Related papers: A scalable end-to-end Gaussian process adapter for…

By treating intervals as inseparable sets, this paper proposes sparse machine learning regressions for high-dimensional interval-valued time series. With LASSO or adaptive LASSO techniques, we develop a penalized minimum distance…

We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…

We consider modeling of angular or directional data viewed as a linear variable wrapped onto a unit circle. In particular, we focus on the spatio-temporal context, motivated by a collection of wave directions obtained as computer model…

The central problem we address in this work is estimation of the parameter support set S, the set of indices corresponding to nonzero parameters, in the context of a sparse parametric likelihood model for discrete multivariate time series.…

Generalized Category Discovery (GCD) seeks to identify novel categories from unlabeled data while retaining the classification ability of seen categories. Prior GCD methods commonly leverage transferable representations from pre-trained…

Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric…

Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…

Uncertainty quantification has been a core of the statistical machine learning, but its computational bottleneck has been a serious challenge for both Bayesians and frequentists. We propose a model-based framework in quantifying…

Subsequence-based time series classification algorithms provide accurate and interpretable models, but training these models is extremely computation intensive. The asymptotic time complexity of subsequence-based algorithms remains a…

We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…

Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning…

Gaussian processes (GPs) stand as crucial tools in machine learning and signal processing, with their effectiveness hinging on kernel design and hyper-parameter optimization. This paper presents a novel GP linear multiple kernel (LMK) and a…

The vast quantity of information brought by big data as well as the evolving computer hardware encourages success stories in the machine learning community. In the meanwhile, it poses challenges for the Gaussian process (GP) regression, a…

Investigating the relationship, particularly the lead-lag effect, between time series is a common question across various disciplines, especially when uncovering biological process. However, analyzing time series presents several…

A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…

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 this paper, we introduce a novel theoretical framework for Gaussian process regression error analysis, leveraging a function-space decomposition. Based on this framework, we develop a weighted Jacobi iterative method that utilizes…

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…

Ensemble learning is a mainstay in modern data science practice. Conventional ensemble algorithms assign to base models a set of deterministic, constant model weights that (1) do not fully account for individual models' varying accuracy…

This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…