Gromov-Wasserstein distance has many applications in machine learning due to its ability to compare measures across metric spaces and its invariance to isometric transformations. However, in certain applications, this invariant property can be too flexible, thus undesirable. Moreover, the Gromov-Wasserstein distance solely considers pairwise sample similarities in input datasets, disregarding the raw feature representations. We propose a new optimal transport formulation, called Augmented Gromov-Wasserstein (AGW), that allows for some control over the level of rigidity to transformations. It also incorporates feature alignments, enabling us to better leverage prior knowledge on the input data for improved performance. We first present theoretical insights into the proposed method. We then demonstrate its usefulness for single-cell multi-omic alignment tasks and heterogeneous domain adaptation in machine learning.

Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this approach leads to better alignments and generalizes both OT and Gromov-Wasserstein distances, we provide a theoretical result showing that it is sensitive to outliers that are omnipresent in real-world data. This prompts us to propose unbalanced COOT for which we provably show its robustness to noise in the compared datasets. To the best of our knowledge, this is the first such result for OT methods in incomparable spaces. With this result in hand, we provide empirical evidence of this robustness for the challenging tasks of heterogeneous domain adaptation with and without varying proportions of classes and simultaneous alignment of samples and features across two single-cell measurements.

MOTIVATION: Genome-wide association studies (GWAS) have discovered thousands of significant genetic effects on disease phenotypes. By considering gene expression as the intermediary between genotype and disease phenotype, expression quantitative trait loci studies have interpreted many of these variants by their regulatory effects on gene expression. However, there remains a considerable gap between genotype-to-gene expression association and genotype-to-gene expression prediction. Accurate prediction of gene expression enables gene-based association studies to be performed post hoc for existing GWAS, reduces multiple testing burden, and can prioritize genes for subsequent experimental investigation. RESULTS: In this work, we develop gene expression prediction methods that relax the independence and additivity assumptions between genetic markers. First, we consider gene expression prediction from a regression perspective and develop the HAPLEXR algorithm which combines haplotype clusterings with allelic dosages. Second, we introduce the new gene expression classification problem, which focuses on identifying expression groups rather than continuous measurements; we formalize the selection of an appropriate number of expression groups using the principle of maximum entropy. Third, we develop the HAPLEXD algorithm that models haplotype sharing with a modified suffix tree data structure and computes expression groups by spectral clustering. In both models, we penalize model complexity by prioritizing genetic clusters that indicate significant effects on expression. We compare HAPLEXR and HAPLEXD with three state-of-the-art expression prediction methods and two novel logistic regression approaches across five GTEx v8 tissues. HAPLEXD exhibits significantly higher classification accuracy overall; HAPLEXR shows higher prediction accuracy on approximately half of the genes tested and the largest number of best predicted genes (r2>0.1) among all methods. We show that variant and haplotype features selected by HAPLEXR are smaller in size than competing methods (and thus more interpretable) and are significantly enriched in functional annotations related to gene regulation. These results demonstrate the importance of explicitly modeling non-dosage dependent and intragenic epistatic effects when predicting expression. AVAILABILITY AND IMPLEMENTATION: Source code and binaries are freely available at https://github.com/rapturous/HAPLEX. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Work-in-Progress. “I felt so dumb, and it's not fair that I cannot grasp this information to save my life, and other people can with no problem.” Why do some students feel empowered in the classroom, and feel they have control over their own learning, while others do not? Our qualitative investigation is a part of a larger mixed-methods study about students' situational motivations in introductory STEM courses. We used grounded theory to analyze students' responses to surveys about emotion, course relevance, and motivation. We investigated two emergent phenomena we called “internalization” and “externalization.” Our definitions of these are based on a student's perception of who or what influences the outcomes of their activities: the students themselves, or external factors such as the instructor, peers, or the educational system as a whole. Our findings indicate that (1) internalization correlates with cognitive autonomy, students' perception of course content having high personal relevance, and group projects in project-based learning environments; and (2) externalization correlates with lecture-based environments and students' perceptions of lack of personal relevance in the course content. Our analyses suggest that project-based learning environments may serve to empower students, but only when course content is found to be relevant.