Exponential Multivariate Hawkes Model
In recent years methods of data analysis for point processes have received some attention, for example, by Cox & Lewis (1966) and Lewis (1964). In particular Bartlett (1963a, b) has introduced methods of analysis based on the point spectrum. Theoretical models are relatively sparse. In this paper the theoretical properties of a class of processes with particular reference to the point spectrum or corresponding covariance density functions are discussed. A particular result is a self-exciting process with the same second-order properties as a certain doubly stochastic process. These are not distinguishable by methods of data analysis based on these properties. …

Coreset-Based Neural Network Compression
We propose a novel Convolutional Neural Network (CNN) compression algorithm based on coreset representations of filters. We exploit the redundancies extant in the space of CNN weights and neuronal activations (across samples) in order to obtain compression. Our method requires no retraining, is easy to implement, and obtains state-of-the-art compression performance across a wide variety of CNN architectures. Coupled with quantization and Huffman coding, we create networks that provide AlexNet-like accuracy, with a memory footprint that is $832\times$ smaller than the original AlexNet, while also introducing significant reductions in inference time as well. Additionally these compressed networks when fine-tuned, successfully generalize to other domains as well. …

HI-VAE
Variational autoencoders (VAEs), as well as other generative models, have been shown to be efficient and accurate to capture the latent structure of vast amounts of complex high-dimensional data. However, existing VAEs can still not directly handle data that are heterogenous (mixed continuous and discrete) or incomplete (with missing data at random), which is indeed common in real-world applications. In this paper, we propose a general framework to design VAEs, suitable for fitting incomplete heterogenous data. The proposed HI-VAE includes likelihood models for real-valued, positive real valued, interval, categorical, ordinal and count data, and allows to estimate (and potentially impute) missing data accurately. Furthermore, HI-VAE presents competitive predictive performance in supervised tasks, outperforming supervised models when trained on incomplete data. …