We discuss these works in more detail in Section 5. Authors are listed in alphabetical order.

The deviated model can be motivated by many applications in science.

The deep Kolmogorov method is a simple and popular deep learning based method for approximating solutions of partial differential equations (PDEs) of the Kolmogorov type. In this work we provide an error analysis for the deep Kolmogorov method for heat PDEs. Specifically, we reveal convergence with convergence rates for the overall mean square distance between the exact solution of the heat PDE and the realization function of the approximating deep neural network (DNN) associated with a stochastic optimization algorithm in terms of the size of the architecture (the depth/number of hidden layers and the width of the hidden layers) of the approximating DNN, in terms of the number of random sample points used in the loss function (the number of input-output data pairs used in the loss function), and in terms of the size of the optimization error made by the employed stochastic optimization method.

The decision tree is a flexible machine learning model that finds its success in numerous applications. It is usually fitted in a recursively greedy manner using CART.

Section 4.1, we consider =3 . In Section 4.2 and Appendix A.1, we examine the performance of different algorithms for the In Figure 5 the performance of both greedy heuristics is very similar under the two one-sided losses. We observe that the objective values are no longer uniformly positive, and are no longer monotonically increasing in the target size. In this section, we present the proofs of all theoretical results. The following lemma shows the submodularity of the objective U in the selection S . If (,M) is convex then U ( S) is submodular in S .

The solid curve in the top panel is the optimal ROC curve. The dashed straight line in the bottom panel is the linear piece that can not be recovered by the weighted method directly. However, after connecting the points linearly, the optimal ROC curve can be recovered.