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Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional…
Foreshock events provide valuable insight to predict imminent major earthquakes. However, it is difficult to identify them in real time. In this paper, I propose an algorithm based on deep learning to instantaneously classify a seismic…
We consider a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (``aftershocks''). An aftershock sequence results in this model from…
Accurately predicting when and where ambulance call-outs occur can reduce response times and ensure the patient receives urgent care sooner. Here we present a novel method for ambulance demand prediction using Gaussian process regression…
Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
The epidemic-type aftershock sequence model (ETAS) is a simple stochastic process modeling seismicity, based on the two best-established empirical laws, the Omori law (power law decay ~1/t^{1+\theta} of seismicity after an earthquake) and…
Forecast models in statistical seismology are commonly evaluated with log-likelihood scores of the full distribution P(n) of earthquake numbers, yet heavy tails and out-of-range observations can bias model ranking. We develop a tail-aware…
Non-stationary time series with non-linear trends are frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of…
In this paper, we explore the application of Gaussian Processes (GPs) for predicting mean-reverting time series with an underlying structure, using relatively unexplored functional and augmented data structures. While many conventional…
Automatic forecasting is the task of receiving a time series and returning a forecast for the next time steps without any human intervention. Gaussian Processes (GPs) are a powerful tool for modeling time series, but so far there are no…
This tutorial aims to provide an intuitive introduction to Gaussian process regression (GPR). GPR models have been widely used in machine learning applications due to their representation flexibility and inherent capability to quantify…
Estimating causal effects in quasi-experiments with spatio-temporal panel data often requires adjusting for unmeasured confounding that varies across space and time. Gaussian Processes (GPs) offer a flexible, nonparametric modeling approach…
Outlier detection of semiconductor devices is important since manufacturing variation is inherently inevitable. In order to properly detect outliers, it is necessary to consider the discrepancy from underlying trend. Conventional methods…
Gaussian process (GP) regression is a powerful interpolation technique due to its flexibility in capturing non-linearity. In this paper, we provide a general framework for understanding the frequentist coverage of point-wise and…
Uncertainty Quantification (UQ) is essential for the reliable application of computational models in engineering and science. Among surrogate modeling techniques, Gaussian Process Regression (GPR) is particularly valuable for its…
Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions, the assumption of Gaussian residuals is invalid since event numbers are both discrete…
Gaussian Processes (GPs) have been widely used in machine learning to model distributions over functions, with applications including multi-modal regression, time-series prediction, and few-shot learning. GPs are particularly useful in the…
Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…