A.1 CommunityDetection The spectral clustering algorithm for directed networks that we consider in this paper is shown in Algorithm A.1. It can be applied either to the weighted adjacency (count) matrixN or the unweighted adjacency matrixA, where Aij =1{Nij >0} and 1{ } denotes the indicator function of the argument. This algorithm is used for the community detection step in our proposed CHIP estimationprocedure. For undirectednetworks, which we use for the theoreticalanalysisin Section 4, spectral clustering is performed by running k-means clustering on the rows of theeigenvector matrix of N or A, not the rows of the concatenated singular vector matrix. A.2 Estimation of Hawkes process parameters Ozaki (1979) derived the log-likelihood function for Hawkes processes with exponential kernels, which takes the form: logL= µT+ The threeparameters µ,α,β can be estimatedby maximizing (A.1) using standard numerical methods for non-linear optimization (Nocedal & Wright, 2006). We provide closed-form equations for estimating mab =αab/βab and µab in (2).

On the technical side, we show that the logarithmic loss and an informationtheoretic quantity called thetriangular discriminationplay a fundamental role in obtaining first-order guarantees, and we combine this observation with new refinements tothe regression oracle reduction framework ofFoster and Rakhlin [29].

Pedestrian pre-collision pose is one of the key factors to determine the degree of pedestrian-vehicle injury in collision. Human pose estimation algorithm is an effective method to estimate pedestrian emergency pose from accident video.

To address this issue, some researchers [3,35,18]havetried toembed BCs into the ansatz.

Itcanbeshown (see [18] andthesupplementary material) thatKsEM-VROpt(n, )= KFIEMOpt(n, )= n2/3O( 1) and KsEM-VRCE (n, )= KFIEMCE (n, )= n+n2/3O( 1). SPIDER estimator employed, Proof Sketch.Whilewe