#gaussian-process — Public Fediverse posts

This blog post about creating Gaussian processes from scratch in Python helped me to make sense it. https://peterroelants.github.io/posts/gaussian-process-tutorial/

#gaussianProcess

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A Gaussian process is a random function, which for me was hard to understand. How do you get these smooth functions if the value of the function at each x position is random?

Now it's making more sense to me. You can pull the whole function out of a hat! The distribution has correlations that encode relationships between the different dimensions (x values). So even though the whole function is random, adjacent points on the function could be closely related.

#gaussianProcess
#TIL
#randomFunction

I’m excited to announce our #SIGGRAPHAsia2025 paper, which makes #rendering of #GaussianProcess implicit surfaces (GPISes) practical:

Project page: https://cs.dartmouth.edu/~wjarosz/publications/xu25practical.html

We achieve this with a novel #procedural noise formulation and by enabling next-event estimation for specular BRDFs. [1/7]

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

https://arxiv.org/abs/2305.13552

#arxivfeed :

"Neural network with optimal neuron activation functions based on additive Gaussian process regression"
https://arxiv.org/abs/2301.05567

#MachineLearning #DeepLearning #GaussianProcess

#arxivfeed :

"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

@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

#arxivfeed :

"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:

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#BayesianStatistics #Ecology

@Inference Hmmm how about #gaussianprocess instead 🤔