On the Complexity and Approximation of Binary Evidence in Lifted Inference

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. The reason is that conditioning on evidence breaks many of the model's symmetries, which can preempt standard lifting techniques. Recent theoretical results show, for example, that conditioning on evidence which corresponds to binary relations is #P-hard, suggesting that no lifting is to be expected in the worst case. In this paper, we balance this negative result by identifying the Boolean rank of the evidence as a key parameter for characterizing the complexity of conditioning in lifted inference. In particular, we show 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, which we investigate both theoretically and empirically.Comment: To appear in Advances in Neural Information Processing Systems 26 (NIPS), Lake Tahoe, USA, December 201

Discovering Coherent Biclusters from Gene Expression Data Using Zero-Suppressed Binary Decision Diagrams

The biclustering method can be a very useful analysis tool when some genes have multiple functions and experimental conditions are diverse in gene expression measurement. This is because the biclustering approach, in contrast to the conventional clustering techniques, focuses on finding a subset of the genes and a subset of the experimental conditions that together exhibit coherent behavior. However, the biclustering problem is inherently intractable, and it is often computationally costly to find biclusters with high levels of coherence. In this work, we propose a novel biclustering algorithm that exploits the zero-suppressed binary decision diagrams (ZBDDs) data structure to cope with the computational challenges. Our method can find all biclusters that satisfy specific input conditions, and it is scalable to practical gene expression data. We also present experimental results confirming the effectiveness of our approach

Multi-layered model of individual HIV infection progression and mechanisms of phenotypical expression

Cite as: Perrin, Dimitri (2008) Multi-layered model of individual HIV infection progression and mechanisms of phenotypical expression. PhD thesis, Dublin City University

Compositional Mining of Multi-Relational Biological Datasets

High-throughput biological screens are yielding ever-growing streams of information about multiple aspects of cellular activity. As more and more categories of datasets come online, there is a corresponding multitude of ways in which inferences can be chained across them, motivating the need for compositional data mining algorithms. In this paper, we argue that such compositional data mining can be effectively realized by functionally cascading redescription mining and biclustering algorithms as primitives. Both these primitives mirror shifts of vocabulary that can be composed in arbitrary ways to create rich chains of inferences. Given a relational database and its schema, we show how the schema can be automatically compiled into a compositional data mining program, and how different domains in the schema can be related through logical sequences of biclustering and redescription invocations. This feature allows us to rapidly prototype new data mining applications, yielding greater understanding of scientific datasets. We describe two applications of compositional data mining: (i) matching terms across categories of the Gene Ontology and (ii) understanding the molecular mechanisms underlying stress response in human cells