AdaScale-TuRBO improves high-dimensional Bayesian optimization by dynamically scaling the GP lengthscale.
problem Inappropriate lengthscale design in TuRBO's local GP model causes suboptimal performance in high dimensions.
method Proposes AdaScale-TuRBO, which scales the GP lengthscale with both problem dimension and trust region size.
result AdaScale-TuRBO robustly outperforms standard TuRBO and other methods on synthetic and real-world tasks.
While Bayesian neural networks have many appealing characteristics, current priors do not easily allow users to specify basic properties such as expected lengthscale or amplitude variance. In this work, we introduce Poisson Process Radial Basis Function Networks, a novel prior that is able to encode amplitude stationar…
New method for causal inference with observed covariates improves learning rates.
problem Causal inference with observed covariates in nonparametric instrumental variable regression.
method Introduces novel Fourier measure for partial smoothing and adapts kernel lengthscales for anisotropic smoothness.
result Upper and lower learning rates for KIV-O show interpolation between NPIV and NPR rates.
A novel GP architecture, Thin and Deep GP, learns lower-dimensional representations without losing interpretability.
problem Challenges in selecting appropriate kernel for Gaussian processes.
method Proposes a novel synthesis of deep and shallow GP approaches, parameterizing lengthscale in a way that maintains interpretability and learns lower-dimensional embeddings.
result TDGP discovers lower-dimensional manifolds in input data, performs well in benchmark datasets, and behaves well with increasing layers.
Vanilla Bayesian optimization performs well in high dimensions.
problem Bayesian optimization's poor performance in high-dimensional problems.
method Identified and addressed degeneracies, proposed scaling of Gaussian process lengthscale prior.
result Vanilla Bayesian optimization outperforms existing algorithms in high-dimensional tasks.
Researchers use Gaussian processes with non-stationary kernels to model precipitation patterns in the Upper Indus Basin.
problem Uncertainty in precipitation patterns in the Upper Indus Basin, Himalayas.
method Proposes Gaussian processes with structured non-stationary kernels to model precipitation patterns, accounting for spatial variation with a latent Gaussian process.
result The proposed model adapts to varying precipitation patterns across distinct topography and outperforms stationary models in ablation experiments.
We present a novel approach for fully non-stationary Gaussian process regression (GPR), where all three key parameters -- noise variance, signal variance and lengthscale -- can be simultaneously input-dependent. We develop gradient-based inference methods to learn the unknown function and the non-stationary model param…
The paper analyzes the statistical cost of tuning kernel hyperparameters in robust regression.
problem Finding the best interpolant from a class of kernels with unknown hyperparameters under adversarial noise.
method Finite-sample guarantees, subsampling guarantee for linear regression, ε-net argument for discretizing kernel parameterizations.
result Hyperparameter optimization increases sample complexity by just a logarithmic factor, compared to known parameters.
Early approaches to multiple-output Gaussian processes (MOGPs) relied on linear combinations of independent, latent, single-output Gaussian processes (GPs). This resulted in cross-covariance functions with limited parametric interpretation, thus conflicting with the ability of single-output GPs to understand lengthscal…
New method speeds up sparse Gaussian processes for large datasets.
problem Efficiently modeling large datasets with many inducing variables.
method Projecting a GP onto B-spline basis functions for sparse linear algebra.
result Efficiently models fast-varying spatial phenomena with tens of thousands of inducing variables.
Deep-HGP uses Bayesian nonparametric approach for complex data regression.
problem Complex data regression with compositional structures.
method Deep Gaussian processes with a squared-exponential kernel, data-driven lengthscale parameters.
result Posterior distribution optimally recovers unknown true regression curve in terms of quadratic loss.
We propose a generic spatiotemporal event forecasting method, which we developed for the National Institute of Justice's (NIJ) Real-Time Crime Forecasting Challenge. Our method is a spatiotemporal forecasting model combining scalable randomized Reproducing Kernel Hilbert Space (RKHS) methods for approximating Gaussian …
Develops a new MCMC-based Wishart prior for Gaussian Process covariance matrix.
problem Difficult inference for multivariate Gaussian Processes with multiple lengthscale parameters.
method Introduces a self-assembled Wishart prior and uses MCMC for Bayesian inference on kernel hyperparameters.
result Demonstrates the effectiveness of the new prior in GP-based learning with empirical results.
Deep neural nets optimize kernel parameters for non-parametric two-sample tests.
problem Determining if two samples come from the same distribution.
method Deep kernels trained to maximize test power, adapting to distribution smoothness and shape.
result Deep kernels outperform simpler kernels in high dimensions and complex data.
The paper proposes a method to learn hyperparameters without validation sets, improving efficiency and accuracy.
problem Training large models on limited data to avoid overfitting and reduce validation set usage.
method Gradient-based learning of hyperparameters via a data-emphasized evidence lower bound (ELBO) objective.
result The data-emphasized ELBO reduces hyperparameter search time from 88+ hours to under 3 hours while maintaining comparable accuracy.
A fast and scalable method for variable selection in high-dimensional Gaussian processes.
problem Inefficient variable selection in high-dimensional Gaussian processes.
method Developed a fast and scalable variational inference algorithm for spike and slab Gaussian processes.
result Consistently outperforms vanilla and sparse variational GPs while retaining similar runtimes.
Maximum likelihood estimation fails to be well-posed in Gaussian process regression.
problem Establishing well-posedness of maximum likelihood estimation in Gaussian process regression.
method Analyzing the conditions under which maximum likelihood estimation is not Lipschitz in the data with respect to the Hellinger distance.
result Maximum likelihood estimation is not well-posed in the noiseless data setting for any Gaussian process with a stationary covariance function whose lengthscale parameter is estimated using maximum likelihood.
We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike, graphs these have some counter-intuitive properties, specifically in the limit of lar…
Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of kernel mean embeddings of probability measures. For characteristic kernels, which inc…
Develops a theoretical framework for scalable Gaussian Process regression methods.
problem Limited scalability of Gaussian Process regression for large datasets.
method Introduces and analyzes Nearest Neighbour Gaussian Process (NNGP) and scalable GPnn methods.
result Derives almost sure pointwise limits for predictive criteria and proves risk minimax rates.
Paper analyzes consistency of Bayesian and machine learning methods for hierarchical parameter estimation.
problem Learning hierarchical parameters in complex and real-world problems.
method Empirical Bayes and Kernel Flow approaches.
result Consistency results for Matérn-like model on the torus, and comparison of algorithms.
BONSAI optimizes parameters while respecting a default configuration, reducing unnecessary changes.
problem Standard BO pushes weakly relevant parameters to the boundary, making it hard to distinguish between important and spurious changes.
method BONSAI is a default-aware BO policy that prunes low-impact deviations from a default configuration while controlling acquisition value loss.
result BONSAI matches the GP-UCB regret rate while recovering the minimal-ℓ0 solution, reducing the number of non-default parameters in recommended configurations. Gaussian processes model sparse data in astrophysics and chemistry.
problem Scarcity of data in high-energy astrophysics and synthetic chemistry.
method Gaussian processes for uncertainty-aware predictions and inferences.
result GPs enable predictions and model latent emission from black holes and molecules.
This paper shows how infinitely wide Tensor Networks converge to Gaussian Processes.
problem Understanding the relationship between Tensor Networks and Gaussian Processes.
method Analyzing the infinite-width limit of Tensor Networks and comparing them to Gaussian Processes.
result Infinitely wide Tensor Networks converge to Gaussian Processes, proving their equivalence.