We consider semi-supervised binary classification for applications in which data points are naturally grouped (e.g., survey responses grouped by state) and the labeled data is biased (e.g., survey respondents are not representative of the population). The groups overlap in the feature space and consequently the input-output patterns are related across the groups. To model the inherent structure in such data, we assume the partition-projected class-conditional invariance across groups, defined in terms of the group-agnostic feature space. We demonstrate that under this assumption, the group carries additional information about the class, over the group-agnostic features, with provably improved area under the ROC curve. Further assuming invariance of partition-projected class-conditional distributions across both labeled and unlabeled data, we derive a semi-supervised algorithm that explicitly leverages the structure to learn an optimal, group-aware, probability-calibrated classifier, despite the bias in the labeled data. Experiments on synthetic and real data demonstrate the efficacy of our algorithm over suitable baselines and ablative models, spanning standard supervised and semi-supervised learning approaches, with and without incorporating the group directly as a feature.

MOTIVATION: Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins and drugs) and edges represent relational ties between these objects (binds-to, interacts-with and regulates). This approach has been highly successful owing to the theory, methodology and software that support analysis and learning on graphs. Graphs, however, suffer from information loss when modeling physical systems due to their inability to accurately represent multiobject relationships. Hypergraphs, a generalization of graphs, provide a framework to mitigate information loss and unify disparate graph-based methodologies. RESULTS: We present a hypergraph-based approach for modeling biological systems and formulate vertex classification, edge classification and link prediction problems on (hyper)graphs as instances of vertex classification on (extended, dual) hypergraphs. We then introduce a novel kernel method on vertex- and edge-labeled (colored) hypergraphs for analysis and learning. The method is based on exact and inexact (via hypergraph edit distances) enumeration of hypergraphlets; i.e. small hypergraphs rooted at a vertex of interest. We empirically evaluate this method on fifteen biological networks and show its potential use in a positive-unlabeled setting to estimate the interactome sizes in various species. AVAILABILITY AND IMPLEMENTATION: https://github.com/jlugomar/hypergraphlet-kernels. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Estimating class proportions has emerged as an important direction in positive-unlabeled learning. Well-estimated class priors are key to accurate approximation of posterior distributions and are necessary for the recovery of true classification performance. While significant progress has been made in the past decade, there remains a need for accurate strategies that scale to big data. Motivated by this need, we propose an intuitive and fast nonparametric algorithm to estimate class proportions. Unlike any of the previous methods, our algorithm uses a sampling strategy to repeatedly (1) draw an example from the set of positives, (2) record the minimum distance to any of the unlabeled examples, and (3) remove the nearest unlabeled example. We show that the point of sharp increase in the recorded distances corresponds to the desired proportion of positives in the unlabeled set and train a deep neural network to identify that point. Our distance-based algorithm is evaluated on forty datasets and compared to all currently available methods. We provide evidence that this new approach results in the most accurate performance and can be readily used on large datasets.