We study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including additivity boil down to invariances of the covariance kernel. These results are extended to a broader class of operators in the Gaussian case, via the Lo\`eve isometry. Several covariance-driven pathwise invariances are illustrated, including fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process regression.

Decision theory focuses on the problem of making decisions under uncertainty. This uncertainty arises from the unknown aspects of the state of the world the decision maker is in or the unknown utility function of performing actions. The uncertainty can be modeled as a probability distribution capturing our belief about the world the decision maker is in. Upon making new observations, the decision maker becomes more confident about this model. In addition, if there is a prior belief on this uncertainty that may have obtained from similar experiments, the Bayesian methods may be employed. The loss incurred by the decision maker can also be utilized for the optimal action selection. Most machine learning algorithms developed though focus on one of these aspects for learning and prediction; either learning the probabilistic model or minimizing the loss. In probabilistic models, approximate inference, the process of obtaining the desired model from the observations when its is not tractable, does not consider the task loss. On the other end of the spectrum, the common practice in learning is to minimize the task loss without considering the uncertainty of prediction model. Therefore, we investigate the intersection of decision theory and machine learning considering both uncertainty in prediction model and the task loss.

We review the challenges of Bayesian network learning, especially parameter learning, and specify the problem of learning with sparse data. We explain how it is possible to incorporate both qualitative knowledge and data with a multinomial parameter learning method to achieve more accurate predictions with sparse data.

A novel proposal for object recognition based on relational grammars and Bayesian Networks is presented. Based on this grammar an object is represented as a hierarchy of features and spatial relations. This representation is transformed to a Bayesian network structure which parameters are learned from examples. Thus, recognition is based on probabilistic inference in the Bayesian network representation. Preliminary results in modeling natural objects are presented.

We present a reformulation of the stochastic optimal control problem in terms of KL divergence minimisation, not only providing a unifying perspective of previous approaches in this area, but also demonstrating that the formalism leads to novel practical approaches to the control problem. Specifically, a natural relaxation of the dual formulation gives rise to exact iterative solutions to the finite and infinite horizon stochastic optimal control problem, while direct application of Bayesian inference methods yields instances of risk sensitive control.

We target the problem of accuracy and robustness in causal inference from finite data sets. Our aim is to combine the inherent robustness of the Bayesian approach with the theoretical strength and clarity of constraint-based methods. We use a Bayesian score to obtain probability estimates on the input statements used in a constraint-based procedure. These are subsequently processed in decreasing order of reliability, letting more reliable decisions take precedence in case of conflicts, until a single output model is obtained. Tests show that a basic implementation of the resulting Bayesian Constraint-based Causal Discovery (BCCD) algorithm already outperforms established procedures such as FCI and Conservative PC. It indicates which causal decisions in the output have high reliability and which do not. The approach is easily adapted to other application areas such as complex independence tests.

Mobile manipulation robots are envisioned to provide many useful services both in domestic environments as well as in the industrial context.  In this paper, we present novel approaches to allow mobile maniplation systems to autonomously adapt to new or changing situations. The approaches developed in this paper cover the following four topics: (1) learning the robot's kinematic structure and properties using actuation and visual feedback, (2) learning about articulated objects in the environment in which the robot is operating, (3) using tactile feedback to augment visual perception, and (4) learning novel manipulation tasks from human demonstrations.

Online content have become an important medium to disseminate information and express opinions. With their proliferation, users are faced with the problem of missing the big picture in a sea of irrelevant and/or diverse content. In this paper, we addresses the problem of information organization of online document collections, and provide algorithms that create a structured representation of the otherwise unstructured content. We leverage the expressiveness of latent probabilistic models (e.g., topic models) and non-parametric Bayes techniques (e.g., Dirichlet processes), and give online and distributed inference algorithms that scale to terabyte datasets and adapt the inferred representation with the arrival of new documents. This paper is an extended abstract of the 2012 ACM SIGKDD best doctoral dissertation award of Ahmed [2011].

This paper concerns building probabilistic models with an underlying ontology that defines the classes and properties used in the model. In particular, it considers the problem of reasoning with properties that may not always be defined. Furthermore, we may even be uncertain about whether a property is defined for a given individual. One approach is to explicitly add a value "undefined" to the range of random variables, forming extended belief networks; however, adding an extra value to a random variable's range has a large computational overhead. In this paper, we propose an alternative, ontologically-based belief networks, where all properties are only used when they are defined, and we show how probabilistic reasoning can be carried out without explicitly using the value "undefined" during inference. We prove this is equivalent to reasoning with the corresponding extended belief network and empirically demonstrate that inference becomes more efficient.

A fault represents some erroneous operation of a system that could result from an action selection error or some abnormal condition. We formally define error models that characterize the likelihood of various faults and consider the problem of fault-tolerant planning, which optimizes performance given an error model. We show that factoring the possibility of errors significantly degrades the performance of stochastic planning algorithms such as LAO*, because the number of reachable states grows dramatically. We introduce an approach to plan for a bounded number of faults and analyze its theoretical properties. When combined with a continual planning paradigm, the k-fault-tolerant planning method can produce near-optimal performance, even when the number of faults exceeds the bound. Empirical results in two challenging domains confirm the effectiveness of the approach in handling different types of runtime errors.