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

Learning with Graphs using Kernels from Propagated Information

Traditional machine learning approaches are designed to learn from independent vector-valued data points. The assumption that instances are independent, however, is not always true. On the contrary, there are numerous domains where data points are cross-linked, for example social networks, where persons are linked by friendship relations. These relations among data points make traditional machine learning diffcult and often insuffcient. Furthermore, data points themselves can have complex structure, for example molecules or proteins constructed from various bindings of different atoms. Networked and structured data are naturally represented by graphs, and for learning we aimto exploit their structure to improve upon non-graph-based methods. However, graphs encountered in real-world applications often come with rich additional information. This naturally implies many challenges for representation and learning: node information is likely to be incomplete leading to partially labeled graphs, information can be aggregated from multiple sources and can therefore be uncertain, or additional information on nodes and edges can be derived from complex sensor measurements, thus being naturally continuous. Although learning with graphs is an active research area, learning with structured data, substantially modeling structural similarities of graphs, mostly assumes fully labeled graphs of reasonable sizes with discrete and certain node and edge information, and learning with networked data, naturally dealing with missing information and huge graphs, mostly assumes homophily and forgets about structural similarity. To close these gaps, we present a novel paradigm for learning with graphs, that exploits the intermediate results of iterative information propagation schemes on graphs. Originally developed for within-network relational and semi-supervised learning, these propagation schemes have two desirable properties: they capture structural information and they can naturally adapt to the aforementioned issues of real-world graph data. Additionally, information propagation can be efficiently realized by random walks leading to fast, flexible, and scalable feature and kernel computations. Further, by considering intermediate random walk distributions, we can model structural similarity for learning with structured and networked data. We develop several approaches based on this paradigm. In particular, we introduce propagation kernels for learning on the graph level and coinciding walk kernels and Markov logic sets for learning on the node level. Finally, we present two application domains where kernels from propagated information successfully tackle real-world problems

Multiple Instance Learning: A Survey of Problem Characteristics and Applications

Multiple instance learning (MIL) is a form of weakly supervised learning where training instances are arranged in sets, called bags, and a label is provided for the entire bag. This formulation is gaining interest because it naturally fits various problems and allows to leverage weakly labeled data. Consequently, it has been used in diverse application fields such as computer vision and document classification. However, learning from bags raises important challenges that are unique to MIL. This paper provides a comprehensive survey of the characteristics which define and differentiate the types of MIL problems. Until now, these problem characteristics have not been formally identified and described. As a result, the variations in performance of MIL algorithms from one data set to another are difficult to explain. In this paper, MIL problem characteristics are grouped into four broad categories: the composition of the bags, the types of data distribution, the ambiguity of instance labels, and the task to be performed. Methods specialized to address each category are reviewed. Then, the extent to which these characteristics manifest themselves in key MIL application areas are described. Finally, experiments are conducted to compare the performance of 16 state-of-the-art MIL methods on selected problem characteristics. This paper provides insight on how the problem characteristics affect MIL algorithms, recommendations for future benchmarking and promising avenues for research

Graph Neural Networks for Graphs with Heterophily: A Survey

Recent years have witnessed fast developments of graph neural networks (GNNs) that have benefited myriads of graph analytic tasks and applications. In general, most GNNs depend on the homophily assumption that nodes belonging to the same class are more likely to be connected. However, as a ubiquitous graph property in numerous real-world scenarios, heterophily, i.e., nodes with different labels tend to be linked, significantly limits the performance of tailor-made homophilic GNNs. Hence, GNNs for heterophilic graphs are gaining increasing research attention to enhance graph learning with heterophily. In this paper, we provide a comprehensive review of GNNs for heterophilic graphs. Specifically, we propose a systematic taxonomy that essentially governs existing heterophilic GNN models, along with a general summary and detailed analysis. Furthermore, we discuss the correlation between graph heterophily and various graph research domains, aiming to facilitate the development of more effective GNNs across a spectrum of practical applications and learning tasks in the graph research community. In the end, we point out the potential directions to advance and stimulate more future research and applications on heterophilic graph learning with GNNs.Comment: 22 page