Related papers: The Dynamical Gaussian Process Latent Variable Mod…

Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications.…

We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…

Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the…

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…

Gaussian process-based latent variable models are flexible and theoretically grounded tools for nonlinear dimension reduction, but generalizing to non-Gaussian data likelihoods within this nonlinear framework is statistically challenging.…

The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension,…

We study time uncertainty-aware modeling of continuous-time dynamics of interacting objects. We introduce a new model that decomposes independent dynamics of single objects accurately from their interactions. By employing latent Gaussian…

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…

Learning identifiable representations and models from low-level observations is helpful for an intelligent spacecraft to complete downstream tasks reliably. For temporal observations, to ensure that the data generating process is provably…

Latent Gaussian models (LGMs) are perhaps the most commonly used class of models in statistical applications. Nevertheless, in areas ranging from longitudinal studies in biostatistics to geostatistics, it is easy to find datasets that…

Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…

Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…

Over the last years, significant advances have been made in robotic manipulation, but still, the handling of non-rigid objects, such as cloth garments, is an open problem. Physical interaction with non-rigid objects is uncertain and complex…

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…

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…

This paper proposes an online learning method of Gaussian process state-space model (GP-SSM). GP-SSM is a probabilistic representation learning scheme that represents unknown state transition and/or measurement models as Gaussian processes…

Despite the availability of ever more data enabled through modern sensor and computer technology, it still remains an open problem to learn dynamical systems in a sample-efficient way. We propose active learning strategies that leverage…

One's ability to learn a generative model of the world without supervision depends on the extent to which one can construct abstract knowledge representations that generalize across experiences. To this end, capturing an accurate…