Related papers: Linearly Constrained Gaussian Processes with Bound…
In the post-Dennard era, optimizing embedded systems requires navigating complex trade-offs between energy efficiency and latency. Traditional heuristic tuning is often inefficient in such high-dimensional, non-smooth landscapes. In this…
In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…
Active learning methods for neural networks are usually based on greedy criteria which ultimately give a single new design point for the evaluation. Such an approach requires either some heuristics to sample a batch of design points at one…
Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…
We consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. On the basis of a simple expression for the generalization error, in terms of the eigenvalue…
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…
Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian…
Bayesian neural networks (BNNs) have recently gained popularity due to their ability to quantify model uncertainty. However, specifying a prior for BNNs that captures relevant domain knowledge is often extremely challenging. In this work,…
Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian…
Automatic forecasting is the task of receiving a time series and returning a forecast for the next time steps without any human intervention. Gaussian Processes (GPs) are a powerful tool for modeling time series, but so far there are no…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure,…
Bayesian Networks may be appealing for clinical decision-making due to their inclusion of causal knowledge, but their practical adoption remains limited as a result of their inability to deal with unstructured data. While neural networks do…
We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…
In large-scale Bayesian inverse problems, it is often necessary to apply approximate forward models to reduce the cost of forward model evaluations, while controlling approximation quality. In the context of Bayesian inverse problems with…
Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as…
The Bayesian learning rule is a natural-gradient variational inference method, which not only contains many existing learning algorithms as special cases but also enables the design of new algorithms. Unfortunately, when variational…
We propose a practical Bayesian optimization method using Gaussian process regression, of which the marginal likelihood is maximized where the number of model selection steps is guided by a pre-defined threshold. Since Bayesian optimization…
Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…
Bayesian optimization (BO) has become a popular strategy for global optimization of expensive real-world functions. Contrary to a common expectation that BO is suited to optimizing black-box functions, it actually requires domain knowledge…