Gaussian Cox processes are widely-used point process models that use a Gaussian process to describe the Bayesian a priori uncertainty present in latent intensity functions. In this paper, we propose a novel Bayesian inference scheme for Gaussian Cox processes by exploiting a conceptually-intuitive {¥it path integral} formulation. The proposed scheme does not rely on domain discretization, scales linearly with the number of observed events, has a lower complexity than the state-of-the-art variational Bayesian schemes with respect to the number of inducing points, and is applicable to a wide range of Gaussian Cox processes with various types of link functions. Our scheme is especially beneficial under the multi-dimensional input setting, where the number of inducing points tends to be large. We evaluate our scheme on synthetic and real-world data, and show that it achieves comparable predictive accuracy while being tens of times faster than reference methods.

Q and P represent the number of gradient descent iterations and the number of MCMC samplings, respectively. For the other symbols, see the main text.

Gaussian Cox processes are widely-used point process models that use a Gaussian process to describe the Bayesian a priori uncertainty present in latent intensity functions. In this paper, we propose a novel Bayesian inference scheme for Gaussian Cox processes by exploiting a conceptually-intuitive path integral formulation. The proposed scheme does not rely on domain discretization, scales linearly with the number of observed events, has a lower complexity than the state-of-the-art variational Bayesian schemes with respect to the number of inducing points, and is applicable to a wide range of Gaussian Cox processes with various types of link functions. Our scheme is especially beneficial under the multi-dimensional input setting, where the number of inducing points tends to be large. We evaluate our scheme on synthetic and real-world data, and show that it achieves comparable predictive accuracy while being tens of times faster than reference methods.

I enjoyed reading this paper, not being terribly familiar with work on survival analysis but very comfortable with GPs it was a bit of a struggle for me to understand certain parts of the paper initially and there still might be things that I've misunderstood and not being completely familiar with the background material my novelty rating should be taken with a grain of salt. Initially I was confused about the model as it seemed very specific but not particularly well motivated. After a bit or reading up on related material I understood that this is very related to Gaussian Cox process, a reference would clarify things here or making the connection in the introductions two last paragraphs clearer between "our prior" and the Gaussian Cox process. The paper is clearly written and well but I wish the authors would make their contributions clearer without the reader having to resort to go through all the related material. This is especially true for Section 3 and the data augumentation.

Gaussian Cox processes are widely-used point process models that use a Gaussian process to describe the Bayesian a priori uncertainty present in latent intensity functions. In this paper, we propose a novel Bayesian inference scheme for Gaussian Cox processes by exploiting a conceptually-intuitive { it path integral} formulation. The proposed scheme does not rely on domain discretization, scales linearly with the number of observed events, has a lower complexity than the state-of-the-art variational Bayesian schemes with respect to the number of inducing points, and is applicable to a wide range of Gaussian Cox processes with various types of link functions. Our scheme is especially beneficial under the multi-dimensional input setting, where the number of inducing points tends to be large. We evaluate our scheme on synthetic and real-world data, and show that it achieves comparable predictive accuracy while being tens of times faster than reference methods.

Temporal point processes (TPPs) are effective for modeling event occurrences over time, but they struggle with sparse and uncertain events in federated systems, where privacy is a major concern. To address this, we propose \textit{FedPP}, a Federated neural nonparametric Point Process model. FedPP integrates neural embeddings into Sigmoidal Gaussian Cox Processes (SGCPs) on the client side, which is a flexible and expressive class of TPPs, allowing it to generate highly flexible intensity functions that capture client-specific event dynamics and uncertainties while efficiently summarizing historical records. For global aggregation, FedPP introduces a divergence-based mechanism that communicates the distributions of SGCPs' kernel hyperparameters between the server and clients, while keeping client-specific parameters local to ensure privacy and personalization. FedPP effectively captures event uncertainty and sparsity, and extensive experiments demonstrate its superior performance in federated settings, particularly with KL divergence and Wasserstein distance-based global aggregation.

A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the cumulative intensity function) in the likelihood resulting in doubly intractable posterior distribution. Here, we propose a nonparametric Bayesian approach for estimating the intensity function of an inhomogeneous Poisson process without reliance on large data augmentation or approximations of the likelihood function. We propose to jointly model the intensity and the cumulative intensity function as a transformed Gaussian process, allowing us to directly bypass the need of approximating the cumulative intensity function in the likelihood. We propose an exact MCMC sampler for posterior inference and evaluate its performance on simulated data. We demonstrate the utility of our method in three real-world scenarios including temporal and spatial event data, as well as aggregated time count data collected at multiple resolutions. Finally, we discuss extensions of our proposed method to other point processes.

Inhomogeneous Poisson process data defined on a continuous spatio-temporal domain has attracted immense attention recently in a wide variety of applications, including reliability analysis in manufacturing systems (Soleimani et al, 2017), event capture in sensing regions (Mutny and Krause, 2021), crime prediction in urban area (Shirota and Gelfand, 2017) and disease diagnosis based on medical records (Lasko, 2014). The reliable training of an inhomogeneous Poisson process model critically relies on a large amount of data to avoid overfitting, especially when modeling high-dimensional point processes. However, one challenge is that the available training data is routinely sparse or even partially missing in specific applications. Taking manufacturing failure and healthcare analysis as motivating examples: the modern manufacturing machines are reliable and sparsely fail; the individuals with healthy constitution will not visit hospital very often. The data missing problems also arise, e.g., the event location capture is intermittent for sensing systems because of weather or other related barriers.