Gradient-flow adaptive importance sampling for Bayesian leave one out cross-validation for sigmoidal classification models.

We introduce a set of gradient-flow-guided adaptive importance sampling (IS) transformations to stabilize Monte-Carlo approximations of point-wise leave one out cross-validated (LOO) predictions for Bayesian classification models. One can leverage this methodology for assessing model generalizability by for instance computing a LOO analogue to the AIC or computing LOO ROC/PRC curves and derived metrics like the AUROC and AUPRC. By the calculus of variations and gradient flow, we derive two simple nonlinear single-step transformations that utilize gradient information to shift a model's pre-trained full-data posterior closer to the target LOO posterior predictive distributions. In doing so, the transformations stabilize importance weights. Because the transformations involve the gradient of the likelihood function, the resulting Monte Carlo integral depends on Jacobian determinants with respect to the model Hessian. We derive closed-form exact formulae for these Jacobian determinants in the cases of logistic regression and shallow ReLU-activated artificial neural networks, and provide a simple approximation that sidesteps the need to compute full Hessian matrices and their spectra. We test the methodology on an n≪p dataset that is known to produce unstable LOO IS weights.

Interpretable (not just posthoc-explainable) medical claims modeling for discharge placement to reduce preventable all-cause readmissions or death.

We developed an inherently interpretable multilevel Bayesian framework for representing variation in regression coefficients that mimics the piecewise linearity of ReLU-activated deep neural networks. We used the framework to formulate a survival model for using medical claims to predict hospital readmission and death that focuses on discharge placement, adjusting for confounding in estimating causal local average treatment effects. We trained the model on a 5% sample of Medicare beneficiaries from 2008 and 2011, based on their 2009-2011 inpatient episodes (approximately 1.2 million), and then tested the model on 2012 episodes (approximately 400 thousand). The model scored an out-of-sample AUROC of approximately 0.75 on predicting all-cause readmissions-defined using official Centers for Medicare and Medicaid Services (CMS) methodology-or death within 30-days of discharge, being competitive against XGBoost and a Bayesian deep neural network, demonstrating that one need-not sacrifice interpretability for accuracy. Crucially, as a regression model, it provides what blackboxes cannot-its exact gold-standard global interpretation, explicitly defining how the model performs its internal "reasoning" for mapping the input data features to predictions. In doing so, we identify relative risk factors and quantify the effect of discharge placement. We also show that the posthoc explainer SHAP provides explanations that are inconsistent with the ground truth model reasoning that our model readily admits.

3D chromatin architecture, BRD4, and Mediator have distinct roles in regulating genome-wide transcriptional bursting and gene network.

Discontinuous transcription is evolutionarily conserved and a fundamental feature of gene regulation; yet, the exact mechanisms underlying transcriptional bursting are unresolved. Analyses of bursting transcriptome-wide have focused on the role of cis-regulatory elements, but other factors that regulate this process remain elusive. We applied mathematical modeling to single-cell RNA sequencing data to infer bursting dynamics transcriptome-wide under multiple conditions to identify possible molecular mechanisms. We found that Mediator complex subunit 26 (MED26) primarily regulates frequency, MYC regulates burst size, while cohesin and Bromodomain-containing protein 4 (BRD4) can modulate both. Despite comparable effects on RNA levels among these perturbations, acute depletion of MED26 had the most profound impact on the entire gene regulatory network, acting downstream of chromatin spatial architecture and without affecting TATA box-binding protein (TBP) recruitment. These results indicate that later steps in the initiation of transcriptional bursts are primary nodes for integrating gene networks in single cells.