We propose Information Lattice Learning (ILL) as a general framework to learn rules of a signal (e.g., an image or a probability distribution). In our definition, a rule is a coarsened signal used to help us gain one interpretable insight about the original signal. To make full sense of what might govern the signal’s intrinsic structure, we seek multiple disentangled rules arranged in a hierarchy, called a lattice. Compared to representation/rule-learning models optimized for a specific task (e.g., classification), ILL focuses on explainability: it is designed to mimic human experiential learning and discover rules akin to those humans can distill and comprehend. This paper details the math and algorithms of ILL, and illustrates how it addresses the fundamental question “what makes X an X” by creating rule-based explanations designed to help humans understand. Our focus is on explaining X rather than (re)generating it. We present applications in knowledge discovery, using ILL to distill music theory from scores and chemical laws from molecules and further revealing connections between them. We show ILL’s efficacy and interpretability on benchmarks and assessments, as well as a demonstration of ILL-enhanced classifiers achieving human-level digit recognition using only one or a few MNIST training examples (1–10 per class).

Inspired by recent interests of developing machine learning and data mining algorithms on hypergraphs, we investigate in this paper the semi-supervised learning algorithm of propagating ”soft labels” (e.g. probability distributions, class membership scores) over hypergraphs, by means of optimal transportation. Borrowing insights from Wasserstein propagation on graphs [Solomon et al. 2014], we re-formulate the label propagation procedure as a message-passing algorithm, which renders itself naturally to a generalization applicable to hypergraphs through Wasserstein barycenters. Furthermore, in a PAC learning framework, we provide generalization error bounds for propagating one-dimensional distributions on graphs and hypergraphs using 2-Wasserstein distance, by establishing the algorithmic stability of the proposed semisupervised learning algorithm. These theoretical results also shed new lights upon deeper understandings of the Wasserstein propagation on graphs.

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We consider the problem of Collaborative Permutation Recovery, i.e. recovering multiple permutations over objects (e.g. preference rankings over different options) from limited pairwise comparisons. We tackle both the problem of how to recover multiple related permutations from limited observations, and the active learning problem of which pairwise comparison queries to ask so as to allow better recovery. There has been much work on recovering single permutations from pairwise comparisons, but we show that considering several related permutations jointly we can leverage their relatedness so as to reduce the number of comparisons needed compared to reconstructing each permutation separately. To do so, we take a collaborative filtering / matrix completion approach and use a trace-norm or max-norm regularized matrix learning model. Our approach can also be seen as a collaborative learning version of Jamieson and Nowak's recent work on constrained permutation recovery, where instead of basing the recovery on known features, we learn the best features de novo.

Synonymous relationships among biomedical terms are extensively annotated within specialized terminologies, implying that synonymy is important for practical computational applications within this field. It remains unclear, however, whether text mining actually benefits from documented synonymy and whether existing biomedical thesauri provide adequate coverage of these linguistic relationships. In this study, we examine the impact and extent of undocumented synonymy within a very large compendium of biomedical thesauri. First, we demonstrate that missing synonymy has a significant negative impact on named entity normalization, an important problem within the field of biomedical text mining. To estimate the amount synonymy currently missing from thesauri, we develop a probabilistic model for the construction of synonym terminologies that is capable of handling a wide range of potential biases, and we evaluate its performance using the broader domain of near-synonymy among general English words. Our model predicts that over 90% of these relationships are currently undocumented, a result that we support experimentally through "crowd-sourcing." Finally, we apply our model to biomedical terminologies and predict that they are missing the vast majority (>90%) of the synonymous relationships they intend to document. Overall, our results expose the dramatic incompleteness of current biomedical thesauri and suggest the need for "next-generation," high-coverage lexical terminologies.

Computational models in biomedicine rely on biological and clinical assumptions. The selection of these assumptions contributes substantially to modeling success or failure. Assumptions used by experts at the cutting edge of research, however, are rarely explicitly described in scientific publications. One can directly collect and assess some of these assumptions through interviews and surveys. Here we investigate diversity in expert views about a complex biological phenomenon, the process of cancer metastasis. We harvested individual viewpoints from 28 experts in clinical and molecular aspects of cancer metastasis and summarized them computationally. While experts predominantly agreed on the definition of individual steps involved in metastasis, no two expert scenarios for metastasis were identical. We computed the probability that any two experts would disagree on k or fewer metastatic stages and found that any two randomly selected experts are likely to disagree about several assumptions. Considering the probability that two or more of these experts review an article or a proposal about metastatic cascades, the probability that they will disagree with elements of a proposed model approaches 1. This diversity of conceptions has clear consequences for advance and deadlock in the field. We suggest that strong, incompatible views are common in biomedicine but largely invisible to biomedical experts themselves. We built a formal Markov model of metastasis to encapsulate expert convergence and divergence regarding the entire sequence of metastatic stages. This model revealed stages of greatest disagreement, including the points at which cancer enters and leaves the bloodstream. The model provides a formal probabilistic hypothesis against which researchers can evaluate data on the process of metastasis. This would enable subsequent improvement of the model through Bayesian probabilistic update. Practically, we propose that model assumptions and hunches be harvested systematically and made available for modelers and scientists.

The use of structured knowledge representations-ontologies and terminologies-has become standard in biomedicine. Definitions of ontologies vary widely, as do the values and philosophies that underlie them. In seeking to make these views explicit, we conducted and summarized interviews with a dozen leading ontologists. Their views clustered into three broad perspectives that we summarize as mathematics, computer code, and Esperanto. Ontology as mathematics puts the ultimate premium on rigor and logic, symmetry and consistency of representation across scientific subfields, and the inclusion of only established, non-contradictory knowledge. Ontology as computer code focuses on utility and cultivates diversity, fitting ontologies to their purpose. Like computer languages C++, Prolog, and HTML, the code perspective holds that diverse applications warrant custom designed ontologies. Ontology as Esperanto focuses on facilitating cross-disciplinary communication, knowledge cross-referencing, and computation across datasets from diverse communities. We show how these views align with classical divides in science and suggest how a synthesis of their concerns could strengthen the next generation of biomedical ontologies.

A scientific ontology is a formal representation of knowledge within a domain, typically including central concepts, their properties, and relations. With the rise of computers and high-throughput data collection, ontologies have become essential to data mining and sharing across communities in the biomedical sciences. Powerful approaches exist for testing the internal consistency of an ontology, but not for assessing the fidelity of its domain representation. We introduce a family of metrics that describe the breadth and depth with which an ontology represents its knowledge domain. We then test these metrics using (1) four of the most common medical ontologies with respect to a corpus of medical documents and (2) seven of the most popular English thesauri with respect to three corpora that sample language from medicine, news, and novels. Here we show that our approach captures the quality of ontological representation and guides efforts to narrow the breach between ontology and collective discourse within a domain. Our results also demonstrate key features of medical ontologies, English thesauri, and discourse from different domains. Medical ontologies have a small intersection, as do English thesauri. Moreover, dialects characteristic of distinct domains vary strikingly as many of the same words are used quite differently in medicine, news, and novels. As ontologies are intended to mirror the state of knowledge, our methods to tighten the fit between ontology and domain will increase their relevance for new areas of biomedical science and improve the accuracy and power of inferences computed across them.