On-line estimation plays an important role in process control and monitoring. Obtaining a theoretical solution to the simultaneous state-parameter estimation problem for non-linear stochastic systems involves solving complex multi-dimensional integrals that are not amenable to analytical solution. While basic sequential Monte-Carlo (SMC) or particle filtering (PF) algorithms for simultaneous estimation exist, it is well recognized that there is a need for making these on-line algorithms non-degenerate, fast and applicable to processes with missing measurements. To overcome the deficiencies in traditional algorithms, this work proposes a Bayesian approach to on-line state and parameter estimation. Its extension to handle missing data in real-time is also provided. The simultaneous estimation is performed by filtering an extended vector of states and parameters using an adaptive sequential-importance-resampling (SIR) filter with a kernel density estimation method. The approach uses an on-line optimization algorithm based on Kullback-Leibler (KL) divergence to allow adaptation of the SIR filter for combined state-parameter estimation. An optimal tuning rule to control the width of the kernel and the variance of the artificial noise added to the parameters is also proposed. The approach is illustrated through numerical examples.

In this paper, we study statistical classification accuracy of two different Markov field environments for pixelwise image segmentation, considering the labels of the image as hidden states and solving the estimation of such labels as a solution of the MAP equation. The emission distribution is assumed the same in all models, and the difference lays in the Markovian prior hypothesis made over the labeling random field. The a priori labeling knowledge will be modeled with a) a second order anisotropic Markov Mesh and b) a classical isotropic Potts model. Under such models, we will consider three different segmentation procedures, 2D Path Constrained Viterbi training for the Hidden Markov Mesh, a Graph Cut based segmentation for the first order isotropic Potts model, and ICM (Iterated Conditional Modes) for the second order isotropic Potts model. We provide a unified view of all three methods, and investigate goodness of fit for classification, studying the influence of parameter estimation, computational gain, and extent of automation in the statistical measures Overall Accuracy, Relative Improvement and Kappa coefficient, allowing robust and accurate statistical analysis on synthetic and real-life experimental data coming from the field of Dental Diagnostic Radiography. All algorithms, using the learned parameters, generate good segmentations with little interaction when the images have a clear multimodal histogram. Suboptimal learning proves to be frail in the case of non-distinctive modes, which limits the complexity of usable models, and hence the achievable error rate as well. All Matlab code written is provided in a toolbox available for download from our website, following the Reproducible Research Paradigm.

A central goal of AI is to reason efficiently in domains that are both complex and uncertain. Most attempts toward this end add probability to a tractable subset of first-order logic, but this results in intractable inference. To address this, Domingos and Webb (2012) introduced tractable Markov logic (TML), the first tractable first-order probabilistic representation. Despite its surprising expressiveness, TML has a number ofsignificant limitations. Chief among these is that it does not explicitly handle existence uncertainty, meaning that all possible worlds contain the same objects and relations. This leads to a number of conceptual problems, such as models that must contain meaningless combinations of attributes (e.g.,horses with wheels). Here we propose a new formalism, tractable probabilistic knowledge bases (TPKBs), that overcomes this problem. Like TML, TPKBs use probabilistic class and part hierarchies to ensure tractability, but TPKBs have a much cleaner and user-friendly object-oriented syntax and a well-founded semantics for existence uncertainty. TML is greatly complicated by the use of probabilistic theorem proving, an inference procedure that is much more powerful than necessary. In contrast, we introduce an inference procedure specifically designed for TPKBs, which makes them far more transparent and amenable to analysis and implementation. TPKBs subsume TML and therefore essentially all tractable models, including many high-treewidth ones.

In this paper, we investigate the problem of predicting people's professions under social context. Previous work considering clothing information as well as fore/background context preliminarily proves the feasibility of predicting professions. In this paper, we discuss this problem in a more general case --- multiple people in one photo with arbitrary poses, and argue that with appropriately built partial body features, spatial relations, and background context, more appealing results are achieved by a probabilistic model. We conduct experiments on $14$ representative professions with over $7000$ images, and demonstrate the model's superiority with impressive results.

Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when computing conditional probabilities, because the evidence breaks many of the model's symmetries.Recent theoretical results paint a grim picture, showing that conditioning on binary relations is #P-hard, and in the worst case, no lifting can be expected. In this paper, we identify Boolean rank of the evidence as a key parameter in the complexity of conditioning. We contrast the hardness result by showing that conditioning on binary evidence with bounded Boolean rank is efficient. This opens up the possibility of approximating evidence by a low-rank Boolean matrix factorization that maintains the model's symmetries and admits efficient lifted inference.

We consider the problem of building relational probabilistic models with an underlying ontology that defines the classes and properties used in the model. Properties in the ontology form random variables when applied to individuals. When an individual is not in the domain of a property, the corresponding random variable is undefined. If we are uncertain about the types of individuals, we may be uncertain about whether random variables are defined. We discuss how to extend a recent result on reasoning with potentially undefined random variables to the relational case. Object properties may have classes of individuals as their ranges, giving rise to random variables whose ranges vary with populations. We identify and discuss some of the issues that arise when constructing relational probabilistic models using the vocabulary and constraints from an ontology, and we outline possible solutions to certain problems.

By handling whole sets of indistinguishable objects together, lifted belief propagation approaches have rendered large, previously intractable, probabilistic inference problems quickly solvable. In this paper, we show that Kumar and Zilberstein's likelihood maximization (LM) approach to MAP inference is liftable, too, and actually provides additional structure for optimization. Specifically, it has been recognized that some pseudo marginals may converge quickly, turning intuitively into pseudo evidence. This additional evidence typically changes the structure of the lifted network: it may expand or reduce it. The current lifted network, however, can be viewed as an upper bound on the size of the lifted network required to finish likelihood maximization. Consequently, we re-lift the network only if the pseudo evidence yields a reduced network, which can efficiently be computed on the current lifted network. Our experimental results on Ising models, image segmentation and relational entity resolution demonstrate that this bootstrapped LM via "reduce and re-lift" finds MAP assignments comparable to those found by the original LM approach, but in a fraction of the time.

The Rao-Blackwell theorem is utilized to analyze and improve the scalability of inference in large probabilistic models that exhibit symmetries. A novel marginal density estimator is introduced and shown both analytically and empirically to outperform standard estimators by several orders of magnitude. The developed theory and algorithms apply to a broad class of probabilistic models including statistical relational models considered not susceptible to lifted probabilistic inference.

This paper is devoted to fair optimization in Multiobjective Markov Decision Processes (MOMDPs). A MOMDP is an extension of the MDP model for planning under uncertainty while trying to optimize several reward functions simultaneously. This applies to multiagent problems when rewards define individual utility functions, or in multicriteria problems when rewards refer to different features. In this setting, we study the determination of policies leading to Lorenz-non-dominated tradeoffs. Lorenz dominance is a refinement of Pareto dominance that was introduced in Social Choice for the measurement of inequalities. In this paper, we introduce methods to efficiently approximate the sets of Lorenz-non-dominated solutions of infinite-horizon, discounted MOMDPs. The approximations are polynomial-sized subsets of those solutions.

Statistical relational learning (SRL) augments probabilistic models with relational representations and facilitates reasoning over sets of objects. When learning the probabilistic parameters for SRL models, however, one often resorts to reasoning over individual objects. To address this challenge, we compile a Markov logic network into a compact and efficient first-order data structure and use weighted first-order model counting to exactly optimize the likelihood of the parameters in a lifted manner. By exploiting the relational structure in the model, it is possible to learn more accurate parameters and dramatically improve the run time of the likelihood calculation. This allows us to calculate the exact likelihood for models where previously only approximate inference was feasible. Results on real-world data sets show that this approach learns more accurate models.