Spectral top-down recovery of latent tree models.

Modeling the distribution of high-dimensional data by a latent tree graphical model is a prevalent approach in multiple scientific domains. A common task is to infer the underlying tree structure, given only observations of its terminal nodes. Many algorithms for tree recovery are computationally intensive, which limits their applicability to trees of moderate size. For large trees, a common approach, termed divide-and-conquer, is to recover the tree structure in two steps. First, separately recover the structure of multiple, possibly random subsets of the terminal nodes. Second, merge the resulting subtrees to form a full tree. Here, we develop spectral top-down recovery (STDR), a deterministic divide-and-conquer approach to infer large latent tree models. Unlike previous methods, STDR partitions the terminal nodes in a non random way, based on the Fiedler vector of a suitable Laplacian matrix related to the observed nodes. We prove that under certain conditions, this partitioning is consistent with the tree structure. This, in turn, leads to a significantly simpler merging procedure of the small subtrees. We prove that STDR is statistically consistent and bound the number of samples required to accurately recover the tree with high probability. Using simulated data from several common tree models in phylogenetics, we demonstrate that STDR has a significant advantage in terms of runtime, with improved or similar accuracy.

Germline genetic variants are associated with development of insulin-dependent diabetes in cancer patients treated with immune checkpoint inhibitors.

BACKGROUND: Immune checkpoint inhibitors (ICIs) have dramatically improved survival in patients with cancer but are often accompanied by severe immune-related adverse events (irAEs), which can sometimes be irreversible. Insulin-dependent diabetes is a rare, but life-altering irAE. Our purpose was to determine whether recurrent somatic or germline mutations are observed in patients who develop insulin-dependent diabetes as an irAE. METHODS: We performed RNA and whole exome sequencing on tumors from 13 patients who developed diabetes due to ICI exposure (ICI-induced diabetes mellitus, ICI-DM) compared with control patients who did not develop diabetes. RESULTS: In tumors from ICI-DM patients, we did not find differences in expression of conventional type 1 diabetes autoantigens, but we did observe significant overexpression of ORM1, PLG, and G6PC, all of which have been implicated in type 1 diabetes or are related to pancreas and islet cell function. Interestingly, we observed a missense mutation in NLRC5 in tumors of 9 of the 13 ICI-DM patients that was not observed in the control patients treated with the same drugs for the same cancers. Germline DNA from the ICI-DM patients was sequenced; all NLRC5 mutations were germline. The prevalence of NLRC5 germline variants was significantly greater than the general population (p=5.98×10-6). Although NLRC5 is implicated in development of type 1 diabetes, germline NLRC5 mutations were not found in public databases from patients with type 1 diabetes, suggesting a different mechanism of insulin-dependent diabetes in immunotherapy-treated patients with cancer. CONCLUSIONS: Validation of the NLRC5 mutation as a potential predictive biomarker is warranted, as it might improve patient selection for treatment regimens. Furthermore, this genetic alteration suggests potential mechanisms of islet cell destruction in the setting of checkpoint inhibitor therapy.

Spectral neighbor joining for reconstruction of latent tree Models.

A common assumption in multiple scientific applications is that the distribution of observed data can be modeled by a latent tree graphical model. An important example is phylogenetics, where the tree models the evolutionary lineages of a set of observed organisms. Given a set of independent realizations of the random variables at the leaves of the tree, a key challenge is to infer the underlying tree topology. In this work we develop Spectral Neighbor Joining (SNJ), a novel method to recover the structure of latent tree graphical models. Given a matrix that contains a measure of similarity between all pairs of observed variables, SNJ computes a spectral measure of cohesion between groups of observed variables. We prove that SNJ is consistent, and derive a sufficient condition for correct tree recovery from an estimated similarity matrix. Combining this condition with a concentration of measure result on the similarity matrix, we bound the number of samples required to recover the tree with high probability. We illustrate via extensive simulations that in comparison to several other reconstruction methods, SNJ requires fewer samples to accurately recover trees with a large number of leaves or long edges.

Impact of healthcare worker shift scheduling on workforce preservation during the COVID-19 pandemic.

Reducing severe acute respiratory coronavirus virus 2 (SARS-CoV-2) infections among healthcare workers is critical. We ran Monte Carlo simulations modeling the spread of SARS-CoV-2 in non-COVID-19 wards, and we found that longer nursing shifts and scheduling designs in which teams of nurses and doctors co-rotate no more frequently than every 3 days can lead to fewer infections.