We propose a new family of probability densities that have closed form normalising constants. Our densities use two layer neural networks as parameters, and strictly generalise exponential families. We show that the squared norm can be integrated in closed form, resulting in the normalizing constant. We call the densities Squared Neural Family (#SNEFY), which are closed under conditioning.
Accepted at #NeurIPS2023. #MachineLearning #Bayesian #GaussianProcess
"Neural network with optimal neuron activation functions based on additive Gaussian process regression"
https://arxiv.org/abs/2301.05567
"Dynamic Bayesian Learning and Calibration of Spatiotemporal Mechanistic Systems"
https://arxiv.org/abs/2208.06528
#DynamicalSystems #ModelCalibration #Bayesian #ParameterEstimation #GaussianProcess
Take the idea of random Fourier features, as applied to #GaussianProcess regression in #MachineLearning. There is a method in the probabilistic numerics textbook about Gaussian quadrature (same Gauss, different method) which gives good convergence with respect to the spectrum of a function. Show that a high quality #kernel (low rank approximation) can be computed efficiently (sublinear in the number of training points).
https://www.jmlr.org/papers/v23/21-0030.html
Been trying out a lot of #GaussianProcess libraries in #python lately. For what my opinion is worth, I'm really enjoying using GPFlow.
It seems to have a good balance that you can customize the things you want, and not have to over-worry about the rest. Documentation includes simple examples to very advanced. Comprehensive enough for a guy like me to get a model up and running in a couple hours on real data.
@FCAI Update on Zheyang’s status: The opponent got there on the last minute, gave an enlightening view of the position of the thesis in #BayesianModeling and #GaussianProcess es, and asked a set of broad and challenging questions. Zheyand did outstandingly well, with still some unsolved questions which he will be eager to pursue when on the job market at some point. Big congrats Zheyang Shen and many thanks opponent Chris Oates! #PhD #AaltoUniversity @FCAI
"Towards Improved Learning in Gaussian Processes: The Best of Two Worlds"
https://arxiv.org/abs/2211.06260
#inference #GaussianProcess #ExpectationPropagation #VariationalInference #classification
Anyone know of an approach to construct a #GaussianProcess prior over strictly monotonic functions? #MachineLearning #Bayesian
I have a variety of #tutorials posted on my website (https://peter-stewart.github.io/posts/) on a variety of topics, including a series on classic ecological #models in #Stan and #RStats, an #occupancy model which handles spatial autocorrelation using a #GaussianProcess, and a variety of useful Windows batch files for dealing with #CameraTrap images.
Here is a quick #thread 🧵 with links to the individual posts:
1/n
@Inference Hmmm how about #gaussianprocess instead 🤔
