Adaptive Kernel Selection for Stein Variational Gradient Descent

A new framework has been developed that integrates sparse variational Gaussian process inference with Kolmogorov-Arnold Networks (KANs), enhancing their capability for uncertainty quantification in scientific machine learning applications. This approach allows for scalable Bayesian inference with reduced computational complexity, addressing a significant limitation of traditional methods.

A new paper has been published on arXiv detailing an unsupervised learning approach for density estimation using a topology-based loss function. This method aims to automate the selection of the optimal kernel bandwidth, a critical hyperparameter that influences the bias-variance trade-off in density estimation, particularly in high-dimensional data where visualization is challenging.

A new study introduces Neural Surrogate Hamiltonian Monte Carlo (HMC), which leverages neural likelihoods to enhance Bayesian inference methods, particularly Markov Chain Monte Carlo (MCMC). This approach addresses the computational challenges associated with likelihood function evaluations by employing machine learning techniques to streamline the process. The method demonstrates significant advantages, including improved efficiency and robustness in simulations.