Identifying accurate biomarkers of cognitive decline is essential for advancing early diagnosis and prevention therapies in Alzheimer’s Disease. The Alzheimer’s Disease DREAM Challenge was designed as a computational crowdsourced project to benchmark the current state-of-the-art in predicting cognitive outcomes in Alzheimer’s Disease based on high-dimensional, publicly available genetic and structural imaging data. This meta-analysis failed to identify a meaningful predictor developed from either data modality, suggesting that alternate approaches should be considered for to prediction of cognitive performance.

Convex clustering is a promising new approach to the classical problem of clustering, combining strong performance in empirical studies with rigorous theoretical foundations. Despite these advantages, convex clustering has not been widely adopted, due to its computationally intensive nature and its lack of compelling visualizations. To address these impediments, we introduce Algorithmic Regularization, an innovative technique for obtaining high-quality estimates of regularization paths using an iterative one-step approximation scheme. We justify our approach with a novel theoretical result, guaranteeing global convergence of the approximate path to the exact solution under easily-checked non-data-dependent assumptions. The application of algorithmic regularization to convex clustering yields the Convex Clustering via Algorithmic Regularization Paths (CARP) algorithm for computing the clustering solution path. On example data sets from genomics and text analysis, CARP delivers over a 100-fold speedup over existing methods, while attaining a finer approximation grid than standard methods. Furthermore, CARP enables improved visualization of clustering solutions: the fine solution grid returned by CARP can be used to construct a convex clusteringbased dendrogram, as well as forming the basis of a dynamic path-wise visualization based on modern web technologies. Our methods are implemented in the open-source R package clustRviz, available at https://github.com/DataSlingers/clustRviz.

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Even though there is a clear link between Alzheimer’s Disease (AD) related neuropathology and cognitive decline, numerous studies have observed that healthy cognition can exist in the presence of extensive AD pathology, a phenomenon sometimes called Cognitive Resilience (CR). To better understand and study CR, we develop the Alzheimer’s Disease Cognitive Resilience Score (AD-CR Score), which we define as the difference between the observed and expected cognition given the observed level of AD pathology. Unlike other definitions of CR, our AD-CR Score is a fully non-parametric, stand-alone, individual-level quantification of CR that is derived independently of other factors or proxy variables. Using data from two ongoing, longitudinal cohort studies of aging, the Religious Orders Study (ROS) and the Rush Memory and Aging Project (MAP), we validate our AD-CR Score by showing strong associations with known factors related to CR such as baseline and longitudinal cognition, non AD-related pathology, education, personality, APOE, parkinsonism, depression, and life activities. Even though the proposed AD-CR Score cannot be directly calculated during an individual’s lifetime because it uses postmortem pathology, we also develop a machine learning framework that achieves promising results in terms of predicting whether an individual will have an extremely high or low AD-CR Score using only measures available during the lifetime. Given this, our AD-CR Score can be used for further investigations into mechanisms of CR, and potentially for subject stratification prior to clinical trials of personalized therapies.

Several modern genomic technologies, such as DNA-Methylation arrays, measure spatially registered probes that number in the hundreds of thousands across multiple chromosomes. The measured probes are by themselves less interesting scientifically; instead scientists seek to discover biologically interpretable genomic regions comprised of contiguous groups of probes which may act as biomarkers of disease or serve as a dimension-reducing pre-processing step for downstream analyses. In this paper, we introduce an unsupervised feature learning technique which maps technological units (probes) to biological units (genomic regions) that are common across all subjects. We use ideas from fusion penalties and convex clustering to introduce a method for Spatial Convex Clustering, or SpaCC. Our method is specifically tailored to detecting multi-subject regions of methylation, but we also test our approach on the well-studied problem of detecting segments of copy number variation. We formulate our method as a convex optimization problem, develop a massively parallelizable algorithm to find its solution, and introduce automated approaches for handling missing values and determining tuning parameters. Through simulation studies based on real methylation and copy number variation data, we show that SpaCC exhibits significant performance gains relative to existing methods. Finally, we illustrate SpaCC’s advantages as a pre-processing technique that reduces large-scale genomics data into a smaller number of genomic regions through several cancer epigenetics case studies on subtype discovery, network estimation, and epigenetic-wide association.