Discrete integration in a high dimensional space of $n$ variables poses fundamental challenges. The WISH algorithm reduces the intractable discrete integration problem into $n$ optimization queries subject to randomized constraints, obtaining a constant approximation guarantee. The optimization queries are expensive, which limits the applicability of WISH. We propose AdaWISH, which is able to obtain the same guarantee, but accesses only a small subset of queries of WISH. For example, when the number of function values is bounded by a constant, AdaWISH issues only $O(\log n)$ queries. The key idea is to query adaptively, taking advantage of the shape of the weight function. In general, we prove that AdaWISH has a regret of no more than $O(\log n)$ relative to an oracle that issues queries at data-dependent optimal points. Experimentally, AdaWISH gives precise estimates for discrete integration problems, of the same quality as that of WISH and better than several competing approaches, on a variety of probabilistic inference benchmarks, while saving substantially on the number of optimization queries compared to WISH. For example, it saves $81.5\%$ of WISH queries while retaining the quality of results on a suite of UAI inference challenge benchmarks.

We derive a general decomposition of the model evidence that allows an efficient divide-and-conquer calculation on every worker without accessing the data in one single place. The combination of the results requires only minimal communication between the workers and no exchange of data. We illustrate the applicability of our method on several challenging applications and show that the computation time is reduced by several orders of magnitude, incurring only a negligible bias. We show how to apply our approach in a reversible jump setting where an MCMC sampler moves between different models. The rest of our work is structured as follows: we discuss related work in Section 2 before presenting our approach on distributed Bayesian model choice in Section 3. In Section 4 we demonstrate the applicability of our approach on several data sets and models before discussing possible extensions in Section 5.

--Subjective Logic (SL) is one of well-known belief models that can explicitly deal with uncertain opinions and infer unknown opinions based on a rich set of operators of fusing multiple opinions. Due to high simplicity and applicability, SL has been substantially applied in a variety of decision making in the area of cybersecurity, opinion models, trust models, and/or social network analysis. However, SL and its variants have exposed limitations in predicting uncertain opinions in real-world dynamic network data mainly in threefold: (1) a lack of scalability to deal with a large-scale network; (2) limited capability to handle heterogeneous topological and temporal dependencies among node-level opinions; and (3) a high sensitivity with conflicting evidence that may generate counterintuitive opinions derived from the evidence. In this work, we proposed a novel deep learning (DL)- based dynamic opinion inference model while node-level opinions are still formalized based on SL meaning that an opinion has a dimension of uncertainty in addition to belief and disbelief in a binomial opinion (i.e., agree or disagree). The proposed DLbased dynamic opinion inference model overcomes the above three limitations by integrating the following techniques: (1) state-of-the-art DL techniques, such as the Graph Convolutional Network (GCN) and the Gated Recurrent Units (GRU) for modeling the topological and temporal heterogeneous dependency information of a given dynamic network; (2) modeling conflicting opinions based on robust statistics; and (3) a highly scalable inference algorithm to predict dynamic, uncertain opinions in a linear computation time. We validated the outperformance of our proposed DLbased algorithm (i.e., GCN-GRU-opinion model) via extensive comparative performance analysis based on four real-world datasets. In the decision making domain, including the fields of evidence and belief theories, reasoning or managing uncertainty has been studied since 1960s. The examples include Fuzzy Logic, Dempster-Shafer Theory (DST), Transferable Belief Model, and Dezert-Smarandache Theory [6]. These theories deal with uncertainty implicitly. In 1990's, as another variant of DST, Subjective Logic (SL) [16] is proposed to deal with a dimension of uncertainty in subjective opinions more explicitely. SL defines a binomial opinion (e.g., agree vs. disagree) with three dimensions, including belief, disbelief, and uncertainty.

Bayesian optimization (BO) is a popular approach for expensive black-box optimization, with applications in parameter tuning, experimental design, robotics, and so on. BO usually models the objective function by a Gaussian process (GP), and iteratively samples the next data point by maximizing some acquisition function. In this paper, we propose a new general framework for BO by generating pseudo-points (i.e., data points whose objective values are not evaluated) to improve the GP model. With the classic acquisition function, i.e., upper confidence bound (UCB), we prove a general bound on the cumulative regret, and show that the generation of pseudo-points can improve the instantaneous regret. Experiments using UCB and other acquisition functions, i.e., probability of improvement (PI) and expectation of improvement (EI), on synthetic as well as real-world problems clearly show the advantage of generating pseudo-points.

It is known that from purely observational data, a causal DAG is identifiable only up to its Markov equivalence class, and for many ground truth DAGs, the direction of a large portion of the edges will be remained unidentified. The golden standard for learning the causal DAG beyond Markov equivalence is to perform a sequence of interventions in the system and use the data gathered from the interventional distributions. We consider a setup in which given a budget $k$, we design $k$ interventions non-adaptively. We cast the problem of finding the best intervention target set as an optimization problem which aims to maximize the number of edges whose directions are identified due to the performed interventions. First, we consider the case that the underlying causal structure is a tree. For this case, we propose an efficient exact algorithm for the worst-case gain setup, as well as an approximate algorithm for the average gain setup. We then show that the proposed approach for the average gain setup can be extended to the case of general causal structures. In this case, besides the design of interventions, calculating the objective function is also challenging. We propose an efficient exact calculator as well as two estimators for this task. We evaluate the proposed methods using synthetic as well as real data.

Probabilistic models can define relationships between variables and be used to calculate probabilities. For example, fully conditional models may require an enormous amount of data to cover all possible cases, and probabilities may be intractable to calculate in practice. Simplifying assumptions such as the conditional independence of all random variables can be effective, such as in the case of Naive Bayes, although it is a drastically simplifying step. An alternative is to develop a model that preserves known conditional dependence between random variables and conditional independence in all other cases. Bayesian networks are a probabilistic graphical model that explicitly capture the known conditional dependence with directed edges in a graph model.

Viral sequence classification is an important task in pathogen detection, epidemiological surveys and evolutionary studies. Statistical learning methods are widely used to classify and identify viral sequences in samples from environments. These methods face several challenges associated with the nature and properties of viral genomes such as recombination, mutation rate and diversity. Also, new generations of sequencing technologies rise other difficulties by generating massive amounts of fragmented sequences. While linear classifiers are often used to classify viruses, there is a lack of exploration of the accuracy space of existing models in the context of alignment free approaches. In this study, we present an exhaustive assessment procedure exploring the power of linear classifiers in genotyping and subtyping partial and complete genomes. It is applied to the Hepatitis C viruses (HCV). Several variables are considered in this investigation such as classifier types (generative and discriminative) and their hyper-parameters (smoothing value and penalty function), the classification task (genotyping and subtyping), the length of the tested sequences (partial and complete) and the length of k-mer words. Overall, several classifiers perform well given a set of precise combination of the experimental variables mentioned above. Finally, we provide the procedure and benchmark data to allow for more robust assessment of classification from virus genomes.

The Zap stochastic approximation (SA) algorithm was introduced recently as a means to accelerate convergence in reinforcement learning algorithms. While numerical results were impressive, stability (in the sense of boundedness of parameter estimates) was established in only a few special cases. This class of algorithms is generalized in this paper, and stability is established under very general conditions. This general result can be applied to a wide range of algorithms found in reinforcement learning. Two classes are considered in this paper: (i)The natural generalization of Watkins' algorithm is not always stable in function approximation settings. Parameter estimates may diverge to infinity even in the \textit{linear} function approximation setting with a simple finite state-action MDP. Under mild conditions, the Zap SA algorithm provides a stable algorithm, even in the case of \textit{nonlinear} function approximation. (ii) The GQ algorithm of Maei et.~al.~2010 is designed to address the stability challenge. Analysis is provided to explain why the algorithm may be very slow to converge in practice. The new Zap GQ algorithm is stable even for nonlinear function approximation.

Existing multi-view learning methods based on kernel function either require the user to select and tune a single predefined kernel or have to compute and store many Gram matrices to perform multiple kernel learning. Apart from the huge consumption of manpower, computation and memory resources, most of these models seek point estimation of their parameters, and are prone to overfit-ting to small training data. This paper presents an adaptive kernel nonlinear max-margin multi-view learning model under the Bayesian framework. Specifically, we regularize the posterior of an efficient multi-view latent variable model by explicitly mapping the latent representations extracted from multiple data views to a random Fourier feature space where max-margin classification constraints are imposed. Assuming these random features are drawn from Dirichlet process Gaussian mixtures, we can adaptively learn shift-invariant kernels from data according to Bochners theorem. For inference, we employ the data augmentation idea for hinge loss, and design an efficient gradient-based MCMC sampler in the augmented space. Having no need to compute the Gram matrix, our algorithm scales linearly with the size of training set. Extensive experiments on real-world datasets demonstrate that our method has superior performance.

Here, we use the nomenclature derived from the meta-learning literature which is the most prevalent at time of writing. Let S {( x l,y l)} L l 1 be a support-set containing input-output pairs, with L equal to one (1-shot) or five (5-shot), and Q { (x m,y m)} M m 1be a query-set (sometimes referred to in the literature as a target-set), with M typically one order of magnitude greater than L. For ease of notation, the support and query sets are grouped in a task T {S, Q}, with the dataset D {T n} N n 1 defined as a collection of such tasks. Models are trained on random tasks sampled from D . Then, given a new task T {S, Q } sampled from a test set, the objective is to condition the model on the samples of the support S to estimate the membership of the samples in the query set Q . In the most common scenario, the inputs x D belong to the same distribution p(x) and are distributed across training, validation, and test sets such that their class membership is non-overlapping. Note that y can be a continuous value (regression) or a discrete one (classification), even though most of the previous work has focused on classification. We also consider the cross-domain scenario, where the inputs are sampled from different distributions at training and test time; this is more representative of real-world scenarios.