We study semi-supervised learning when the data consists of multiple intersecting manifolds. We give a finite sample analysis to quantify the potential gain of using unlabeled data in this multi-manifold setting. We then propose a semi-supervised learning algorithm that separates different manifolds into decision sets, and performs supervised learning within each set. Our algorithm involves a novel application of Hellinger distance and size-constrained spectral clustering. Experiments demonstrate the benefit of our multimanifold semi-supervised learning approach.

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Users of topic modeling methods often have knowledge about the composition of words that should have high or low probability in various topics. We incorporate such domain knowledge using a novel Dirichlet Forest prior in a Latent Dirichlet Allocation framework. The prior is a mixture of Dirichlet tree distributions with special structures. We present its construction, and inference via collapsed Gibbs sampling. Experiments on synthetic and real datasets demonstrate our model’s ability to follow and generalize beyond user-specified domain knowledge.

Kernel conditional random fields (KCRFs) are introduced as a framework for discriminative modeling of graph-structured data. A representer theorem for conditional graphical models is given which shows how kernel conditional random fields arise from risk minimization procedures defined using Mercer kernels on labeled graphs. A procedure for greedily selecting cliques in the dual representation is then proposed, which allows sparse representations. By incorporating kernels and implicit feature spaces into conditional graphical models, the framework enables semi-supervised learning algorithms for structured data through the use of graph kernels. The framework and clique selection methods are demonstrated in synthetic data experiments, and are also applied to the problem of protein secondary structure prediction.

Background Prior text analysis of R01 critiques suggested that female applicants may be disadvantaged in NIH peer review, particularly for R01 renewals. NIH altered its review format in 2009. The authors examined R01 critiques and scoring in the new format for differences due to principal investigator (PI) sex. Method The authors analyzed 739 critiques—268 from 88 unfunded and 471 from 153 funded applications for grants awarded to 125 PIs (M = 76, 61% F = 49, 39%) at the University of Wisconsin-Madison between 2010 and 2014. The authors used 7 word categories for text analysis: ability, achievement, agentic, negative evaluation, positive evaluation, research, and standout adjectives. The authors used regression models to compare priority and criteria scores, and results from text analysis for differences due to PI sex and whether the application was for a new (Type 1) or renewal (Type 2) R01. Results Approach scores predicted priority scores for all PIs’ applications (P<.001); but scores and critiques differed significantly for male and female PIs’ Type 2 applications. Reviewers assigned significantly worse priority, approach, and significance scores to female than male PIs’ Type 2 applications, despite using standout adjectives (e.g., “outstanding,” “excellent”) and making references to ability in more of their critiques (P<.05 for all comparisons). Conclusions The authors’ analyses suggest that subtle gender bias may continue to operate in the post-2009 NIH review format in ways that could lead reviewers to implicitly hold male and female applicants to different standards of evaluation, particularly for R01 renewals.