Score functions for learning the structure of Bayesian networks in the literature assume that data are a homogeneous set of observations; whereas it is often the case that they comprise different related, but not homogeneous, data sets collected in different ways. In this paper we propose a new Bayesian Dirichlet score, which we call Bayesian Hierarchical Dirichlet (BHD). The proposed score is based on a hierarchical model that pools information across data sets to learn a single encompassing network structure, while taking into account the differences in their probabilistic structures. We derive a closed-form expression for BHD using a variational approximation of the marginal likelihood and we study its performance using simulated data. We find that, when data comprise multiple related data sets, BHD outperforms the Bayesian Dirichlet equivalent uniform (BDeu) score in terms of reconstruction accuracy as measured by the Structural Hamming distance, and that it is as accurate as BDeu when data are homogeneous. Moreover, the estimated networks are sparser and therefore more interpretable than those obtained with BDeu, thanks to a lower number of false positive arcs.

Common experience suggests that agents who know each other well are better able to work together. In this work, we address the problem of calibrating intention and capabilities in human-robot collaboration. In particular, we focus on scenarios where the robot is attempting to assist a human who is unable to directly communicate her intent. Moreover, both agents may have differing capabilities that are unknown to one another. We adopt a decision-theoretic approach and propose the TICC-POMDP for modeling this setting, with an associated online solver. Experiments show our approach leads to better team performance both in simulation and in a real-world study with human subjects.

OWL ontologies are nowadays a quite popular way to describe structured knowledge in terms of classes, relations among classes and class instances. In this paper, given a target class T of an OWL ontology, we address the problem of learning fuzzy concept inclusion axioms that describe sufficient conditions for being an individual instance of T. To do so, we present Fuzzy OWL-BOOST that relies on the Real AdaBoost boosting algorithm adapted to the (fuzzy) OWL case. We illustrate its effectiveness by means of an experimentation. An interesting feature is that the learned rules can be represented directly into Fuzzy OWL 2. As a consequence, any Fuzzy OWL 2 reasoner can then be used to automatically determine/classify (and to which degree) whether an individual belongs to the target class T.

We present a review and taxonomy of 200 models from the literature on driver behavior modeling. We begin by introducing a mathematical formulation based on the partially observable stochastic game, which serves as a common framework for comparing and contrasting different driver models. Our taxonomy is constructed around the core modeling tasks of state estimation, intention estimation, trait estimation, and motion prediction, and also discusses the auxiliary tasks of risk estimation, anomaly detection, behavior imitation and microscopic traffic simulation. Existing driver models are categorized based on the specific tasks they address and key attributes of their approach.

It is applied to knowledge discovery via dimension reducing and clustering in many fields. However, its generalization error had not been yet clarified since it is a singular statistical model where there is no one to one map from parameters to probability distributions. In this paper, we give the exact asymptotic form of its generalization error and marginal likelihood, by theoretical analysis of its learning coefficient using algebraic geometry. The theoretical result shows that the Bayesian generalization error in LDA is expressed in terms of that in matrix factorization and a penalty from the simplex restriction of LDA's parameter region.

Finding the best model that describes a high dimensional dataset, is a daunting task. For binary data, we show that this becomes feasible, if the search is restricted to simple models. These models -- that we call Minimally Complex Models (MCMs) -- are simple because they are composed of independent components of minimal complexity, in terms of description length. Simple models are easy to infer and to sample from. In addition, model selection within the MCMs' class is invariant with respect to changes in the representation of the data. They portray the structure of dependencies among variables in a simple way. They provide robust predictions on dependencies and symmetries, as illustrated in several examples. MCMs may contain interactions between variables of any order. So, for example, our approach reveals whether a dataset is appropriately described by a pairwise interaction model.

A structural causal model is made of endogenous (manifest) and exogenous (latent) variables. We show that endogenous observations induce linear constraints on the probabilities of the exogenous variables. This allows to exactly map a causal model into a credal network. Causal inferences, such as interventions and counterfactuals, can consequently be obtained by standard algorithms for the updating of credal nets. These natively return sharp values in the identifiable case, while intervals corresponding to the exact bounds are produced for unidentifiable queries. A characterization of the causal models that allow the map above to be compactly derived is given, along with a discussion about the scalability for general models. This contribution should be regarded as a systematic approach to represent structural causal models by credal networks and hence to systematically compute causal inferences. A number of demonstrative examples is presented to clarify our methodology. Extensive experiments show that approximate algorithms for credal networks can immediately be used to do causal inference in real-size problems.

A common assumption in generative models is that the generator immerses the latent space into a Euclidean ambient space. Instead, we consider the ambient space to be a Riemannian manifold, which allows for encoding domain knowledge through the associated Riemannian metric. Shortest paths can then be defined accordingly in the latent space to both follow the learned manifold and respect the ambient geometry. Through careful design of the ambient metric we can ensure that shortest paths are well-behaved even for deterministic generators that otherwise would exhibit a misleading bias. Experimentally we show that our approach improves interpretability of learned representations both using stochastic and deterministic generators.

Dynamic discrete choice models are used to estimate the intertemporal preferences of an agent as described by a reward function based upon observable histories of states and implemented actions. However, in many applications, such as reliability and healthcare, the system state is partially observable or hidden (e.g., the level of deterioration of an engine, the condition of a disease), and the decision maker only has access to information imperfectly correlated with the true value of the hidden state. In this paper, we consider the estimation of a dynamic discrete choice model with state variables and system dynamics that are hidden (or partially observed) to both the agent and the modeler, thus generalizing Rust's model to partially observable cases. We analyze the structural properties of the model and prove that this model is still identifiable if the cardinality of the state space, the discount factor, the distribution of random shocks, and the rewards for a given (reference) action are given. We analyze both theoretically and numerically the potential mis-specification errors that may be incurred when Rust's model is improperly used in partially observable settings. We further apply the developed model to a subset of Rust's dataset for bus engine mileage and replacement decisions. The results show that our model can improve model fit as measured by the $\log$-likelihood function by $17.7\%$ and the $\log$-likelihood ratio test shows that our model statistically outperforms Rust's model. Interestingly, our hidden state model also reveals an economically meaningful route assignment behavior in the dataset which was hitherto ignored, i.e. routes with lower mileage are assigned to buses believed to be in worse condition.

We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference, and (ii) it allows the incorporation of expert knowledge through rule-based systems. The blending of those two different frameworks can be particularly beneficial for various domains (e.g. engineering), where, even though the significance of uncertainty quantification motivates a Bayesian approach, there is no simple way to incorporate researcher intuition into the model. We validate our models by applying them to synthetic applications: a simple linear regression problem and two more complex structures based on partial differential equations. Finally, we review the advantages of our methodology, which include the simplicity of the implementation, the uncertainty reduction due to the added information and, in some occasions, the derivation of better point predictions, and we address limitations, mainly from the computational complexity perspective, such as the difficulty in choosing an appropriate algorithm and the added computational burden.