Related papers: Optimal change point detection in Gaussian process…

This paper considers the problems of detecting a change point and estimating the location in the correlation matrices of a sequence of high-dimensional vectors, where the dimension is large enough to be comparable to the sample size or even…

Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…

This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a…

We investigate the behavior of the Generalized Likelihood Ratio Test (GLRT) (Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193]) for time varying coefficient models where the regressors and errors are non-stationary time series and can…

The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. The pre-change observations are assumed to be stationary with a known distribution, while the post-change…

Online changepoint detection algorithms that are based on likelihood-ratio tests have been shown to have excellent statistical properties. However, a simple online implementation is computationally infeasible as, at time $T$, it involves…

Unmeasured or latent variables are often the cause of correlations between multivariate measurements, which are studied in a variety of fields such as psychology, ecology, and medicine. For Gaussian measurements, there are classical tools…

Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of $K$ Gaussians with generic means…

We study nonparametric Bayesian inference for the intensity function of a covariate-driven point process. We extend recent results from the literature, showing that a wide class of Gaussian priors, combined with flexible link functions,…

We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model…

Change point tests for abrupt changes in the mean of functional data, i.e., random elements in infinite-dimensional Hilbert spaces, are either based on dimension reduction techniques, e.g., based on principal components, or directly based…

In the analysis of sequential data, the detection of abrupt changes is important in predicting future changes. In this paper, we propose statistical hypothesis tests for detecting covariance structure changes in locally smooth time series…

Testing for change points in sequences of covariance matrices is an important and equally challenging problem in statistical methodology with applications in various fields. Motivated by the observation that even in cases where the ratio…

We introduce a novel unsupervised learning method for time series data with latent dynamical structure: the recognition-parametrized Gaussian state space model (RP-GSSM). The RP-GSSM is a probabilistic model that learns Markovian Gaussian…

Gaussian Process (GP) models are popular statistical surrogates used for emulating computationally expensive computer simulators. The quality of a GP model fit can be assessed by a goodness of fit measure based on optimized likelihood.…

We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…

We derive an asymptotic expansion for the log likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for…

The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially…

The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to…

High-dimensional changepoint inference, adaptable to diverse alternative scenarios, has attracted significant attention in recent years. In this paper, we propose an adaptive and robust approach to changepoint testing. Specifically, by…