Intelligent robots are redefining a multitude of critical domains but are still far from being fully capable of assisting human peers in day-to-day tasks. An important requirement of collaboration is for each teammate to maintain and respect an understanding of the others' expectations of itself. Lack of which may lead to serious issues such as loose coordination between teammates, reduced situation awareness, and ultimately teaming failures. Hence, it is important for robots to behave explicably by meeting the human's expectations. One of the challenges here is that the expectations of the human are often hidden and can change dynamically as the human interacts with the robot. However, existing approaches to generating explicable plans often assume that the human's expectations are known and static. In this paper, we propose the idea of active explicable planning to relax this assumption. We apply a Bayesian approach to model and predict dynamic human belief and expectations to make explicable planning more anticipatory. We hypothesize that active explicable plans can be more efficient and explicable at the same time, when compared to explicable plans generated by the existing methods. In our experimental evaluation, we verify that our approach generates more efficient explicable plans while successfully capturing the dynamic belief change of the human teammate.

Data augmentation (DA) algorithms are widely used for Bayesian inference due to their simplicity. In massive data settings, however, DA algorithms are prohibitively slow because they pass through the full data in any iteration, imposing serious restrictions on their usage despite the advantages. Addressing this problem, we develop a framework for extending any DA that exploits asynchronous and distributed computing. The extended DA algorithm is indexed by a parameter $r \in (0, 1)$ and is called Asynchronous and Distributed (AD) DA with the original DA as its parent. Any ADDA starts by dividing the full data into $k$ smaller disjoint subsets and storing them on $k$ processes, which could be machines or processors. Every iteration of ADDA augments only an $r$-fraction of the $k$ data subsets with some positive probability and leaves the remaining $(1-r)$-fraction of the augmented data unchanged. The parameter draws are obtained using the $r$-fraction of new and $(1-r)$-fraction of old augmented data. For many choices of $k$ and $r$, the fractional updates of ADDA lead to a significant speed-up over the parent DA in massive data settings, and it reduces to the distributed version of its parent DA when $r=1$. We show that the ADDA Markov chain is Harris ergodic with the desired stationary distribution under mild conditions on the parent DA algorithm. We demonstrate the numerical advantages of the ADDA in three representative examples corresponding to different kinds of massive data settings encountered in applications. In all these examples, our DA generalization is significantly faster than its parent DA algorithm for all the choices of $k$ and $r$. We also establish geometric ergodicity of the ADDA Markov chain for all three examples, which in turn yields asymptotically valid standard errors for estimates of desired posterior quantities.

There is a strong link between the general concept of intelligence and the ability to collect and use information. The theory of Bayes-adaptive exploration offers an attractive optimality framework for training machines to perform complex information gathering tasks. However, the computational complexity of the resulting optimal control problem has limited the diffusion of the theory to mainstream deep AI research. In this paper we exploit the inherent mathematical structure of Bayes-adaptive problems in order to dramatically simplify the problem by making the reward structure denser while simultaneously decoupling the learning of exploitation and exploration policies. The key to this simplification comes from the novel concept of cross-value (i.e. the value of being in an environment while acting optimally according to another), which we use to quantify the value of currently available information. This results in a new denser reward structure that "cashes in" all future rewards that can be predicted from the current information state. In a set of experiments we show that the approach makes it possible to learn challenging information gathering tasks without the use of shaping and heuristic bonuses in situations where the standard RL algorithms fail.

The path-specific Another commonly used method for these problems is bottleneck on a path between a source and a target node in a Upper Confidence Bound (UCB) (Auer 2002), which utilizes network is defined as the edge with a maximal cost or weight optimism to balance exploration and exploitation. UCB according to some criterion such as transfer time, load, commute has been adapted to combinatorial settings (Chen, Wang, and time, distance, etc. Then, the goal of bottleneck identification Yuan 2013), and also exists in Bayesian variants (Kaufmann, and avoidance is to find a path whose bottleneck is Cappé, and Garivier 2012). Recently, a variant of UCB has minimal. Thus, one may model bottleneck identification as been studied for bottleneck avoidance problems in a combinatorial the problem of computing the minimax edge over the given pure exploration setting (Du, Kuroki, and Chen network/graph, to obtain an edge with a minimal largest gap 2021). They consider a different problem setting and method between the source and target nodes. Equivalently, it can be than ours, though their bottleneck reward function is similar formulated as a widest path problem or maximum capacity to the one we use in our approximation method.

In this article, we will discuss the mathematical intuition behind Naive Bayes Classifiers, and we'll also see how to implement this on Python. This model is easy to build and is mostly used for large datasets. It is a probabilistic machine learning model that is used for classification problems. The core of the classifier depends on the Bayes theorem with an assumption of independence among predictors. That means changing the value of a feature doesn't change the value of another feature.

The commonly used latent space embedding techniques, such as Principal Component Analysis, Factor Analysis, and manifold learning techniques, are typically used for learning effective representations of homogeneous data. However, they do not readily extend to heterogeneous data that are a combination of numerical and categorical variables, e.g., arising from linked GPS and text data. In this paper, we are interested in learning probabilistic generative models from high-dimensional heterogeneous data in an unsupervised fashion. The learned generative model provides latent unified representations that capture the factors common to the multiple dimensions of the data, and thus enable fusing multimodal data for various machine learning tasks. Following a Bayesian approach, we propose a general framework that combines disparate data types through the natural parameterization of the exponential family of distributions. To scale the model inference to millions of instances with thousands of features, we use the Laplace-Bernstein approximation for posterior computations involving nonlinear link functions. The proposed algorithm is presented in detail for the commonly encountered heterogeneous datasets with real-valued (Gaussian) and categorical (multinomial) features. Experiments on two high-dimensional and heterogeneous datasets (NYC Taxi and MovieLens-10M) demonstrate the scalability and competitive performance of the proposed algorithm on different machine learning tasks such as anomaly detection, data imputation, and recommender systems.

We consider the problem of learning the behavioral preferences of an expert engaged in a task from noisy and partially-observable demonstrations. This is motivated by real-world applications such as a line robot learning from observing a human worker, where some observations are occluded by environmental objects that cannot be removed. Furthermore, robotic perception tends to be imperfect and noisy. Previous techniques for inverse reinforcement learning (IRL) take the approach of either omitting the missing portions or inferring it as part of expectation-maximization, which tends to be slow and prone to local optima. We present a new method that generalizes the well-known Bayesian maximum-a-posteriori (MAP) IRL method by marginalizing the occluded portions of the trajectory. This is additionally extended with an observation model to account for perception noise. We show that the marginal MAP (MMAP) approach significantly improves on the previous IRL technique under occlusion in both formative evaluations on a toy problem and in a summative evaluation on an onion sorting line task by a robot.

While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function for regression uncertainty estimation based on the Bayesian Validation Metric (BVM) framework while using ensemble learning. A series of experiments on in-distribution data show that the proposed method is competitive with existing state-of-the-art methods. In addition, experiments on out-of-distribution data show that the proposed method is robust to statistical change and exhibits superior predictive capability.

The Wishart distribution is the standard conjugate prior for the precision of the multivariate Gaussian likelihood, when the mean is known -- while the normal-Wishart can be used when the mean is also unknown. It is however not so obvious how to assign values to the hyperparameters of these distributions. In particular, when forming non-informative limits of these distributions, the shape (or degrees of freedom) parameter of the Wishart must be handled with care. The intuitive solution of directly interpreting the shape as a pseudocount and letting it go to zero, as proposed by some authors, violates the restrictions on the shape parameter. We show how to use the scaled KL-divergence between multivariate Gaussians as an energy function to construct Wishart and normal-Wishart conjugate priors. When used as informative priors, the salient feature of these distributions is the mode, while the KL scaling factor serves as the pseudocount. The scale factor can be taken down to the limit at zero, to form non-informative priors that do not violate the restrictions on the Wishart shape parameter. This limit is non-informative in the sense that the posterior mode is identical to the maximum likelihood estimate of the parameters of the Gaussian.

We propose solving the general Stochastic Shortest-Path Markov Decision Process (SSP MDP) as probabilistic inference. Furthermore, we discuss online and offline methods for planning under uncertainty. In an SSP MDP, the horizon is indefinite and unknown a priori. SSP MDPs generalize finite and infinite horizon MDPs and are widely used in the artificial intelligence community. Additionally, we highlight some of the differences between solving an MDP using dynamic programming approaches widely used in the artificial intelligence community and approaches used in the active inference community.