Working Papers

Early-stage working papers

Looking for collaborators

My work currently is developing a Geometric Gaussian Mixture Program.

It is always interesting either to find theoretic tools like Measure Theoretic Probability to help with the program itself or to find applications in seemingly separate fields like Computer Graphics and Stochastic Geometric Control.

If you share the same sentiment about collaboration then just drop me a line at: ali.darijani@iosb.fraunhofer.de .

3 working papers · Early-stage drafts and work in progress. Ranging from abstracts to preprint ready.

Dirichlet Gaussian Distributions on Embedded Simplices

Ali Darijani
Draft
Abstract
We derive a geometry-independent Gaussian approximation for distributions near embedded simplices, combining arbitrary-parameter Dirichlet distributions with in- dependent Gaussian noise in orthogonal normal spaces. The optimal ambient Gaussian matches the mean and covariance, yielding an explicit minimum forward KL divergence depending only on intrinsic dimension and Dirichlet parameters. For finite mixtures with shared weights, we prove a global upper bound given by the weighted sum of component- wise divergences. In the uniform case, this bound depends only on intrinsic dimension, independently of ambient dimension, simplex geometry, and normal covariances.
LaTeX Source PDF

Dwarf Based Probabilistic Scientific Computing Using Gaussian Mixture

Ali Darijani
Draft
Abstract
We like to reduce as many as problems as we can in the 7 dwaarves form and by exploiting the Schwartz space characteristics of the Gaussian solve them quasi piece wise linear like.

Implicit Diffeomorphism Using Gaussian Mixture

Ali Darijani
Draft
Abstract
If a domain is sufficiently representedby a Gaussian Mixture over a triangulation and the mapping is linearized over a triangulation then we can implicitely have joint Probability Density Function of the input and the output domain as a Gaussian Mixture due to the Schwartz property of the Gaussian Mixture. Our aim is to make this intuition rigorous or at least computational.