Induction of Interpretable Possibilistic Logic Theories from Relational Data

The field of Statistical Relational Learning (SRL) is concerned with learning probabilistic models from relational data. Learned SRL models are typically represented using some kind of weighted logical formulas, which make them considerably more interpretable than those obtained by e.g. neural networks. In practice, however, these models are often still difficult to interpret correctly, as they can contain many formulas that interact in non-trivial ways and weights do not always have an intuitive meaning. To address this, we propose a new SRL method which uses possibilistic logic to encode relational models. Learned models are then essentially stratified classical theories, which explicitly encode what can be derived with a given level of certainty. Compared to Markov Logic Networks (MLNs), our method is faster and produces considerably more interpretable models.Comment: Longer version of a paper appearing in IJCAI 201

kLog: A Language for Logical and Relational Learning with Kernels

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

Coarse-to-Fine Lifted MAP Inference in Computer Vision

There is a vast body of theoretical research on lifted inference in probabilistic graphical models (PGMs). However, few demonstrations exist where lifting is applied in conjunction with top of the line applied algorithms. We pursue the applicability of lifted inference for computer vision (CV), with the insight that a globally optimal (MAP) labeling will likely have the same label for two symmetric pixels. The success of our approach lies in efficiently handling a distinct unary potential on every node (pixel), typical of CV applications. This allows us to lift the large class of algorithms that model a CV problem via PGM inference. We propose a generic template for coarse-to-fine (C2F) inference in CV, which progressively refines an initial coarsely lifted PGM for varying quality-time trade-offs. We demonstrate the performance of C2F inference by developing lifted versions of two near state-of-the-art CV algorithms for stereo vision and interactive image segmentation. We find that, against flat algorithms, the lifted versions have a much superior anytime performance, without any loss in final solution quality.Comment: Published in IJCAI 201