**DeepSOFA**

Traditional methods for assessing illness severity and predicting in-hospital mortality among critically ill patients require manual, time-consuming, and error-prone calculations that are further hindered by the use of static variable thresholds derived from aggregate patient populations. These coarse frameworks do not capture time-sensitive individual physiological patterns and are not suitable for instantaneous assessment of patients’ acuity trajectories, a critical task for the ICU where conditions often change rapidly. Furthermore, they are ill-suited to capitalize on the emerging availability of streaming electronic health record data. We propose a novel acuity score framework (DeepSOFA) that leverages temporal patient measurements in conjunction with deep learning models to make accurate assessments of a patient’s illness severity at any point during their ICU stay. We compare DeepSOFA with SOFA baseline models using the same predictors and find that at any point during an ICU admission, DeepSOFA yields more accurate predictions of in-hospital mortality. … **Multicollinearity**

In statistics, multicollinearity (also collinearity) is a phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, meaning that one can be linearly predicted from the others with a non-trivial degree of accuracy. In this situation the coefficient estimates of the multiple regression may change erratically in response to small changes in the model or the data. Multicollinearity does not reduce the predictive power or reliability of the model as a whole, at least within the sample data set; it only affects calculations regarding individual predictors. That is, a multiple regression model with correlated predictors can indicate how well the entire bundle of predictors predicts the outcome variable, but it may not give valid results about any individual predictor, or about which predictors are redundant with respect to others. In case of perfect multicollinearity the predictor matrix is singular and therefore cannot be inverted. Under these circumstances, the ordinary least-squares estimator \hat{\beta} = (X’X)^{-1}X’y does not exist. Note that in statements of the assumptions underlying regression analyses such as ordinary least squares, the phrase ‘no multicollinearity’ is sometimes used to mean the absence of perfect multicollinearity, which is an exact (non-stochastic) linear relation among the regressors. … **Expected Policy Gradient (EPG)**

We propose expected policy gradients (EPG), which unify stochastic policy gradients (SPG) and deterministic policy gradients (DPG) for reinforcement learning. Inspired by expected sarsa, EPG integrates (or sums) across actions when estimating the gradient, instead of relying only on the action in the sampled trajectory. For continuous action spaces, we first derive a practical result for Gaussian policies and quadric critics and then extend it to an analytical method for the universal case, covering a broad class of actors and critics, including Gaussian, exponential families, and reparameterised policies with bounded support. For Gaussian policies, we show that it is optimal to explore using covariance proportional to the matrix exponential of the scaled Hessian of the critic with respect to the actions. EPG also provides a general framework for reasoning about policy gradient methods, which we use to establish a new general policy gradient theorem, of which the stochastic and deterministic policy gradient theorems are special cases. Furthermore, we prove that EPG reduces the variance of the gradient estimates without requiring deterministic policies and with little computational overhead. Finally, we show that EPG outperforms existing approaches on six challenging domains involving the simulated control of physical systems. …

# If you did not already know

**28**
*Saturday*
Apr 2018

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