Feng Zhou

Feng Zhou, Quyu Kong, Zhijie Deng et al.

This paper presents a novel extension of multi-task Gaussian Cox processes for modeling multiple heterogeneous correlated tasks jointly, e.g., classification and regression, via multi-output Gaussian processes (MOGP). A MOGP prior over the parameters of the dedicated likelihoods for classification, regression and point process tasks can facilitate sharing of information between heterogeneous tasks, while allowing for nonparametric parameter estimation. To circumvent the non-conjugate Bayesian inference in the MOGP modulated heterogeneous multi-task framework, we employ the data augmentation technique and derive a mean-field approximation to realize closed-form iterative updates for estimating model parameters. We demonstrate the performance and inference on both 1D synthetic data as well as 2D urban data of Vancouver.

Hua Wang, Yuqiong Wu, Yushun Zhang et al.

Logs are valuable information for oil and gas fields as they help to determine the lithology of the formations surrounding the borehole and the location and reserves of subsurface oil and gas reservoirs. However, important logs are often missing in horizontal or old wells, which poses a challenge in field applications. In this paper, we utilize data from the 2020 machine learning competition of the SPWLA, which aims to predict the missing compressional wave slowness and shear wave slowness logs using other logs in the same borehole. We employ the NGBoost algorithm to construct an Ensemble Learning model that can predicate the results as well as their uncertainty. Furthermore, we combine the SHAP method to investigate the interpretability of the machine learning model. We compare the performance of the NGBosst model with four other commonly used Ensemble Learning methods, including Random Forest, GBDT, XGBoost, LightGBM. The results show that the NGBoost model performs well in the testing set and can provide a probability distribution for the prediction results. In addition, the variance of the probability distribution of the predicted log can be used to justify the quality of the constructed log. Using the SHAP explainable machine learning model, we calculate the importance of each input log to the predicted results as well as the coupling relationship among input logs. Our findings reveal that the NGBoost model tends to provide greater slowness prediction results when the neutron porosity and gamma ray are large, which is consistent with the cognition of petrophysical models. Furthermore, the machine learning model can capture the influence of the changing borehole caliper on slowness, where the influence of borehole caliper on slowness is complex and not easy to establish a direct relationship. These findings are in line with the physical principle of borehole acoustics.

Feng Zhou, Quyu Kong, Yixuan Zhang et al.

Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to three key hypotheses: parametric, linear and homogeneous. Recent work has attempted to address these limitations separately. This work aims to overcome all three assumptions simultaneously by proposing the flexible state-switching Hawkes processes: a flexible, nonlinear and nonhomogeneous variant where a state process is incorporated to interact with the point processes. The proposed model empowers Hawkes processes to be applied to time-varying systems. For inference, we utilize the latent variable augmentation technique to design two efficient Bayesian inference algorithms: Gibbs sampler and mean-field variational inference, with analytical iterative updates to estimate the posterior. In experiments, our model achieves superior performance compared to the state-of-the-art competitors.

Feng Zhou, Yixuan Zhang, Jun Zhu

Hawkes process provides an effective statistical framework for analyzing the time-dependent interaction of neuronal spiking activities. Although utilized in many real applications, the classic Hawkes process is incapable of modelling inhibitory interactions among neurons. Instead, the nonlinear Hawkes process allows for a more flexible influence pattern with excitatory or inhibitory interactions. In this paper, three sets of auxiliary latent variables (Pólya-Gamma variables, latent marked Poisson processes and sparsity variables) are augmented to make functional connection weights in a Gaussian form, which allows for a simple iterative algorithm with analytical updates. As a result, an efficient expectation-maximization (EM) algorithm is derived to obtain the maximum a posteriori (MAP) estimate. We demonstrate the accuracy and efficiency performance of our algorithm on synthetic and real data. For real neural recordings, we show our algorithm can estimate the temporal dynamics of interaction and reveal the interpretable functional connectivity underlying neural spike trains.

Simon Luo, Feng Zhou, Lamiae Azizi et al.

We present the Additive Poisson Process (APP), a novel framework that can model the higher-order interaction effects of the intensity functions in stochastic processes using lower dimensional projections. Our model combines the techniques in information geometry to model higher-order interactions on a statistical manifold and in generalized additive models to use lower-dimensional projections to overcome the effects from the curse of dimensionality. Our approach solves a convex optimization problem by minimizing the KL divergence from a sample distribution in lower dimensional projections to the distribution modeled by an intensity function in the stochastic process. Our empirical results show that our model is able to use samples observed in the lower dimensional space to estimate the higher-order intensity function with extremely sparse observations.

Feng Zhou, Zhidong Li, Xuhui Fan et al.

In this paper, we consider the sigmoid Gaussian Hawkes process model: the baseline intensity and triggering kernel of Hawkes process are both modeled as the sigmoid transformation of random trajectories drawn from Gaussian processes (GP). By introducing auxiliary latent random variables (branching structure, Pólya-Gamma random variables and latent marked Poisson processes), the likelihood is converted to two decoupled components with a Gaussian form which allows for an efficient conjugate analytical inference. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum a posteriori (MAP) estimate. Furthermore, we extend the EM algorithm to an efficient approximate Bayesian inference algorithm: mean-field variational inference. We demonstrate the performance of two algorithms on simulated fictitious data. Experiments on real data show that our proposed inference algorithms can recover well the underlying prompting characteristics efficiently.

Feng Zhou, Zhidong Li, Xuhui Fan et al.

In classical Hawkes process, the baseline intensity and triggering kernel are assumed to be a constant and parametric function respectively, which limits the model flexibility. To generalize it, we present a fully Bayesian nonparametric model, namely Gaussian process modulated Hawkes process and propose an EM-variational inference scheme. In this model, a transformation of Gaussian process is used as a prior on the baseline intensity and triggering kernel. By introducing a latent branching structure, the inference of baseline intensity and triggering kernel is decoupled and the variational inference scheme is embedded into an EM framework naturally. We also provide a series of schemes to accelerate the inference. Results of synthetic and real data experiments show that the underlying baseline intensity and triggering kernel can be recovered without parametric restriction and our Bayesian nonparametric estimation is superior to other state of the arts.