We propose two algorithms for episodic stochastic shortest path problems with linear function approximation. The first is computationally expensive but provably obtains $\tilde{O} (\sqrt{B_\star^3 d^3 K/c_{min}} )$ regret, where $B_\star$ is a (known) upper bound on the optimal cost-to-go function, $d$ is the feature dimension, $K$ is the number of episodes, and $c_{min}$ is the minimal cost of non-goal state-action pairs (assumed to be positive). The second is computationally efficient in practice, and we conjecture that it obtains the same regret bound. Both algorithms are based on an optimistic least-squares version of value iteration analogous to the finite-horizon backward induction approach from Jin et al. 2020. To the best of our knowledge, these are the first regret bounds for stochastic shortest path that are independent of the size of the state and action spaces.

The current pandemic has introduced substantial uncertainty to traditional methods for demand planning. These uncertainties stem from the disease progression, government interventions, economy and consumer behavior. While most of the emerging literature on the pandemic has focused on disease progression, a few have focused on consequent regulations and their impact on individual behavior. The contributions of this paper include a quantitative behavior model of fear of COVID-19, impact of government interventions on consumer behavior, and impact of consumer behavior on consumer choice and hence demand for goods. It brings together multiple models for disease progression, consumer behavior and demand estimation-thus bridging the gap between disease progression and consumer demand. We use panel regression to understand the drivers of demand during the pandemic and Bayesian inference to simplify the regulation landscape that can help build scenarios for resilient demand planning. We illustrate this resilient demand planning model using a specific example of gas retailing. We find that demand is sensitive to fear of COVID-19: as the number of COVID-19 cases increase over the previous week, the demand for gas decreases -- though this dissipates over time. Further, government regulations restrict access to different services, thereby reducing mobility, which in itself reduces demand.

Bayesian optimisation (BO) uses probabilistic surrogate models - usually Gaussian processes (GPs) - for the optimisation of expensive black-box functions. At each BO iteration, the GP hyperparameters are fit to previously-evaluated data by maximising the marginal likelihood. However, this fails to account for uncertainty in the hyperparameters themselves, leading to overconfident model predictions. This uncertainty can be accounted for by taking the Bayesian approach of marginalising out the model hyperparameters. We investigate whether a fully-Bayesian treatment of the Gaussian process hyperparameters in BO (FBBO) leads to improved optimisation performance. Since an analytic approach is intractable, we compare FBBO using three approximate inference schemes to the maximum likelihood approach, using the Expected Improvement (EI) and Upper Confidence Bound (UCB) acquisition functions paired with ARD and isotropic Matern kernels, across 15 well-known benchmark problems for 4 observational noise settings. FBBO using EI with an ARD kernel leads to the best performance in the noise-free setting, with much less difference between combinations of BO components when the noise is increased. FBBO leads to over-exploration with UCB, but is not detrimental with EI. Therefore, we recommend that FBBO using EI with an ARD kernel as the default choice for BO.

The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an inferential perspective, most notably the absence of explicit conditioning formula. This paper extends earlier work on linear PDEs to a general class of initial value problems specified by nonlinear PDEs, motivated by problems for which evaluations of the right-hand-side, initial conditions, or boundary conditions of the PDE have a high computational cost. The proposed method can be viewed as exact Bayesian inference under an approximate likelihood, which is based on discretisation of the nonlinear differential operator. Proof-of-concept experimental results demonstrate that meaningful probabilistic uncertainty quantification for the unknown solution of the PDE can be performed, while controlling the number of times the right-hand-side, initial and boundary conditions are evaluated. A suitable prior model for the solution of the PDE is identified using novel theoretical analysis of the sample path properties of Mat\'{e}rn processes, which may be of independent interest.

We propose a new method to estimate causal effects from nonexperimental data. Each pair of sample units is first associated with a stochastic 'treatment' - differences in factors between units - and an effect - a resultant outcome difference. It is then proposed that all such pairs can be combined to provide more accurate estimates of causal effects in observational data, provided a statistical model connecting combinatorial properties of treatments to the accuracy and unbiasedness of their effects. The article introduces one such model and a Bayesian approach to combine the $O(n^2)$ pairwise observations typically available in nonexperimnetal data. This also leads to an interpretation of nonexperimental datasets as incomplete, or noisy, versions of ideal factorial experimental designs. This approach to causal effect estimation has several advantages: (1) it expands the number of observations, converting thousands of individuals into millions of observational treatments; (2) starting with treatments closest to the experimental ideal, it identifies noncausal variables that can be ignored in the future, making estimation easier in each subsequent iteration while departing minimally from experiment-like conditions; (3) it recovers individual causal effects in heterogeneous populations. We evaluate the method in simulations and the National Supported Work (NSW) program, an intensively studied program whose effects are known from randomized field experiments. We demonstrate that the proposed approach recovers causal effects in common NSW samples, as well as in arbitrary subpopulations and an order-of-magnitude larger supersample with the entire national program data, outperforming Statistical, Econometrics and Machine Learning estimators in all cases...

A Bayesian network is a probabilistic graphical model, which represents conditional independence relationships between a set of random variables by a directed acyclic graph (DAG).The problem of DAG learning from observational data is hard (Chickering 1996), and the number of DAGs grows super-exponentially with the number of nodes. Hence, developing and implementing methods to learn an underlying DAG from observational data in reasonable time continues to be the focus of much research (Bartlett and Cussens 2017; Goudie and Mukherjee 2016; Scanagatta, de Campos, and Corani 2015). Drton and Maathuis (2017) provide an overview of the approaches for structure learning of graphical models including Bayesian networks. The R (R Development Core Team 2008) packages pcalg (Kalisch, Mächler, Colombo, Maathuis, and Bühlmann 2012), BNlearn (Scutari 2010), bnstruct (Franzin, Sambo, and Camillo 2017) and the Java-based toolbox TETRAD (Glymour, Scheines, Spirtes, and Ramsey 2017) implement multiple approaches to structure learning, including both constraint-based and searcharXiv:2105.00488v1

The term Delay/Disruption-Tolerant Networks (DTN) invented to describe and cover all types of long-delay, disconnected, intermittently connected networks, where mobility and outages or scheduled contacts may be experienced. This environment is characterized by frequent network partitioning, intermittent connectivity, large or variable delay, asymmetric data rate, and low transmission reliability. There have been routing protocols developed in DTN. However, those routing algorithms are design based upon specific assumptions. The assumption makes existing algorithms suitable for specific environment scenarios. Different routing algorithm uses different relay node selection criteria to select the replication node. Too Frequently forwarding messages can result in excessive packet loss and large buffer and network overhead. On the other hand, less frequent transmission leads to a lower delivery ratio. In DTN there is a trade-off off between delivery ratio and overhead. In this study, we proposed context-adaptive reinforcement learning based routing(CARL-DTN) protocol to determine optimal replicas of the message based on the real-time density. Our routing protocol jointly uses a real-time physical context, social-tie strength, and real-time message context using fuzzy logic in the routing decision. Multi-hop forwarding probability is also considered for the relay node selection by employing Q-Learning algorithm to estimate the encounter probability between nodes and to learn about nodes available in the neighbor by discounting reward. The performance of the proposed protocol is evaluated based on various simulation scenarios. The result shows that the proposed protocol has better performance in terms of message delivery ratio and overhead.

I often hear people say that the results from Bayesian methods are the same as the results from frequentist methods, at least under certain conditions. And sometimes it even comes from people who understand Bayesian methods. Today I saw this tweet from Julia Rohrer: "Running a Bayesian multi-membership multi-level probit model with a custom function to generate average marginal effects only to find that the estimate is precisely the same as the one generated by linear regression with dummy-coded group membership." Which elicited what I interpret as good-natured teasing, like this tweet from Daniël Lakens: "I always love it when people realize that the main difference between a frequentist and Bayesian analysis is that for the latter approach you first need to wait 24 hours for the results." Ok, that's funny, but there is a serious point here I want to respond to because both of these comments are based on the premise that we can compare the results from Bayesian and frequentist methods.

The Semantic Web emerged as an extension to the traditional Web, towards adding meaning to a distributed Web of structured and linked data. At its core, the concept of ontology provides the means to semantically describe and structure information and data and expose it to software and human agents in a machine and human-readable form. For software agents to be realized, it is crucial to develop powerful artificial intelligence and machine learning techniques, able to extract knowledge from information and data sources and represent it in the underlying ontology. This survey aims to provide insight into key aspects of ontology-based knowledge extraction, from various sources such as text, images, databases and human expertise, with emphasis on the task of feature selection. First, some of the most common classification and feature selection algorithms are briefly presented. Then, selected methodologies, which utilize ontologies to represent features and perform feature selection and classification, are described. The presented examples span diverse application domains, e.g., medicine, tourism, mechanical and civil engineering, and demonstrate the feasibility and applicability of such methods.

We consider the problem of recommending relevant content to users of an internet platform in the form of lists of items, called slates. We introduce a variational Bayesian Recurrent Neural Net recommender system that acts on time series of interactions between the internet platform and the user, and which scales to real world industrial situations. The recommender system is tested both online on real users, and on an offline dataset collected from a Norwegian web-based marketplace, FINN.no, that is made public for research. This is one of the first publicly available datasets which includes all the slates that are presented to users as well as which items (if any) in the slates were clicked on. Such a data set allows us to move beyond the common assumption that implicitly assumes that users are considering all possible items at each interaction. Instead we build our likelihood using the items that are actually in the slate, and evaluate the strengths and weaknesses of both approaches theoretically and in experiments. We also introduce a hierarchical prior for the item parameters based on group memberships. Both item parameters and user preferences are learned probabilistically. Furthermore, we combine our model with bandit strategies to ensure learning, and introduce `in-slate Thompson Sampling' which makes use of the slates to maximise explorative opportunities. We show experimentally that explorative recommender strategies perform on par or above their greedy counterparts. Even without making use of exploration to learn more effectively, click rates increase simply because of improved diversity in the recommended slates.