A key obstacle to the successful deployment of machine learning (ML) methods to important application domains is the (lack of) explainability of predictions. Explainable ML is challenging since explanations must be tailored (personalized) to individual users with varying backgrounds. On one extreme, users can have received graduate level education in machine learning while on the other extreme, users might have no formal education in linear algebra. Linear regression with few features might be perfectly interpretable for the first group but must be considered a black-box for the latter. Using a simple probabilistic model for the predictions and user knowledge, we formalize explainable ML using information theory. Providing an explanation is then considered as the task of reducing the "surprise" incurred by a prediction. Moreover, the effect of an explanation is measured by the conditional mutual information between the explanation and prediction, given the user background.

We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic samplers, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. To guard against noise misspecification, we assess the performance of three variants: (i) GPs with Student-$t$ observations; (ii) Student-$t$ processes (TPs); and (iii) classification GPs modeling the sign of the response. In conjunction with these metamodels, we analyze several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. This also motivates our development of (approximate) updating formulas to efficiently compute such acquisition functions. Our schemes are benchmarked by using a variety of synthetic experiments in 1--6 dimensions. We also consider an application of level set estimation for determining the optimal exercise policy of Bermudan options in finance.

Gradient-based approximate inference methods, such as Stein variational gradient descent (SVGD), provide simple and general-purpose inference engines for differentiable continuous distributions. However, existing forms of SVGD cannot be directly applied to discrete distributions. In this work, we fill this gap by proposing a simple yet general framework that transforms discrete distributions to equivalent piecewise continuous distributions, on which the gradient-free SVGD is applied to perform efficient approximate inference. The empirical results show that our method outperforms traditional algorithms such as Gibbs sampling and discontinuous Hamiltonian Monte Carlo on various challenging benchmarks of discrete graphical models. We demonstrate that our method provides a promising tool for learning ensembles of binarized neural network (BNN), outperforming other widely used ensemble methods on learning binarized AlexNet on CIFAR-10 dataset. In addition, such transform can be straightforwardly employed in gradient-free kernelized Stein discrepancy to perform goodness-of-fit (GOF) test on discrete distributions. Our proposed method outperforms existing GOF test methods for intractable discrete distributions.

In the present paper, we propose an extension of the Deep Planning Network (PlaNet), also referred to as PlaNet of the Bayesians (PlaNet-Bayes). There has been a growing demand in model predictive control (MPC) in partially observable environments in which complete information is unavailable because of, for example, lack of expensive sensors. PlaNet is a promising solution to realize such latent MPC, as it is used to train state-space models via model-based reinforcement learning (MBRL) and to conduct planning in the latent space. However, recent state-of-the-art strategies mentioned in MBRR literature, such as involving uncertainty into training and planning, have not been considered, significantly suppressing the training performance. The proposed extension is to make PlaNet uncertainty-aware on the basis of Bayesian inference, in which both model and action uncertainty are incorporated. Uncertainty in latent models is represented using a neural network ensemble to approximately infer model posteriors. The ensemble of optimal action candidates is also employed to capture multimodal uncertainty in the optimality. The concept of the action ensemble relies on a general variational inference MPC (VI-MPC) framework and its instance, probabilistic action ensemble with trajectory sampling (PaETS). In this paper, we extend VI-MPC and PaETS, which have been originally introduced in previous literature, to address partially observable cases. We experimentally compare the performances on continuous control tasks, and conclude that our method can consistently improve the asymptotic performance compared with PlaNet.

We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the distribution with a weighted sum of functions from a set of continuous functions. Central to the approach is the use of sampling to approximate multiplications in the Bayes filter. We provide theoretical analysis, giving conditions for sampling to give good approximation. We next specialize to the case of weighted sums of Gaussians, and show how properties of Gaussians enable closed-form transition and efficient multiplication. Lastly, we conduct preliminary experiments on a robot localization problem and compare performance with the particle filter, to demonstrate the potential of the proposed method.

Tumor segmentation in oncological PET images is challenging, a major reason being the partial-volume effects that arise from low system resolution and a finite pixel size. The latter results in pixels containing more than one region, also referred to as tissue-fraction effects. Conventional classification-based segmentation approaches are inherently limited in accounting for the tissue-fraction effects. To address this limitation, we pose the segmentation task as an estimation problem. We propose a Bayesian method that estimates the posterior mean of the tumorfraction area within each pixel and uses these estimates to define the segmented tumor boundary. The method was implemented using an autoencoder. Quantitative evaluation of the method was performed using realistic simulation studies conducted in the context of segmenting the primary tumor in PET images of patients with lung cancer. For these studies, a framework was developed to generate clinically realistic simulated PET images. Realism of these images was quantitatively confirmed using a two-alternative-forced-choice study by six trained readers with expertise in reading PET scans. The evaluation studies demonstrated that the proposed segmentation method was accurate, significantly outperformed widely used conventional methods on the tasks of tumor segmentation and estimation of tumor-fraction areas, was relatively insensitive to partial-volume effects, and reliably estimated the ground-truth tumor boundaries. Further, these results were obtained across different clinical-scanner configurations. This proof-of-concept study demonstrates the efficacy of an estimation-based approach to PET segmentation.

In this work, we propose a hybrid approach to synchronize large scale networks. In particular, we draw on Kalman Filtering (KF) along with time-stamps generated by the Precision Time Protocol (PTP) for pairwise node synchronization. Furthermore, we investigate the merit of Factor Graphs (FGs) along with Belief Propagation (BP) algorithm in achieving high precision end-to-end network synchronization. Finally, we present the idea of dividing the large-scale network into local synchronization domains, for each of which a suitable sync algorithm is utilized. The simulation results indicate that, despite the simplifications in the hybrid approach, the error in the offset estimation remains below 5 ns.

No comprehensive review of Bayesian networks (BNs) in healthcare has been published in the past, making it difficult to organize the research contributions in the present and identify challenges and neglected areas that need to be addressed in the future. This unique and novel scoping review of BNs in healthcare provides an analytical framework for comprehensively characterizing the domain and its current state. The review shows that: (1) BNs in healthcare are not used to their full potential; (2) a generic BN development process is lacking; (3) limitations exists in the way BNs in healthcare are presented in the literature, which impacts understanding, consensus towards systematic methodologies, practice and adoption of BNs; and (4) a gap exists between having an accurate BN and a useful BN that impacts clinical practice. This review empowers researchers and clinicians with an analytical framework and findings that will enable understanding of the need to address the problems of restricted aims of BNs, ad hoc BN development methods, and the lack of BN adoption in practice. To map the way forward, the paper proposes future research directions and makes recommendations regarding BN development methods and adoption in practice.

Reinforcement learning (RL) methods often rely on massive exploration data to search optimal policies, and suffer from poor sampling efficiency. This paper presents a mixed reinforcement learning (mixed RL) algorithm by simultaneously using dual representations of environmental dynamics to search the optimal policy with the purpose of improving both learning accuracy and training speed. The dual representations indicate the environmental model and the state-action data: the former can accelerate the learning process of RL, while its inherent model uncertainty generally leads to worse policy accuracy than the latter, which comes from direct measurements of states and actions. In the framework design of the mixed RL, the compensation of the additive stochastic model uncertainty is embedded inside the policy iteration RL framework by using explored state-action data via iterative Bayesian estimator (IBE). The optimal policy is then computed in an iterative way by alternating between policy evaluation (PEV) and policy improvement (PIM). The convergence of the mixed RL is proved using the Bellman's principle of optimality, and the recursive stability of the generated policy is proved via the Lyapunov's direct method. The effectiveness of the mixed RL is demonstrated by a typical optimal control problem of stochastic non-affine nonlinear systems (i.e., double lane change task with an automated vehicle).

A decision-maker must consider cofounding bias when attempting to apply machine learning prediction, and, while feature selection is widely recognized as important process in data-analysis, it could cause cofounding bias. A causal Bayesian network is a standard tool for describing causal relationships, and if relationships are known, then adjustment criteria can determine with which features cofounding bias disappears. A standard modification would thus utilize causal discovery algorithms for preventing cofounding bias in feature selection. Causal discovery algorithms, however, essentially rely on the faithfulness assumption, which turn out to be easily violated in practical feature selection settings. In this paper, we propose a meta-algorithm that can remedy existing feature selection algorithms in terms of cofounding bias. Our algorithm is induced from a novel adjustment criterion that requires rather than faithfulness, an assumption which can be induced from another well-known assumption of the causal sufficiency. We further prove that the features added through our modification convert cofounding bias into prediction variance. With the aid of existing robust optimization technologies that regularize risky strategies with high variance, then, we are able to successfully improve the throughput performance of decision-making optimization, as is shown in our experimental results.