We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization problems. Recently, it was shown that the underlying principle behind their success is an extended form of convexity over the geodesics in the manifold of positive definite matrices. A modern approach to improve estimation accuracy is to exploit prior knowledge via additional constraints, e.g., restricting the attention to specific classes of covariances which adhere to prior symmetry structures. In this paper, we prove that such group symmetry constraints are also geodesically convex and can therefore be incorporated into various non-Gaussian covariance estimators. Practical examples of such sets include: circulant, persymmetric and complex/quaternion proper structures. We provide a simple numerical technique for finding maximum likelihood estimates under such constraints, and demonstrate their performance advantage using synthetic experiments.

Conditional independence tests (CI tests) have received special attention lately in Machine Learning and Computational Intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of Probabilistic Graphical Models (PGM)--which includes Bayesian Networks (BN) models--CI tests are especially important for the task of learning the PGM structure from data. In this paper, we propose the Full Bayesian Significance Test (FBST) for tests of conditional independence for discrete datasets. FBST is a powerful Bayesian test for precise hypothesis, as an alternative to frequentist's significance tests (characterized by the calculation of the \emph{p-value}).

The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov Random Field, from very limited samples. We propose a novel algorithm for solving the resulting optimization problem which is a regularized log-determinant program. In contrast to recent state-of-the-art methods that largely use first order gradient information, our algorithm is based on Newton's method and employs a quadratic approximation, but with some modifications that leverage the structure of the sparse Gaussian MLE problem. We show that our method is superlinearly convergent, and present experimental results using synthetic and real-world application data that demonstrate the considerable improvements in performance of our method when compared to other state-of-the-art methods.

Expert finding is an information retrieval task concerned with the search for the most knowledgeable people, in some topic, with basis on documents describing peoples activities. The task involves taking a user query as input and returning a list of people sorted by their level of expertise regarding the user query. This paper introduces a novel approach for combining multiple estimators of expertise based on a multisensor data fusion framework together with the Dempster-Shafer theory of evidence and Shannon's entropy. More specifically, we defined three sensors which detect heterogeneous information derived from the textual contents, from the graph structure of the citation patterns for the community of experts, and from profile information about the academic experts. Given the evidences collected, each sensor may define different candidates as experts and consequently do not agree in a final ranking decision. To deal with these conflicts, we applied the Dempster-Shafer theory of evidence combined with Shannon's Entropy formula to fuse this information and come up with a more accurate and reliable final ranking list. Experiments made over two datasets of academic publications from the Computer Science domain attest for the adequacy of the proposed approach over the traditional state of the art approaches. We also made experiments against representative supervised state of the art algorithms. Results revealed that the proposed method achieved a similar performance when compared to these supervised techniques, confirming the capabilities of the proposed framework.

Bayesian Reinforcement Learning (RL) is capable of not only incorporating domain knowledge, but also solving the exploration-exploitation dilemma in a natural way. As Bayesian RL is intractable except for special cases, previous work has proposed several approximation methods. However, these methods are usually too sensitive to parameter values, and finding an acceptable parameter setting is practically impossible in many applications. In this paper, we propose a new algorithm that greedily approximates Bayesian RL to achieve robustness in parameter space. We show that for a desired learning behavior, our proposed algorithm has a polynomial sample complexity that is lower than those of existing algorithms. We also demonstrate that the proposed algorithm naturally outperforms other existing algorithms when the prior distributions are not significantly misleading. On the other hand, the proposed algorithm cannot handle greatly misspecified priors as well as the other algorithms can. This is a natural consequence of the fact that the proposed algorithm is greedier than the other algorithms. Accordingly, we discuss a way to select an appropriate algorithm for different tasks based on the algorithms' greediness. We also introduce a new way of simplifying Bayesian planning, based on which future work would be able to derive new algorithms.

The performance of a modulation classifier is highly sensitive to channel signal-to-noise ratio (SNR). In this paper, we focus on amplitude-phase modulations and propose a modulation classification framework based on centralized data fusion using multiple radios and the hybrid maximum likelihood (ML) approach. In order to alleviate the computational complexity associated with ML estimation, we adopt the Expectation Maximization (EM) algorithm. Due to SNR diversity, the proposed multi-radio framework provides robustness to channel SNR. Numerical results show the superiority of the proposed approach with respect to single radio approaches as well as to modulation classifiers using moments based estimators.

We address efficient planning of maintenance activities in infrastructural networks, inspired by the real-world problem of servicing a highway network. A road authority is responsible for the quality, throughput and maintenance costs of the network, while the actual maintenance is performed by autonomous, third-party contractors. From a (multi-agent) planning and scheduling perspective, many interesting challenges can be identified. First, planned maintenance activities might have an uncertain duration due to unexpected delays. Second, since maintenance activities influence the traffic flow in the network, careful coordination of the planned activities is required in order to minimise their impact on the network throughput. Third, as we are dealing with selfish agents in a private-values setting, the road authority faces an incentive-design problem to truthfully elicit agent costs, complicated by the fact that it needs to balance multiple objectives. The main contributions of this work are: 1) multi-agent coordination on a network level through a novel combination of planning under uncertainty and dynamic mechanism design, applied to real-world problems, 2) accurate modelling and solving of maintenance-planning problems and 3) empirical exploration of the complexities that arise in these problems. We introduce a formal model of the problem domain, present experimental insights and identify open challenges for both the planning and scheduling as well as the mechanism design communities.

Multi-modal journey planning, which allows multiple types of transport within a single trip, is becoming increasingly popular, due to a strong practical interest and an increasing availability of data. In real life, transport networks feature uncertainty. Yet, most approaches assume a deterministic environment, making plans more prone to failures such as major delays in the arrival. We model the scenario as a non-deterministic planning problem with continuous time and time-dependent probabilities of non-deterministic effects. We present new hardness results. We introduce a heuristic search planner, based on Weighted AO* (WAO*). The planner includes search enhancements such as sound pruning, based on state dominance, and an admissible heuristic. Focusing on plans that are robust to uncertainty, we demonstrate our ideas on data compiled from real historical data from Dublin, Ireland. Repeated calls to WAO*, with decreasing weights, have a good any-time performance. Our search enhancements play an important role in the planner's performance.

Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals involving the Gaussian prior and non-conjugate likelihoods. Algorithms based on variational Gaussian (VG) approximations are widely employed since they strike a favorable balance between accuracy, generality, speed, and ease of use. However, the structure of the optimization problems associated with these approximations remains poorly understood, and standard solvers take too long to converge. We derive a novel dual variational inference approach that exploits the convexity property of the VG approximations. We obtain an algorithm that solves a convex optimization problem, reduces the number of variational parameters, and converges much faster than previous methods. Using real-world data, we demonstrate these advantages on a variety of LGMs, including Gaussian process classification, and latent Gaussian Markov random fields.

We propose a technique for increasing the efficiency of gradient-based inference and learning in Bayesian networks with multiple layers of continuous latent vari- ables. We show that, in many cases, it is possible to express such models in an auxiliary form, where continuous latent variables are conditionally deterministic given their parents and a set of independent auxiliary variables. Variables of mod- els in this auxiliary form have much larger Markov blankets, leading to significant speedups in gradient-based inference, e.g. rapid mixing Hybrid Monte Carlo and efficient gradient-based optimization. The relative efficiency is confirmed in ex- periments.