Bayesian networks are a useful tool in the representation of uncertain knowledge. This paper proposes a new algorithm called ACO-E, to learn the structure of a Bayesian network. It does this by conducting a search through the space of equivalence classes of Bayesian networks using Ant Colony Optimization (ACO). To this end, two novel extensions of traditional ACO techniques are proposed and implemented. Firstly, multiple types of moves are allowed. Secondly, moves can be given in terms of indices that are not based on construction graph nodes. The results of testing show that ACO-E performs better than a greedy search and other state-of-the-art and metaheuristic algorithms whilst searching in the space of equivalence classes.

Inference in Bayes Nets (BAYES) is an important problem with numerous applications in probabilistic reasoning. Counting the number of satisfying assignments of a propositional formula (#SAT) is a closely related problem of fundamental theoretical importance. Both these problems, and others, are members of the class of sum-of-products (SUMPROD) problems. In this paper we show that standard backtracking search when augmented with a simple memoization scheme (caching) can solve any sum-of-products problem with time complexity that is at least as good any other state-of-the-art exact algorithm, and that it can also achieve the best known time-space tradeoff. Furthermore, backtracking's ability to utilize more flexible variable orderings allows us to prove that it can achieve an exponential speedup over other standard algorithms for SUMPROD on some instances. The ideas presented here have been utilized in a number of solvers that have been applied to various types of sum-of-product problems. These system's have exploited the fact that backtracking can naturally exploit more of the problem's structure to achieve improved performance on a range of probleminstances. Empirical evidence of this performance gain has appeared in published works describing these solvers, and we provide references to these works.

Accurate calibration of probabilistic predictive models learned is critical for many practical prediction and decision-making tasks. There are two main categories of methods for building calibrated classifiers. One approach is to develop methods for learning probabilistic models that are well-calibrated, ab initio. The other approach is to use some post-processing methods for transforming the output of a classifier to be well calibrated, as for example histogram binning, Platt scaling, and isotonic regression. One advantage of the post-processing approach is that it can be applied to any existing probabilistic classification model that was constructed using any machine-learning method. In this paper, we first introduce two measures for evaluating how well a classifier is calibrated. We prove three theorems showing that using a simple histogram binning post-processing method, it is possible to make a classifier be well calibrated while retaining its discrimination capability. Also, by casting the histogram binning method as a density-based non-parametric binary classifier, we can extend it using two simple non-parametric density estimation methods. We demonstrate the performance of the proposed calibration methods on synthetic and real datasets. Experimental results show that the proposed methods either outperform or are comparable to existing calibration methods.

In this survey, we present and compare different approaches to estimate Mutual Information (MI) from data to analyse general dependencies between variables of interest in a system. We demonstrate the performance difference of MI versus correlation analysis, which is only optimal in case of linear dependencies. First, we use a piece-wise constant Bayesian methodology using a general Dirichlet prior. In this estimation method, we use a two-stage approach where we approximate the probability distribution first and then calculate the marginal and joint entropies. Here, we demonstrate the performance of this Bayesian approach versus the others for computing the dependency between different variables. We also compare these with linear correlation analysis. Finally, we apply MI and correlation analysis to the identification of the bias in the determination of the aerosol optical depth (AOD) by the satellite based Moderate Resolution Imaging Spectroradiometer (MODIS) and the ground based AErosol RObotic NETwork (AERONET). Here, we observe that the AOD measurements by these two instruments might be different for the same location. The reason of this bias is explored by quantifying the dependencies between the bias and 15 other variables including cloud cover, surface reflectivity and others.

We present exact algorithms for identifying deterministic-actions effects and preconditions in dynamic partially observable domains. They apply when one does not know the action model(the way actions affect the world) of a domain and must learn it from partial observations over time. Such scenarios are common in real world applications. They are challenging for AI tasks because traditional domain structures that underly tractability (e.g., conditional independence) fail there (e.g., world features become correlated). Our work departs from traditional assumptions about partial observations and action models. In particular, it focuses on problems in which actions are deterministic of simple logical structure and observation models have all features observed with some frequency. We yield tractable algorithms for the modified problem for such domains. Our algorithms take sequences of partial observations over time as input, and output deterministic action models that could have lead to those observations. The algorithms output all or one of those models (depending on our choice), and are exact in that no model is misclassified given the observations. Our algorithms take polynomial time in the number of time steps and state features for some traditional action classes examined in the AI-planning literature, e.g., STRIPS actions. In contrast, traditional approaches for HMMs and Reinforcement Learning are inexact and exponentially intractable for such domains. Our experiments verify the theoretical tractability guarantees, and show that we identify action models exactly. Several applications in planning, autonomous exploration, and adventure-game playing already use these results. They are also promising for probabilistic settings, partially observable reinforcement learning, and diagnosis.

This paper proposes and experimentally validates a Bayesian network model of a range finder adapted to dynamic environments. All modeling assumptions are rigorously explained, and all model parameters have a physical interpretation. This approach results in a transparent and intuitive model. With respect to the state of the art beam model this paper: (i) proposes a different functional form for the probability of range measurements caused by unmodeled objects, (ii) intuitively explains the discontinuity encountered in te state of the art beam model, and (iii) reduces the number of model parameters, while maintaining the same representational power for experimental data. The proposed beam model is called RBBM, short for Rigorously Bayesian Beam Model. A maximum likelihood and a variational Bayesian estimator (both based on expectation-maximization) are proposed to learn the model parameters. Furthermore, the RBBM is extended to a full scan model in two steps: first, to a full scan model for static environments and next, to a full scan model for general, dynamic environments. The full scan model accounts for the dependency between beams and adapts to the local sample density when using a particle filter. In contrast to Gaussian-based state of the art models, the proposed full scan model uses a sample-based approximation. This sample-based approximation enables handling dynamic environments and capturing multi-modality, which occurs even in simple static environments.

This paper presents Networks of Influence Diagrams (NID), a compact, natural and highly expressive language for reasoning about agents' beliefs and decision-making processes. NIDs are graphical structures in which agents' mental models are represented as nodes in a network; a mental model for an agent may itself use descriptions of the mental models of other agents. NIDs are demonstrated by examples, showing how they can be used to describe conflicting and cyclic belief structures, and certain forms of bounded rationality. In an opponent modeling domain, NIDs were able to outperform other computational agents whose strategies were not known in advance. NIDs are equivalent in representation to Bayesian games but they are more compact and structured than this formalism. In particular, the equilibrium definition for NIDs makes an explicit distinction between agents' optimal strategies, and how they actually behave in reality.

A set of probabilistic predictions is well calibrated if the events that are predicted to occur with probability p do in fact occur about p fraction of the time. Well calibrated predictions are particularly important when machine learning models are used in decision analysis. This paper presents two new non-parametric methods for calibrating outputs of binary classification models: a method based on the Bayes optimal selection and a method based on the Bayesian model averaging. The advantage of these methods is that they are independent of the algorithm used to learn a predictive model, and they can be applied in a post-processing step, after the model is learned. This makes them applicable to a wide variety of machine learning models and methods. These calibration methods, as well as other methods, are tested on a variety of datasets in terms of both discrimination and calibration performance. The results show the methods either outperform or are comparable in performance to the state-of-the-art calibration methods.

Scientists often express their understanding of the world through a computationally demanding simulation program. Analyzing the posterior distribution of the parameters given observations (the inverse problem) can be extremely challenging. The Approximate Bayesian Computation (ABC) framework is the standard statistical tool to handle these likelihood free problems, but they require a very large number of simulations. In this work we develop two new ABC sampling algorithms that significantly reduce the number of simulations necessary for posterior inference. Both algorithms use confidence estimates for the accept probability in the Metropolis Hastings step to adaptively choose the number of necessary simulations. Our GPS-ABC algorithm stores the information obtained from every simulation in a Gaussian process which acts as a surrogate function for the simulated statistics. Experiments on a challenging realistic biological problem illustrate the potential of these algorithms.

Recently, a number of mostly $\ell_1$-norm regularized least squares type deterministic algorithms have been proposed to address the problem of \emph{sparse} adaptive signal estimation and system identification. From a Bayesian perspective, this task is equivalent to maximum a posteriori probability estimation under a sparsity promoting heavy-tailed prior for the parameters of interest. Following a different approach, this paper develops a unifying framework of sparse \emph{variational Bayes} algorithms that employ heavy-tailed priors in conjugate hierarchical form to facilitate posterior inference. The resulting fully automated variational schemes are first presented in a batch iterative form. Then it is shown that by properly exploiting the structure of the batch estimation task, new sparse adaptive variational Bayes algorithms can be derived, which have the ability to impose and track sparsity during real-time processing in a time-varying environment. The most important feature of the proposed algorithms is that they completely eliminate the need for computationally costly parameter fine-tuning, a necessary ingredient of sparse adaptive deterministic algorithms. Extensive simulation results are provided to demonstrate the effectiveness of the new sparse variational Bayes algorithms against state-of-the-art deterministic techniques for adaptive channel estimation. The results show that the proposed algorithms are numerically robust and exhibit in general superior estimation performance compared to their deterministic counterparts.