulation opens the door for extensive further research on this interesting and realistic problem.

Immersive simulations are increasingly used for teaching and training in many societally important arenas including healthcare, disaster response and science education. The interactions of participants in such settings lead to a complex array of emergent outcomes that present challenges for analysis. This paper studies a central element of such an analysis, namely the interpretability of models for inferring structure in time series data. This problem is explored in the context of modeling student interactions in an immersive ecological-system simulation. Unsupervised machine learning is applied to data on system dynamics with the aim of helping teachers determine the effects of students' actions on these dynamics. We address the question of choosing the optimal machine learning model, considering both statistical information criteria and interpretabilty quality. The results of a user study show that the models that are the best understood by people are not those that optimize information theoretic criteria. In addition, a model using a fully Bayesian approach performed well on both statistical measures and on human-subject tests of interpretabilty, making it a good candidate for automated model selection that does not require human-in-the-loop evaluation. The results from this paper are already being used in the classroom and can inform the design of interpretable models for a broad range of socially relevant domains. 1 Introduction There is increasing evidence of the value of multi-person embodied simulations for engaging learners in a variety of applications, such as healthcare, disaster response and education (Alinier et al. 2014; Amir and Gal 2013).

Active inference is a first (Bayesian) principles account of how autonomous agents might operate in dynamic, non-stationary environments. The optimization of congruent formulations of the free energy functional (variational and expected), in active inference, enables agents to make inferences about the environment and select optimal behaviors. The agent achieves this by evaluating (sensory) evidence in relation to its internal generative model that entails beliefs about future (hidden) states and sequence of actions that it can choose. In contrast to analogous frameworks $-$ by operating in a pure belief-based setting (free energy functional of beliefs about states) $-$ active inference agents can carry out epistemic exploration and naturally account for uncertainty about their environment. Through this review, we disambiguate these properties, by providing a condensed overview of the theory underpinning active inference. A T-maze simulation is used to demonstrate how these behaviors emerge naturally, as the agent makes inferences about the observed outcomes and optimizes its generative model (via belief updating). Additionally, the discrete state-space and time formulation presented provides an accessible guide on how to derive the (variational and expected) free energy equations and belief updating rules. We conclude by noting that this formalism can be applied in other engineering applications; e.g., robotic arm movement, playing Atari games, etc., if appropriate underlying probability distributions (i.e. generative model) can be formulated.

While it provides a good foundation to system modeling, analysis, and an understanding of the real world, its application to algorithm design suffers from computational intractability. In this work, we develop a new framework of uncertainty variables to model uncertainty. A simple uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set map, from a given realization of a variable to a set of possible realizations of another variable. We prove Bayes' law and the law of total probability equivalents for uncertainty variables. We define a notion of independence, conditional independence, and pairwise independence for a collection of uncertainty variables, and show that this new notion of independence preserves the properties of independence defined over random variables. We then develop a graphical model, namely Bayesian uncertainty network, a Bayesian network equivalent defined over a collection of uncertainty variables, and show that all the natural conditional independence properties, expected out of a Bayesian network, hold for the Bayesian uncertainty network. We also define the notion of point estimate, and show its relation with the maximum a posteriori estimate.

For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer their modes from observations in real time. The modes can be real or complex. For a real mode, we infer its damping rate, mode shape and amplitude. For a complex mode, we infer its frequency, damping rate, (complex) mode shape and (complex) amplitude. The work is motivated and illustrated by the problem of detection of oscillations in power flow in AC electrical networks. Suggestions of other applications are given.

Decentralized stochastic gradient method emerges as a promising solution for solving large-scale machine learning problems. This paper studies the decentralized Markov chain gradient descent (DMGD) algorithm - a variant of the decentralized stochastic gradient methods where the random samples are taken along the trajectory of a Markov chain. This setting is well-motivated when obtaining independent samples is costly or impossible, which excludes the use of the traditional stochastic gradient algorithms. Specifically, we consider the first- and zeroth-order versions of decentralized Markov chain gradient descent over a connected network, where each node only communicates with its neighbors about intermediate results. The nonergodic convergence and the ergodic convergence rate of the proposed algorithms have been rigorously established, and their critical dependences on the network topology and the mixing time of Markov chain have been highlighted. The numerical tests further validate the sample efficiency of our algorithm.

In the Bayesian analysis of signals immersed in noise [1], we seek a representation for the posterior probability of one or more parameters that govern the shape of the signals. Unless the parameter-to-signal map (the forward model) is very simple, the analysis (or inverse solution) comes at significant computational cost, as it requires the stochastic exploration of the likelihood surface at a large number of locations in parameter space. Such is the case, for instance, of parameter estimation for gravitational-wave sources such as the compact binaries detected by LIGO-Virgo [2, 3]; here each likelihood evaluation requires that we generate the gravitational waveform corresponding to a set of source parameters, and compute its noise-weighted correlation with detector data [4]. Waveform generation is usually the costlier operation, so gravitational-wave analysts often utilize faster, less accurate waveform models [5, 6], or accelerated surrogates of slower, more accurate models [7]. Extending the analysis from the data we have to the data we might measure (i.e., characterizing the parameter-estimation prospects of future experiments) compounds the expense, since we need to explore posteriors for many noise realizations, and across the domain of possible source parameters. For concreteness, we price the evaluation of a single Bayesian posterior at null 10 6 times the cost of generating a waveform, and the characterization of parameter-estimation prospects at null 10 6 times the cost of a posterior. With current computational resources, this means that (for instance) accurate component-mass estimates only become available hours or days after the detection of a binary black-hole coalescence [8, 9], while any extensive study of parameter-estimation prospects must rely on less reliable techniques such as the Fisher-matrix approximation [10]. In this Letter, we show how one-or two-dimensional marginalized Bayesian posteriors may be produced using deep neural networks [11] trained on large ensembles of signal noise data streams.