Neural Hawkes Process google
Many events occur in the world. Some event types are stochastically excited or inhibited—in the sense of having their probabilities elevated or decreased—by patterns in the sequence of previous events. Discovering such patterns can help us predict which type of event will happen next and when. Learning such structure should benefit various applications, including medical prognosis, consumer behavior, and social media activity prediction. We propose to model streams of discrete events in continuous time, by constructing a neurally self-modulating multivariate point process. This generative model allows past events to influence the future in complex ways, by conditioning future event intensities on the hidden state of a recurrent neural network that has consumed the stream of past events. We evaluate our model on multiple datasets and show that it significantly outperforms other strong baselines. …

Tensor Rank Decomposition google
In multilinear algebra, the tensor rank decomposition or canonical polyadic decomposition (CPD) may be regarded as a generalization of the matrix singular value decomposition (SVD) to tensors, which has found application in statistics, signal processing, psychometrics, linguistics and chemometrics. It was introduced by Hitchcock in 1927 and later rediscovered several times, notably in psychometrics. For this reason, the tensor rank decomposition is sometimes historically referred to as PARAFAC or CANDECOMP. …

Output Range Analysis google
Deep neural networks (NN) are extensively used for machine learning tasks such as image classification, perception and control of autonomous systems. Increasingly, these deep NNs are also been deployed in high-assurance applications. Thus, there is a pressing need for developing techniques to verify neural networks to check whether certain user-expected properties are satisfied. In this paper, we study a specific verification problem of computing a guaranteed range for the output of a deep neural network given a set of inputs represented as a convex polyhedron. Range estimation is a key primitive for verifying deep NNs. We present an efficient range estimation algorithm that uses a combination of local search and linear programming problems to efficiently find the maximum and minimum values taken by the outputs of the NN over the given input set. In contrast to recently proposed ‘monolithic’ optimization approaches, we use local gradient descent to repeatedly find and eliminate local minima of the function. The final global optimum is certified using a mixed integer programming instance. We implement our approach and compare it with Reluplex, a recently proposed solver for deep neural networks. We demonstrate the effectiveness of the proposed approach for verification of NNs used in automated control as well as those used in classification. …

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