相关论文: Nonlinear Planning Model With a Gaussian Criterion…

We propose a Gaussian variational inference framework for the motion planning problem. In this framework, motion planning is formulated as an optimization over the distribution of the trajectories to approximate the desired trajectory…

We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…

There are so many models in the literature that it is difficult for practitioners to decide which combinations are likely to be effective for a new task. This paper attempts to address this question by capturing relationships among…

The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear…

In consumer theory, ranking available objects by means of preference relations yields the most common description of individual choices. However, preference-based models assume that individuals: (1) give their preferences only between pairs…

Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true…

Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime. We establish an explicit equivalence between GPs and a class of linear diffusion models,…

We develop a class of nearest-neighbor mixture models that provide direct, computationally efficient, probabilistic modeling for non-Gaussian geospatial data. The class is defined over a directed acyclic graph, which implies conditional…

This paper is devoted to filtering, smoothing, and prediction of polynomial processes that are partially observed. These problems are known to allow for an explicit solution in the simpler case of linear Gaussian state space models. The key…

Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…

Margin-based structured prediction commonly uses a maximum loss over all possible structured outputs \cite{Altun03,Collins04b,Taskar03}. In natural language processing, recent work \cite{Zhang14,Zhang15} has proposed the use of the maximum…

Gaussian process (GP) predictors are an important component of many Bayesian approaches to machine learning. However, even a straightforward implementation of Gaussian process regression (GPR) requires O(n^2) space and O(n^3) time for a…

We propose a novel planning technique for satisfying tasks specified in temporal logic in partially revealed environments. We define high-level actions derived from the environment and the given task itself, and estimate how each action…

Gaussian processes are important models in the field of probabilistic numerics. We present a procedure for optimizing Mat\'ern kernel temporal Gaussian processes with respect to the kernel covariance function's hyperparameters. It is based…

Nonparametric Bayesian approaches based on Gaussian processes have recently become popular in the empirical learning community. They encompass many classical methods of statistics, like Radial Basis Functions or various splines, and are…

We study the problem of selecting $k$ experiments from a larger candidate pool, where the goal is to maximize mutual information (MI) between the selected subset and the underlying parameters. Finding the exact solution is to this…

The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current…

In this paper we introduce a novel online time series forecasting model we refer to as the pM-GP filter. We show that our model is equivalent to Gaussian process regression, with the advantage that both online forecasting and online…

Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…

We study parameter estimation in linear Gaussian covariance models, which are $p$-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex…