Relational logistic regression (RLR) was presented at the 14th International Conference on Principles of Knowledge Representation and Reasoning (KR-2014). RLR is the directed analogue of Markov logic networks. Whereas Markov logic networks define distributions in terms of weighted formulae, RLR defines conditional probabilities in terms of weighted formulae. They agree for the supervised learning case when all variables except a query leaf variable are observed. However, they are quite different in representing distributions. The KR-2014 paper defined the RLR formalism, defined canonical forms for RLR in terms of positive conjunctive formulae, indicated the class of conditional probability distributions that can and cannot be represented by RLR, and defined many other aggregators in terms of RLR. In this paper, we summarize these results and compare RLR to Markov logic networks.

Lifted inference algorithms take advantage of symmetries in first-order probabilistic logic representations such as Markov logic networks (MLNs), and are naturally more scalable than propositional inference algorithms which ground the MLN. However, lifted inference algorithms have an "evidence problem" -- evidence breaks symmetries, and the performance of lifted inference algorithms is the same as propositional inference algorithms (or sometimes worse, due to overhead). In this paper, we propose a general method for addressing this problem. The main idea in our method is to approximate the given MLN having, say, n objects by an MLN having k objects such that k is much lesser than n and the results obtained by running potentially much faster inference on the smaller MLN are as close as possible to the ones obtained by running inference on the larger MLN. We achieve this by finding clusters of "similar" groundings using standard clustering algorithms (e.g., K-means), and replacing all groundings in the cluster by their cluster center. To this end, we develop a novel distance (or similarity) function for measuring the similarity between two groundings, based on the evidence presented to the MLN. We evaluated our approach on different benchmarks utilizing various clustering and inference algorithms. Our experiments clearly show the generality and scalability of our approach.

It is generally challenging to obtain the exact disease prevalence, as the true cases of a disease in the population level are not easy to identify. Available and relevant data sources such as administrative or clinical health data are used in public health surveillance as a proxy to estimate the disease prevalence. Traditionally, these data sources span through healthcare utilization information such as emergency department visits, pharmacy drug sales, or laboratory test orders. In addition to incompleteness, these data sources are not usually available in a timely manner. Timeliness is an important factor for prevalence estimation for some conditions such as infectious diseases, especially at the time of an epidemic. For instance, in an influenza pandemic such estimates must be obtained within a day or two. In recent years several non-clinical and non-traditional data sources have been introduced to public health with the potentials to provide signals on a disease rate or to provide a feedback on the trends of a disease. Ideally, combining these new sources with the ones routinely used should help to identify disease cases more efficiently. However, building a construct capable of incorporating data from these various sources in a coherent manner is not trivial. In this research, we consider the case of H1N1 pandemic as the infectious disease of interest and we use media reports of deaths from H1N1 on the web as a non traditional data source. We propose to use dynamic Bayesian networks from the class of probabilistic graphical models in order to combine this new data source with traditional ones through exploration of the possible probabilistic relationships between these data streams. This is an initial step towards building a framework that can potentially support aggregation of heterogeneous data for a real-time estimation of a disease prevalence. Our preliminary results show that the proposed model generalizes well.

Inference in large scale graphical models is an important task in many domains, and in particular probabilistic relational models (e.g. Markov logic networks). Such models often exhibit considerable symmetry, and it is a challenge to devise algorithms that exploit this symmetry to speed up inference. Recently, the automorphism group has been proposed to formalize mathematically what "exploiting symmetry" means. However, obtaining symmetry derived from automorphism is GI-hard, and consequently only a small fraction of the symmetry is easily available for effective employment. In this paper, we improve upon efficiency in two ways. First, we introduce the Cluster Signature Graph (CSG), a platform on which greater portions of the symmetries can be revealed and exploited. CSGs classify clusters of variables by projecting relations between cluster members onto a graph, allowing for the efficient pruning of symmetrical clusters even before their generation. Second, we introduce a novel framework based on CSGs for the Sherali-Adams hierarchy of linear program (LP) relaxations, dedicated to exploiting this symmetry for the benefit of tight Maximum A Posteriori (MAP) approximations. Combined with the pruning power of CSG, the framework quickly generates compact formulations for otherwise intractable LPs, as demonstrated by several empirical results.

Many graph clustering quality functions suffer from a resolution limit, the inability to find small clusters in large graphs. So called resolution-limit-free quality functions do not have this limit. This property was previously introduced for hard clustering, that is, graph partitioning. We investigate the resolution-limit-free property in the context of Non-negative Matrix Factorization (NMF) for hard and soft graph clustering. To use NMF in the hard clustering setting, a common approach is to assign each node to its highest membership cluster. We show that in this case symmetric NMF is not resolution-limit-free, but that it becomes so when hardness constraints are used as part of the optimization. The resulting function is strongly linked to the Constant Potts Model. In soft clustering, nodes can belong to more than one cluster, with varying degrees of membership. In this setting resolution-limit-free turns out to be too strong a property. Therefore we introduce locality, which roughly states that changing one part of the graph does not affect the clustering of other parts of the graph. We argue that this is a desirable property, provide conditions under which NMF quality functions are local, and propose a novel class of local probabilistic NMF quality functions for soft graph clustering.

Predictive state representations (PSRs) offer an expressive framework for modelling partially observable systems. By compactly representing systems as functions of observable quantities, the PSR learning approach avoids using local-minima prone expectation-maximization and instead employs a globally optimal moment-based algorithm. Moreover, since PSRs do not require a predetermined latent state structure as an input, they offer an attractive framework for model-based reinforcement learning when agents must plan without a priori access to a system model. Unfortunately, the expressiveness of PSRs comes with significant computational cost, and this cost is a major factor inhibiting the use of PSRs in applications. In order to alleviate this shortcoming, we introduce the notion of compressed PSRs (CPSRs). The CPSR learning approach combines recent advancements in dimensionality reduction, incremental matrix decomposition, and compressed sensing. We show how this approach provides a principled avenue for learning accurate approximations of PSRs, drastically reducing the computational costs associated with learning while also providing effective regularization. Going further, we propose a planning framework which exploits these learned models. And we show that this approach facilitates model-learning and planning in large complex partially observable domains, a task that is infeasible without the principled use of compression.

Kernel-based reinforcement learning (KBRL) stands out among reinforcement learning algorithms for its strong theoretical guarantees. By casting the learning problem as a local kernel approximation, KBRL provides a way of computing a decision policy which is statistically consistent and converges to a unique solution. Unfortunately, the model constructed by KBRL grows with the number of sample transitions, resulting in a computational cost that precludes its application to large-scale or on-line domains. In this paper we introduce an algorithm that turns KBRL into a practical reinforcement learning tool. Kernel-based stochastic factorization (KBSF) builds on a simple idea: when a transition matrix is represented as the product of two stochastic matrices, one can swap the factors of the multiplication to obtain another transition matrix, potentially much smaller, which retains some fundamental properties of its precursor. KBSF exploits such an insight to compress the information contained in KBRL's model into an approximator of fixed size. This makes it possible to build an approximation that takes into account both the difficulty of the problem and the associated computational cost. KBSF's computational complexity is linear in the number of sample transitions, which is the best one can do without discarding data. Moreover, the algorithm's simple mechanics allow for a fully incremental implementation that makes the amount of memory used independent of the number of sample transitions. The result is a kernel-based reinforcement learning algorithm that can be applied to large-scale problems in both off-line and on-line regimes. We derive upper bounds for the distance between the value functions computed by KBRL and KBSF using the same data. We also illustrate the potential of our algorithm in an extensive empirical study in which KBSF is applied to difficult tasks based on real-world data.

Crowdsourcing has been proven to be an effective and efficient tool to annotate large datasets. User annotations are often noisy, so methods to combine the annotations to produce reliable estimates of the ground truth are necessary. We claim that considering the existence of clusters of users in this combination step can improve the performance. This is especially important in early stages of crowdsourcing implementations, where the number of annotations is low. At this stage there is not enough information to accurately estimate the bias introduced by each annotator separately, so we have to resort to models that consider the statistical links among them. In addition, finding these clusters is interesting in itself as knowing the behavior of the pool of annotators allows implementing efficient active learning strategies. Based on this, we propose in this paper two new fully unsupervised models based on a Chinese Restaurant Process (CRP) prior and a hierarchical structure that allows inferring these groups jointly with the ground truth and the properties of the users. Efficient inference algorithms based on Gibbs sampling with auxiliary variables are proposed. Finally, we perform experiments, both on synthetic and real databases, to show the advantages of our models over state-of-the-art algorithms.

In this paper, we address the problem of real-time detection of viruses docking to nanowires, especially when multiple viruses dock to the same nano-wire. The task becomes more complicated when there is an array of nanowires coated with different antibodies, where different viruses can dock to each coated nanowire at different binding strengths. We model the array response to a viral agent as a pattern of conductance change over nanowires with known modifier --- this representation permits analysis of the output of such an array via belief network (Bayes) methods, as well as novel generative models like the Hidden Semi-Markov Model (HSMM).

Neural connectomics has begun producing massive amounts of data, necessitating new analysis methods to discover the biological and computational structure. It has long been assumed that discovering neuron types and their relation to microcircuitry is crucial to understanding neural function. Here we developed a nonparametric Bayesian technique that identifies neuron types and microcircuitry patterns in connectomics data. It combines the information traditionally used by biologists, including connectivity, cell body location and the spatial distribution of synapses, in a principled and probabilistically-coherent manner. We show that the approach recovers known neuron types in the retina and enables predictions of connectivity, better than simpler algorithms. It also can reveal interesting structure in the nervous system of C. elegans, and automatically discovers the structure of a microprocessor. Our approach extracts structural meaning from connectomics, enabling new approaches of automatically deriving anatomical insights from these emerging datasets.