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Structural learning of Bayesian Networks (BNs) is a NP-hard problem, which is further complicated by many theoretical issues, such as the I-equivalence among different structures. In this work, we focus on a specific subclass of BNs, named…
A difficult task in modeling with Bayesian networks is the elicitation of numerical parameters of Bayesian networks. A large number of parameters is needed to specify a conditional probability table (CPT) that has a larger parent set. In…
Random events in space and time often exhibit a locally dependent structure. When the events are very rare and dependent structure is not too complicated, various studies in the literature have shown that Poisson and compound Poisson…
Bayesian Belief Networks have been largely overlooked by Expert Systems practitioners on the grounds that they do not correspond to the human inference mechanism. In this paper, we introduce an explanation mechanism designed to generate…
In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model…
We analyze the computational efficiency of approximate Bayesian computation (ABC), which approximates a likelihood function by drawing pseudo-samples from the associated model. For the rejection sampling version of ABC, it is known that…
Statistical analysis of max-stable processes used to model spatial extremes has been limited by the difficulty in calculating the joint likelihood function. This precludes all standard likelihood-based approaches, including Bayesian…
Approximate Bayesian computation (ABC) is a popular likelihood-free inference method for models with intractable likelihood functions. As ABC methods usually rely on comparing summary statistics of observed and simulated data, the choice of…
A case-based reasoning (CBR) system solves a new problem by retrieving `cases' that are similar to the given problem. If such a system can achieve high accuracy, it is appealing owing to its simplicity, interpretability, and scalability. In…
Causal models are crucial for understanding complex systems and identifying causal relationships among variables. Even though causal models are extremely popular, conditional probability calculation of formulas involving interventions pose…
We show an alternative way of representing a Bayesian belief network by sensitivities and probability distributions. This representation is equivalent to the traditional representation by conditional probabilities, but makes dependencies…
In the following article we consider approximate Bayesian computation (ABC) for certain classes of time series models. In particular, we focus upon scenarios where the likelihoods of the observations and parameter are intractable, by which…
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
Structure and parameters in a Bayesian network uniquely specify the probability distribution of the modeled domain. The locality of both structure and probabilistic information are the great benefits of Bayesian networks and require the…
A new approach to inference in state space models is proposed, based on approximate Bayesian computation (ABC). ABC avoids evaluation of the likelihood function by matching observed summary statistics with statistics computed from data…
Correlation Networks (CNs) inherently suffer from redundant information in their network topology. Bayesian Networks (BNs), on the other hand, include only non-redundant information (from a probabilistic perspective) resulting in a sparse…
Validating and controlling safety-critical systems in uncertain environments necessitates probabilistic reachable sets of future state evolutions. The existing methods of computing probabilistic reachable sets normally assume that…
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
Normative expert systems have not become commonplace because they have been difficult to build and use. Over the past decade, however, researchers have developed the influence diagram, a graphical representation of a decision maker's…