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Found 15 papers, 9 papers with code
Consistent Validation for Predictive Methods in Spatial Settings
Unfortunately, classical approaches for validation fail to handle mismatch between locations available for validation and (test) locations where we want to make predictions.
Gaussian processes at the Helm(holtz): A more fluid model for ocean currents
Given sparse observations of buoy velocities, oceanographers are interested in reconstructing ocean currents away from the buoys and identifying divergences in a current vector field.
Sparse Gaussian Process Hyperparameters: Optimize or Integrate?
In this work we propose an algorithm for sparse Gaussian process regression which leverages MCMC to sample from the hyperparameter posterior within the variational inducing point framework of Titsias (2009).
Numerically Stable Sparse Gaussian Processes via Minimum Separation using Cover Trees
For low-dimensional tasks such as geospatial modeling, we propose an automated method for computing inducing points satisfying these conditions.
A Note on the Chernoff Bound for Random Variables in the Unit Interval
The Chernoff bound is a well-known tool for obtaining a high probability bound on the expectation of a Bernoulli random variable in terms of its sample average.
Wide Mean-Field Bayesian Neural Networks Ignore the Data
Finally, we show that the optimal approximate posterior need not tend to the prior if the activation function is not odd, showing that our statements cannot be generalized arbitrarily.
Barely Biased Learning for Gaussian Process Regression
We suggest a method that adaptively selects the amount of computation to use when estimating the log marginal likelihood so that the bias of the objective function is guaranteed to be small.
How Tight Can PAC-Bayes be in the Small Data Regime?
Interestingly, this lower bound recovers the Chernoff test set bound if the posterior is equal to the prior.
Tighter Bounds on the Log Marginal Likelihood of Gaussian Process Regression Using Conjugate Gradients
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.
Understanding Variational Inference in Function-Space
Then, we propose (featurized) Bayesian linear regression as a benchmark for `function-space' inference methods that directly measures approximation quality.
Convergence of Sparse Variational Inference in Gaussian Processes Regression
Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling.
Variational Orthogonal Features
We present a construction of features for any stationary prior kernel that allow for computation of an unbiased estimator to the ELBO using $T$ Monte Carlo samples in $\mathcal{O}(\tilde{N}T+M^2T)$ and in $\mathcal{O}(\tilde{N}T+MT)$ with an additional approximation.
Bandit optimisation of functions in the Matérn kernel RKHS
We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Mat\'ern kernel with smoothness parameter $\nu$ over the domain $[0, 1]^d$ under noisy bandit feedback.
On the Expressiveness of Approximate Inference in Bayesian Neural Networks
While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood.
Rates of Convergence for Sparse Variational Gaussian Process Regression
Excellent variational approximations to Gaussian process posteriors have been developed which avoid the $\mathcal{O}\left(N^3\right)$ scaling with dataset size $N$.
