Zhaoyue Chen

Zhaoyue Chen, Nick Koudas, Zhe Zhang et al.

Machine Learning (ML) applications are proliferating in the enterprise. Relational data which are prevalent in enterprise applications are typically normalized; as a result, data has to be denormalized via primary/foreign-key joins to be provided as input to ML algorithms. In this paper, we study the implementation of popular nonlinear ML models, Gaussian Mixture Models (GMM) and Neural Networks (NN), over normalized data addressing both cases of binary and multi-way joins over normalized relations. For the case of GMM, we show how it is possible to decompose computation in a systematic way both for binary joins and for multi-way joins to construct mixture models. We demonstrate that by factoring the computation, one can conduct the training of the models much faster compared to other applicable approaches, without any loss in accuracy. For the case of NN, we propose algorithms to train the network taking normalized data as the input. Similarly, we present algorithms that can conduct the training of the network in a factorized way and offer performance advantages. The redundancy introduced by denormalization can be exploited for certain types of activation functions. However, we demonstrate that attempting to explore this redundancy is helpful up to a certain point; exploring redundancy at higher layers of the network will always result in increased costs and is not recommended. We present the results of a thorough experimental evaluation, varying several parameters of the input relations involved and demonstrate that our proposals for the training of GMM and NN yield drastic performance improvements typically starting at 100%, which become increasingly higher as parameters of the underlying data vary, without any loss in accuracy.

Yingru Liu, Yucheng Xing, Xuewen Yang et al.

Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and observed data are high-dimensional, it is generally impossible to derive a precise continuous-time stochastic process to describe the system behaviors. To solve the above problem, we apply Variational Bayesian method and propose a flexible continuous-time stochastic recurrent neural network named Variational Stochastic Differential Networks (VSDN), which embeds the complicated dynamics of the sporadic time series by neural Stochastic Differential Equations (SDE). VSDNs capture the stochastic dependency among latent states and observations by deep neural networks. We also incorporate two differential Evidence Lower Bounds to efficiently train the models. Through comprehensive experiments, we show that VSDNs outperform state-of-the-art continuous-time deep learning models and achieve remarkable performance on prediction and interpolation tasks for sporadic time series.