Young Lee

Thanh Vinh Vo, Trong Nghia Hoang, Young Lee et al.

Many modern applications collect data that comes in federated spirit, with data kept locally and undisclosed. Till date, most insight into the causal inference requires data to be stored in a central repository. We present a novel framework for causal inference with federated data sources. We assess and integrate local causal effects from different private data sources without centralizing them. Then, the treatment effects on subjects from observational data using a non-parametric reformulation of the classical potential outcomes framework is estimated. We model the potential outcomes as a random function distributed by Gaussian processes, whose defining parameters can be efficiently learned from multiple data sources, respecting privacy constraints. We demonstrate the promise and efficiency of the proposed approach through a set of simulated and real-world benchmark examples.

Minsuk Shin, Young Lee, Jun S. Liu

Uncertainty quantification has been a core of the statistical machine learning, but its computational bottleneck has been a serious challenge for both Bayesians and frequentists. We propose a model-based framework in quantifying uncertainty, called predictive-matching Generative Parameter Sampler (GPS). This procedure considers an Uncertainty Quantification (UQ) distribution on the targeted parameter, which matches the corresponding predictive distribution to the observed data. This framework adopts a hierarchical modeling perspective such that each observation is modeled by an individual parameter. This individual parameterization permits the resulting inference to be computationally scalable and robust to outliers. Our approach is illustrated for linear models, Poisson processes, and deep neural networks for classification. The results show that the GPS is successful in providing uncertainty quantification as well as additional flexibility beyond what is allowed by classical statistical procedures under the postulated statistical models.

Kar Wai Lim, Young Lee, Leif Hanlen et al.

We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying intensities. We demonstrate that inter-arrival times can be decomposed into simpler auxiliary variables that can be sampled directly, giving exact simulation with no approximation. We establish that the auxiliary variables provides information on the parent process for each event time. The algorithm correctness is shown by verifying the simulated intensities with their theoretical moments. A modular inference procedure consisting of Gibbs samplers through the auxiliary variable augmentation and adaptive rejection sampling is presented. Finally, we compare our proposed simulation method against existing methods, and find significant improvement in terms of algorithm speed. Our inference algorithm is used to discover the strengths of mutually excitations in real dark networks.

Hongyi Ding, Young Lee, Issei Sato et al.

We present the first framework for Gaussian-process-modulated Poisson processes when the temporal data appear in the form of panel counts. Panel count data frequently arise when experimental subjects are observed only at discrete time points and only the numbers of occurrences of the events between subsequent observation times are available. The exact occurrence timestamps of the events are unknown. The method of conducting the efficient variational inference is presented, based on the assumption of a Gaussian-process-modulated intensity function. We derive a tractable lower bound to alleviate the problems of the intractable evidence lower bound inherent in the variational inference framework. Our algorithm outperforms classical methods on both synthetic and three real panel count sets.

Marian-Andrei Rizoiu, Young Lee, Swapnil Mishra et al.

This chapter provides an accessible introduction for point processes, and especially Hawkes processes, for modeling discrete, inter-dependent events over continuous time. We start by reviewing the definitions and the key concepts in point processes. We then introduce the Hawkes process, its event intensity function, as well as schemes for event simulation and parameter estimation. We also describe a practical example drawn from social media data - we show how to model retweet cascades using a Hawkes self-exciting process. We presents a design of the memory kernel, and results on estimating parameters and predicting popularity. The code and sample event data are available as an online appendix

Young Lee, Kar Wai Lim, Cheng Soon Ong

We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We generalize a recent algorithm for simulating draws from Hawkes processes whose levels of excitation are stochastic processes, and propose a hybrid Markov chain Monte Carlo approach for model fitting. Our sampling procedure scales linearly with the number of required events and does not require stationarity of the point process. A modular inference procedure consisting of a combination between Gibbs and Metropolis Hastings steps is put forward. We recover expectation maximization as a special case. Our general approach is illustrated for contagion following geometric Brownian motion and exponential Langevin dynamics.