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Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality. For example, extending the inference process with auxiliary variables leads to improved sample quality. While there are many such multivariate diffusions to explore, each new one requires significant model-specific analysis, hindering rapid prototyping and evaluation. In this work, we study Multivariate Diffusion Models (MDMs). For any number of auxiliary variables, we provide a recipe for maximizing a lower-bound on the MDMs likelihood without requiring any model-specific analysis. We then demonstrate how to parameterize the diffusion for a specified target noise distribution; these two points together enable optimizing the inference diffusion process. Optimizing the diffusion expands easy experimentation from just a few well-known processes to an automatic search over all linear diffusions. To demonstrate these ideas, we introduce two new specific diffusions as well as learn a diffusion process on the MNIST, CIFAR10, and ImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs) relative to fixed choices of diffusions for a given dataset and model architecture. 

Abstract AimsMyocardial infarction and heart failure are major cardiovascular diseases that affect millions of people in the USA with morbidity and mortality being highest among patients who develop cardiogenic shock. Early recognition of cardiogenic shock allows prompt implementation of treatment measures. Our objective is to develop a new dynamic risk score, called CShock, to improve early detection of cardiogenic shock in the cardiac intensive care unit (ICU). Methods and resultsWe developed and externally validated a deep learning-based risk stratification tool, called CShock, for patients admitted into the cardiac ICU with acute decompensated heart failure and/or myocardial infarction to predict the onset of cardiogenic shock. We prepared a cardiac ICU dataset using the Medical Information Mart for Intensive Care-III database by annotating with physician-adjudicated outcomes. This dataset which consisted of 1500 patients with 204 having cardiogenic/mixed shock was then used to train CShock. The features used to train the model for CShock included patient demographics, cardiac ICU admission diagnoses, routinely measured laboratory values and vital signs, and relevant features manually extracted from echocardiogram and left heart catheterization reports. We externally validated the risk model on the New York University (NYU) Langone Health cardiac ICU database which was also annotated with physician-adjudicated outcomes. The external validation cohort consisted of 131 patients with 25 patients experiencing cardiogenic/mixed shock. CShock achieved an area under the receiver operator characteristic curve (AUROC) of 0.821 (95% CI 0.792–0.850). CShock was externally validated in the more contemporary NYU cohort and achieved an AUROC of 0.800 (95% CI 0.717–0.884), demonstrating its generalizability in other cardiac ICUs. Having an elevated heart rate is most predictive of cardiogenic shock development based on Shapley values. The other top 10 predictors are having an admission diagnosis of myocardial infarction with ST-segment elevation, having an admission diagnosis of acute decompensated heart failure, Braden Scale, Glasgow Coma Scale, blood urea nitrogen, systolic blood pressure, serum chloride, serum sodium, and arterial blood pH. ConclusionThe novel CShock score has the potential to provide automated detection and early warning for cardiogenic shock and improve the outcomes for millions of patients who suffer from myocardial infarction and heart failure. 

Deep models trained through maximum likelihood have achieved state-of-the-art results for survival analysis. Despite this training scheme, practitioners evaluate models under other criteria, such as binary classification losses at a chosen set of time horizons, e.g. Brier score (BS) and Bernoulli log likelihood (BLL). Models trained with maximum likelihood may have poor BS or BLL since maximum likelihood does not directly optimize these criteria. Directly optimizing criteria like BS requires inverse-weighting by the censoring distribution. However, estimating the censoring model under these metrics requires inverse-weighting by the failure distribution. The objective for each model requires the other, but neither are known. To resolve this dilemma, we introduce Inverse-Weighted Survival Games. In these games, objectives for each model are built from re-weighted estimates featuring the other model, where the latter is held fixed during training. When the loss is proper, we show that the games always have the true failure and censoring distributions as a stationary point. This means models in the game do not leave the correct distributions once reached. We construct one case where this stationary point is unique. We show that these games optimize BS on simulations and then apply these principles on real world cancer and critically-ill patient data. Supplementary Material: pdf 

Deep models trained through maximum likelihood have achieved state-of-the-art results for survival analysis. Despite this training scheme, practitioners evaluate models under other criteria, such as binary classification losses at a chosen set of time horizons, e.g. Brier score (BS) and Bernoulli log likelihood (BLL). Models trained with maximum likelihood may have poor BS or BLL since maximum likelihood does not directly optimize these criteria. Directly optimizing criteria like BS requires inverse-weighting by the censoring distribution. However, estimating the censoring model under these metrics requires inverse-weighting by the failure distribution. The objective for each model requires the other, but neither are known. To resolve this dilemma, we introduce Inverse-Weighted Survival Games. In these games, objectives for each model are built from re-weighted estimates featuring the other model, where the latter is held fixed during training. When the loss is proper, we show that the games always have the true failure and censoring distributions as a stationary point. This means models in the game do not leave the correct distributions once reached. We construct one case where this stationary point is unique. We show that these games optimize BS on simulations and then apply these principles on real world cancer and critically-ill patient data.