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"Mixture modeling with normalizing flows for spherical density estimati" by Tin Lok James Ng and Andrew Zammit-Mangion

Normalizing flows are objects used for modeling complicated probability density functions, and have attracted considerable interest in recent years. Many flexible families of normalizing flows have been developed. However, the focus to date has largely been on normalizing flows on Euclidean domains; while normalizing flows have been developed for spherical and other non-Euclidean domains, these are generally less flexible than their Euclidean counterparts. To address this shortcoming, in this work we introduce a mixture-of-normalizing-flows model to construct complicated probability density functions on the sphere. This model provides a flexible alternative to existing parametric, semiparametric, and nonparametric, finite mixture models. Model estimation is performed using the expectation maximization algorithm and a variant thereof. The model is applied to simulated data, where the benefit over the conventional (single component) normalizing flow is verified. The model is then applied ....

Mixture Model , Normalizing Flows , Pherical Density Estimation ,

Six HBCUS Receive Energy Department Funding for Accelerated, Inclusive Research (FAIR) Grants : The Journal of Blacks in Higher Education

Six HBCUS Receive Energy Department Funding for Accelerated, Inclusive Research (FAIR) Grants : The Journal of Blacks in Higher Education
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Reflected Diffusion Models

Diffusion models are trained to reverse a stochastic process through score matching. However, a lot of diffusion models rely on a small but critical implementation detail called thresholding. Thresholding projects the sampling process to the data support after each discretized diffusion step, stabilizing generation at the cost of breaking the theoretical framework. Interestingly, as one limits the number of steps to infinity, thresholding converges to a reflected stochastic differential equation. In this blog post, we will be discussing our recent work on Reflected Diffusion Models, which explores this connection to develop a new class of diffusion models which correctly trains for thresholded sampling and respects general boundary constraints. ....

Monte Carlo , Euler Maruyama , Reflected Diffusion , Reflected Diffusion Models , Normalizing Flows , Stable Diffusion , Solve Reverse Reflected , Constrained Langevin Dynamics , Probability Flow , Machine Learning , Geometric Deep Learning , Aaron Lou ,

"Spherical Poisson point process intensity function modeling and estima" by Tin Lok James Ng and Andrew Zammit-Mangion

Recent years have seen an increased interest in the application of methods and techniques commonly associated with machine learning and artificial intelligence to spatial statistics. Here, in a celebration of the ten-year anniversary of the journal Spatial Statistics, we bring together normalizing flows, commonly used for density function estimation in machine learning, and spherical point processes, a topic of particular interest to the journal's readership, to present a new approach for modeling non-homogeneous Poisson process intensity functions on the sphere. The central idea of this framework is to build, and estimate, a flexible bijective map that transforms the underlying intensity function of interest on the sphere into a simpler, reference, intensity function, also on the sphere. Map estimation can be done efficiently using automatic differentiation and stochastic gradient descent, and uncertainty quantification can be done straightforwardly via nonparametric bootstrap. W ....

Pacific Ocean , Spatial Statistics , North Pacific , Exponential Map , Maximum Likelihood , Normalizing Flows , Adial Flows , Rapping Potential Functions ,