SignificanceIn modern hospital systems where complicated, severely ill patient populations are the norm, there is currently no reliable way to forecast the use of perishable medical resources to enable a smart and economic way to deliver optimal patient care. We here demonstrate a statistical model using hospital patient data to quantitatively forecast, days in advance, the need for platelet transfusions. This approach can be leveraged to significantly decrease platelet wastage, and, if adopted nationwide, would save approximately 80 million dollars per year. We believe our approach can be generalized to all other aspects of patient care involving timely delivery of perishable medical resources.
We study recovery of piecewise-constant signals on graphs by the estimator minimizing an l 0 -edge-penalized objective. Although exact minimization of this objective may be computationally intractable, we show that the same statistical risk guarantees are achieved by the α-expansion algorithm which computes an approximate minimizer in polynomial time. We establish that for graphs with small average vertex degree, these guarantees are minimax rate-optimal over classes of edge-sparse signals. For spatially inhomogeneous graphs, we propose minimization of an edge-weighted objective where each edge is weighted by its effective resistance or another measure of its contribution to the graph's connectivity. We establish minimax optimality of the resulting estimators over corresponding edge-weighted sparsity classes. We show theoretically that these risk guarantees are not always achieved by the estimator minimizing the l 1 /total-variation relaxation, and empirically that the l 0 -based estimates are more accurate in high signal-to-noise settings.
We consider the multi-class classification problem when the training data and the out-of-sample test data may have different distributions and propose a method called BCOPS (balanced and conformal optimized prediction sets). BCOPS constructs a prediction set C(x) as a subset of class labels, possibly empty. It tries to optimize the out-of-sample performance, aiming to include the correct class as often as possible, but also detecting outliers x, for which the method returns no prediction (corresponding to C(x) equal to the empty set). The proposed method combines supervised-learning algorithms with the method of conformal prediction to minimize a misclassification loss averaged over the out-of-sample distribution. The constructed prediction sets have a finite-sample coverage guarantee without distributional assumptions.We also propose a method to estimate the outlier detection rate of a given method. We prove asymptotic consistency and optimality of our proposals under suitable assumptions and illustrate our methods on real data examples.
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