Related papers: Deep Random Splines for Point Process Intensity Es…

This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…

We introduce Deep Sigma Point Processes, a class of parametric models inspired by the compositional structure of Deep Gaussian Processes (DGPs). Deep Sigma Point Processes (DSPPs) retain many of the attractive features of (variational)…

The composition of multiple Gaussian Processes as a Deep Gaussian Process (DGP) enables a deep probabilistic nonparametric approach to flexibly tackle complex machine learning problems with sound quantification of uncertainty. Existing…

A neural network (NN) is a parameterised function that can be tuned via gradient descent to approximate a labelled collection of data with high precision. A Gaussian process (GP), on the other hand, is a probabilistic model that defines a…

Gaussian processes are now commonly used in dimensionality reduction approaches tailored to neuroscience, especially to describe changes in high-dimensional neural activity over time. As recording capabilities expand to include neuronal…

Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of…

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

Point processes are becoming very popular in modeling asynchronous sequential data due to their sound mathematical foundation and strength in modeling a variety of real-world phenomena. Currently, they are often characterized via intensity…

Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…

We propose stochastic, non-parametric activation functions that are fully learnable and individual to each neuron. Complexity and the risk of overfitting are controlled by placing a Gaussian process prior over these functions. The result is…

Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…

Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…

Deep Gaussian Processes (DGPs) compose GP layers to warp inputs, enabling improved emulation of computer models with nonstationary input-output behavior compared with ordinary GPs. In contrast to GPs, the predictive uncertainty for DGP…

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables…

Many applications in speech, robotics, finance, and biology deal with sequential data, where ordering matters and recurrent structures are common. However, this structure cannot be easily captured by standard kernel functions. To model such…

Neural network approaches for meta-learning distributions over functions have desirable properties such as increased flexibility and a reduced complexity of inference. Building on the successes of denoising diffusion models for generative…

We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates…

Learning the dynamics of spatiotemporal events is a fundamental problem. Neural point processes enhance the expressivity of point process models with deep neural networks. However, most existing methods only consider temporal dynamics…

Deep Gaussian Processes (DGPs) are multi-layer, flexible extensions of Gaussian processes but their training remains challenging. Sparse approximations simplify the training but often require optimization over a large number of inducing…