We introduce kLog, a novel approach to statistical relational learning. Unlike standard approaches, kLog does not represent a probability distribution directly. It is rather a language to perform kernel-based learning on expressive logical and relational representations. kLog allows users to specify learning problems declaratively. It builds on simple but powerful concepts: learning from interpretations, entity/relationship data modeling, logic programming, and deductive databases. Access by the kernel to the rich representation is mediated by a technique we call graphicalization: the relational representation is first transformed into a graph --- in particular, a grounded entity/relationship diagram. Subsequently, a choice of graph kernel defines the feature space. kLog supports mixed numerical and symbolic data, as well as background knowledge in the form of Prolog or Datalog programs as in inductive logic programming systems. The kLog framework can be applied to tackle the same range of tasks that has made statistical relational learning so popular, including classification, regression, multitask learning, and collective classification. We also report about empirical comparisons, showing that kLog can be either more accurate, or much faster at the same level of accuracy, than Tilde and Alchemy. kLog is GPLv3 licensed and is available at http://klog.dinfo.unifi.it along with tutorials.

We introduce a logic for reasoning about evidence, that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete axiomatization for the logic, and consider the complexity of the decision problem. Although the reasoning in the logic is mainly propositional, we allow variables representing numbers and quantification over them. This expressive power seems necessary to capture important properties of evidence.

We consider how an agent should update her uncertainty when it is represented by a set P of probability distributions and the agent observes that a random variable X takes on value x, given that the agent makes decisions using the minimax criterion, perhaps the best-studied and most commonly-used criterion in the literature. We adopt a game-theoretic framework, where the agent plays against a bookie, who chooses some distribution from P. We consider two reasonable games that differ in what the bookie knows when he makes his choice. Anomalies that have been observed before, like time inconsistency, can be understood as arising because different games are being played, against bookies with different information. We characterize the important special cases in which the optimal decision rules according to the minimax criterion amount to either conditioning or simply ignoring the information. Finally, we consider the relationship between conditioning and calibration when uncertainty is described by sets of probabilities.

It is commonly-accepted wisdom that more information is better, and that information should never be ignored. Here we argue, using both a Bayesian and a non-Bayesian analysis, that in some situations you are better off ignoring information if your uncertainty is represented by a set of probability measures. These include situations in which the information is relevant for the prediction task at hand. In the non-Bayesian analysis, we show how ignoring information avoids dilation, the phenomenon that additional pieces of information sometimes lead to an increase in uncertainty. In the Bayesian analysis, we show that for small sample sizes and certain prediction tasks, the Bayesian posterior based on a noninformative prior yields worse predictions than simply ignoring the given information.

A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining algebraic conditional plausibility measures. It is shown that the technology of Bayesian networks can be applied to algebraic conditional plausibility measures.

In mixture model-based clustering applications, it is common to fit several models from a family and report clustering results from only the `best' one. In such circumstances, selection of this best model is achieved using a model selection criterion, most often the Bayesian information criterion. Rather than throw away all but the best model, we average multiple models that are in some sense close to the best one, thereby producing a weighted average of clustering results. Two (weighted) averaging approaches are considered: averaging the component membership probabilities and averaging models. In both cases, Occam's window is used to determine closeness to the best model and weights are computed within a Bayesian model averaging paradigm. In some cases, we need to merge components before averaging; we introduce a method for merging mixture components based on the adjusted Rand index. The effectiveness of our model-based clustering averaging approaches is illustrated using a family of Gaussian mixture models on real and simulated data.

Learning Structured Outputs from Partial Labels using Forest Ensemble Truyen Tran, Dinh Phung, Svetha V enkatesh Centre for Pattern Recognition and Data Analytics Deakin University, Australia Abstract Learning structured outputs with general structures is computationally challenging, except for tree-structured models. Thus we propose an efficient boosting-based algorithm AdaBoost.MRF for this task. The idea is based on the realization that a graph is a superimposition of trees. Different from most existing work, our algorithm can handle partial labelling, and thus is particularly attractive in practice where reliable labels are often sparsely observed. In addition, our method works exclusively on trees and thus is guaranteed to converge. We apply the AdaBoost.MRF algorithm to an indoor video surveillance scenario, where activities are modelled at multiple levels. 1 Introduction There has been a growing research interest in developing probabilistic temporal graphical models for recognising human activities from sensory data. In this paper we address an important aspect of the problem in that there are multiple levels of abstraction, that is, an activity is often composed of several sub-activities. A popular approach to deal with such a hierarchical nature is to build a cascaded model: each level is modelled separately, and the output of the lower levels is subsequently used as the input for the upper levels [20]. This approach is sub-optimal because the information at the higher level is often very discriminative to infer about the lower levels, but it is not modelled. Moreover, the layered approach often suffers from the so-called cascading error problem, as the error introduced from the lower level will propagate to higher tasks. A better and more holistic approach is to build a joint representation at all layers. Emerging methods include generative/directed models such as abstract hidden Markov models (AH-MMs) [4], hierarchical HMMs [19], dynamic Bayesian networks [10], and their discriminative/undirected counterparts such as hierarchical conditional random field (HCRF) [17], and dynamic CRF (DCRF) [28].

How to forecast next year's portfolio-wide credit default rate based on last year's default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple) case of a finite mixture model where the mixture components are fixed and only the weights of the components are estimated. The optimum weights provide a forecast of next year's portfolio-wide default rate. We point out that the maximum-likelihood (ML) approach to fitting the mixture distribution not only gives an optimum but even an exact fit if we allow the mixture components to vary but keep their density ratio fix. From this observation we can conclude that the standard default rate forecast based on last year's conditional default rates will always be located between last year's portfolio-wide default rate and the ML forecast for next year. As an application example, then cost quantification is discussed. We also discuss how the mixture model based estimation methods can be used to forecast total loss. This involves the reinterpretation of an individual classification problem as a collective quantification problem.

Markov Logic Networks (MLNs) provide a unifying framework that incorporates first-order logic and probability. However, learning the structure of MLNs is a computationally hard task due to the large search space and the intractable clause evaluation. In this paper, we propose a random walk-based approach to learn MLN structure in a scalable manner. It uses the interactions existing among the objects to constrain the search space of candidate clauses. Specifically, we obtain representative subset of simple paths by sampling from all sequences of distinct objects. We then transform each sampled path into possible ground atoms, and use them to form clauses. Based on the resulting ground network, we finally attach a set of weights to the clauses by optimizing l 1 -constrained conditional likelihood. The experimental results demonstrate that our approach performs favorably compared to previous approaches.

Using Markov logic to integrate logical and distributional information in natural-language semantics results in complex inference problems involving long, complicated formulae. Current inference methods for Markov logic are ineffective on such problems. To address this problem, we propose a new inference algorithm based on SampleSearch that computes probabilities of complete formulae rather than ground atoms. We also introduce a modified closed-world assumption that significantly reduces the size of the ground network, thereby making inference feasible. Our approach is evaluated on the recognizing textual entailment task, and experiments demonstrate its dramatic impact on the efficiency of inference.