Related papers: Efficient Non-parametric Bayesian Hawkes Processes
Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…
The Hawkes process is a simple point process that has long memory, clustering effect, self-exciting property and is in general non-Markovian. The future evolution of a self-exciting point process is influenced by the timing of the past…
We consider models for multivariate point processes where the intensity is given nonparametrically in terms of functions in a reproducing kernel Hilbert space. The likelihood function involves a time integral and is consequently not given…
Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…
We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…
This paper proposes a nonparametric Bayesian framework called VariScan for simultaneous clustering, variable selection, and prediction in high-throughput regression settings. Poisson-Dirichlet processes are utilized to detect…
Forecasting in probabilistic time series is a complex endeavor that extends beyond predicting future values to also quantifying the uncertainty inherent in these predictions. Gaussian process regression stands out as a Bayesian machine…
We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over…
We introduce the Hyperedge-triggered Hawkes (HTH) process for inferring higher-order interaction structure in multi-cellular systems from asynchronous event-time data. Beyond standard pairwise excitation, the HTH intensity includes a term…
Bayesian optimisation is a popular technique for hyperparameter learning but typically requires initial exploration even in cases where similar prior tasks have been solved. We propose to transfer information across tasks using learnt…
In this abstract paper, we introduce a new kernel learning method by a nonparametric density estimator. The estimator consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected…
We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does…
We propose a flexible procedure for large-scale image search by hash functions with kernels. Our method treats binary codes and pairwise semantic similarity as latent and observed variables, respectively, in a probabilistic model based on…
We propose a novel framework for modeling multiple multivariate point processes, each with heterogeneous event types that share an underlying space and obey the same generative mechanism. Focusing on Hawkes processes and their variants that…
Recent work has developed Bayesian methods for the automatic statistical analysis and description of single time series as well as of homogeneous sets of time series data. We extend prior work to create an interpretable kernel embedding for…
Nonparametric Bayesian approaches provide a flexible framework for clustering without pre-specifying the number of groups, yet they are well known to overestimate the number of clusters, especially for functional data. We show that a…
We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…
The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…
One major impediment to the wider use of deep learning for clinical decision making is the difficulty of assigning a level of confidence to model predictions. Currently, deep Bayesian neural networks and sparse Gaussian processes are the…