Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and derive an inference algorithm by performing inference on an aggregated sum of Gaussian Processes. Approximate Bayesian inference is achieved via data augmentation, and we describe a mean-field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from different domains and compare it to previously reported results.

Este trabajo prueba la hipótesis de eficiencia débil al comprobar la hipótesis de martingala en diferencias en los retornos del Índice General de la Bolsa de Valores de Colombia, IGBC. Se considera una estructura de dependencia condicional de primer orden mediante el modelo auto-regresivo fraccionalmente integrado de medias móviles, ARFIMA, y de segundo orden con el modelo hiperbólico asimétrico potencial autorregresivo condicionalmente heterocedástico, HYAPARCH, el cual captura todos los hechos estilizados encontrados en la investigación empírica. Los resultados rechazan la hipótesis de eficiencia débil al mostrar que el proceso generador de los retornos parece obedecer a un modelo auto-regresivo fraccionalmente integrado, arfi, en mediacondicional y a un hiperbólico asimétrico autorregresivo condicionalmente heterocedástico, HYAGARCH, en varianza condicional.

Time plays an important role regarding user preferences for products. It introduces asymmetries into the adoption of products which should be considered in the context of recommender systems and business intelligence. We therefore investigate how temporally asymmetric user preferences can be analyzed using a latent factor model called Decomposition Into Directional Components (DEDICOM). We introduce a new scalable hybrid algorithm that combines projected gradient descent and alternating least squares updates to compute DEDICOM and imposes semi-nonnegativity constraints to better interpret the resulting factors. We apply our model to analyze user churn and migration between different computer games in a social gaming environment.

In this paper, we propose to leverage the Bayesian uncertainty information encoded in parameter distributions to inform the learning procedure for Bayesian models. We derive a first principle stochastic differential equation for the training dynamics of the mean and uncertainty parameter in the variational distributions. On the basis of the derived Bayesian stochastic differential equation, we apply the methodology of stochastic optimal control on the variational parameters to obtain individually controlled learning rates. We show that the resulting optimizer, StochControlSGD, is significantly more robust to large learning rates and can adaptively and individually control the learning rates of the variational parameters. The evolution of the control suggests separate and distinct dynamical behaviours in the training regimes for the mean and uncertainty parameters in Bayesian neural networks.

A Schrödinger bridge is a stochastic process connecting two given probability distributions over time. It has been recently applied as an approach for generative data modelling. The computational training of such bridges requires the repeated estimation of the drift function for a time-reversed stochastic process using samples generated by the corresponding forward process. We introduce a modified score- function-based method for computing such reverse drifts, which can be efficiently implemented by a feed-forward neural network. We applied our approach to artificial datasets with increasing complexity. Finally, we evaluated its performance on genetic data, where Schrödinger bridges can be used to model the time evolution of single-cell RNA measurements.