Latent Similarity Identifies Important Functional Connections for Phenotype Prediction

Objective: Endophenotypes such as brain age and fluid intelligence are important biomarkers of disease status. However, brain imaging studies to identify these biomarkers often encounter limited numbers of subjects and high dimensional imaging features, hindering reproducibility. Therefore, we develop an interpretable, multivariate classification/regression algorithm, called Latent Similarity (LatSim), suitable for small sample size, high feature dimension datasets. Methods: LatSim combines metric learning with a kernel similarity function and softmax aggregation to identify task-related similarities between subjects. Inter-subject similarity is utilized to improve performance on three prediction tasks using multi-paradigm fMRI data. A greedy selection algorithm, made possible by LatSim's computational efficiency, is developed as an interpretability method. Results: LatSim achieved significantly higher predictive accuracy at small sample sizes on the Philadelphia Neurodevelopmental Cohort (PNC) dataset. Connections identified by LatSim gave superior discriminative power compared to those identified by other methods. We identified 4 functional brain networks enriched in connections for predicting brain age, sex, and intelligence. Conclusion: We find that most information for a predictive task comes from only a few (1-5) connections. Additionally, we find that the default mode network is over-represented in the top connections of all predictive tasks. Significance: We propose a novel algorithm for small sample, high feature dimension datasets and use it to identify connections in task fMRI data. Our work should lead to new insights in both algorithm design and neuroscience research. Code and demo are available at https://github.com/aorliche/LatentSimilarity/.Comment: 12 page

Escaping the Curse of Dimensionality in Similarity Learning: Efficient Frank-Wolfe Algorithm and Generalization Bounds

Similarity and metric learning provides a principled approach to construct a task-specific similarity from weakly supervised data. However, these methods are subject to the curse of dimensionality: as the number of features grows large, poor generalization is to be expected and training becomes intractable due to high computational and memory costs. In this paper, we propose a similarity learning method that can efficiently deal with high-dimensional sparse data. This is achieved through a parameterization of similarity functions by convex combinations of sparse rank-one matrices, together with the use of a greedy approximate Frank-Wolfe algorithm which provides an efficient way to control the number of active features. We show that the convergence rate of the algorithm, as well as its time and memory complexity, are independent of the data dimension. We further provide a theoretical justification of our modeling choices through an analysis of the generalization error, which depends logarithmically on the sparsity of the solution rather than on the number of features. Our experiments on datasets with up to one million features demonstrate the ability of our approach to generalize well despite the high dimensionality as well as its superiority compared to several competing methods