A nonparametric kernel-based method for realizing Bayes' rule is proposed, based on kernel representations of probabilities in reproducing kernel Hilbert spaces. The prior and conditional probabilities are expressed as empirical kernel mean and covariance operators, respectively, and the kernel mean of the posterior distribution is computed in the form of a weighted sample. The kernel Bayes' rule can be applied to a wide variety of Bayesian inference problems: we demonstrate Bayesian computation without likelihood, and filtering with a nonparametric statespace model. A consistency rate for the posterior estimate is established.

We propose a new sparse Bayesian model for multi-task regression and classification. The model is able to capture correlations between tasks, or more specifically a low-rank approximation of the covariance matrix, while being sparse in the features. We introduce a general family of group sparsity inducing priors based on matrix-variate Gaussian scale mixtures. We show the amount of sparsity can be learnt from the data by combining an approximate inference approach with type II maximum likelihood estimation of the hyperparameters. Empirical evaluations on data sets from biology and vision demonstrate the applicability of the model, where on both regression and classification tasks it achieves competitive predictive performance compared to previously proposed methods.

We introduce hierarchically supervised latent Dirichlet allocation (HSLDA), a model for hierarchically and multiply labeled bag-of-word data. Examples of such data include web pages and their placement in directories, product descriptions and associated categories from product hierarchies, and free-text clinical records and their assigned diagnosis codes. Out-of-sample label prediction is the primary goal of this work, but improved lower-dimensional representations of the bagof-word data are also of interest. We demonstrate HSLDA on large-scale data from clinical document labeling and retail product categorization tasks. We show that leveraging the structure from hierarchical labels improves out-of-sample label prediction substantially when compared to models that do not.

The distance dependent Chinese restaurant process (ddCRP) was recently introduced to accommodate random partitions of non-exchangeable data [1]. The dd-CRP clusters data in a biased way: each data point is more likely to be clustered with other data that are near it in an external sense. This paper examines the dd-CRP in a spatial setting with the goal of natural image segmentation. We explore the biases of the spatial ddCRP model and propose a novel hierarchical extension better suited for producing "human-like" segmentations. We then study the sensitivity of the models to various distance and appearance hyperparameters, and provide the first rigorous comparison of nonparametric Bayesian models in the image segmentation domain. On unsupervised image segmentation, we demonstrate that similar performance to existing nonparametric Bayesian models is possible with substantially simpler models and algorithms.

The difficulty in inverse reinforcement learning (IRL) arises in choosing the best reward function since there are typically an infinite number of reward functions that yield the given behaviour data as optimal. Using a Bayesian framework, we address this challenge by using the maximum a posteriori (MAP) estimation for the reward function, and show that most of the previous IRL algorithms can be modeled into our framework. We also present a gradient method for the MAP estimation based on the (sub)differentiability of the posterior distribution. We show the effectiveness of our approach by comparing the performance of the proposed method to those of the previous algorithms.

We consider the computational complexity of probabilistic inference in Latent Dirichlet Allocation (LDA). First, we study the problem of finding the maximum a posteriori (MAP) assignment of topics to words, where the document's topic distribution is integrated out. We show that, when the e ective number of topics per document is small, exact inference takes polynomial time. In contrast, we show that, when a document has a large number of topics, finding the MAP assignment of topics to words in LDA is NP-hard. Next, we consider the problem of finding the MAP topic distribution for a document, where the topic-word assignments are integrated out. We show that this problem is also NP-hard. Finally, we briefly discuss the problem of sampling from the posterior, showing that this is NP-hard in one restricted setting, but leaving open the general question.

A Bayesian approach to partitioning distance matrices is presented. It is inspired by the Translation-invariant Wishart-Dirichlet process (TIWD) in [1] and shares a number of advantageous properties like the fully probabilistic nature of the inference model, automatic selection of the number of clusters and applicability in semi-supervised settings. In addition, our method (which we call fastTIWD) overcomes the main shortcoming of the original TIWD, namely its high computational costs.

In this work, we study the out-of-distribution (OOD) detection problem through the use of the feature space of a pre-trained deep classifier. We show that learning the density of in-distribution (ID) features with an energy-based models (EBM) leads to competitive detection results. However, we found that the non-mixing of MCMC sampling during the EBM's training undermines its detection performance. To overcome this an energy-based correction of a mixture of class-conditional Gaussian distributions. We obtains favorable results when compared to a strong baseline like the KNN detector on the CIFAR-10/CIFAR-100 OOD detection benchmarks.

Lifted inference exploits symmetries in probabilistic graphical models by using a representative for indistinguishable objects, thereby speeding up query answering while maintaining exact answers. Even though lifting is a well-established technique for the task of probabilistic inference in relational domains, it has not yet been applied to the task of causal inference. In this paper, we show how lifting can be applied to efficiently compute causal effects in relational domains. More specifically, we introduce parametric causal factor graphs as an extension of parametric factor graphs incorporating causal knowledge and give a formal semantics of interventions therein. We further present the lifted causal inference algorithm to compute causal effects on a lifted level, thereby drastically speeding up causal inference compared to propositional inference, e.g., in causal Bayesian networks. In our empirical evaluation, we demonstrate the effectiveness of our approach.

Recent research on mobile robot navigation has focused on socially aware navigation in crowded environments. However, existing methods do not adequately account for human robot interactions and demand accurate location information from omnidirectional sensors, rendering them unsuitable for practical applications. In response to this need, this study introduces a novel algorithm, BNBRL+, predicated on the partially observable Markov decision process framework to assess risks in unobservable areas and formulate movement strategies under uncertainty. BNBRL+ consolidates belief algorithms with Bayesian neural networks to probabilistically infer beliefs based on the positional data of humans. It further integrates the dynamics between the robot, humans, and inferred beliefs to determine the navigation paths and embeds social norms within the reward function, thereby facilitating socially aware navigation. Through experiments in various risk laden scenarios, this study validates the effectiveness of BNBRL+ in navigating crowded environments with blind spots. The model's ability to navigate effectively in spaces with limited visibility and avoid obstacles dynamically can significantly improve the safety and reliability of autonomous vehicles.