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A generic Mixture Density Networks (MDN) implementation for distribution and uncertainty estimation by using Keras (TensorFlow)
| Date | Stars |
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| 2026-07-24 | 361 |
| 2026-07-25 | 362 |
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| 2026-08-06 | 362 |
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# Mixture Density Networks implementation for distribution and uncertainty estimation A generic Mixture Density Networks implementation for distribution and uncertainty estimation by using Keras (TensorFlow) This repository is a collection of [Jupyter](https://jupyter.org/) notebooks intended to solve a lot of problems in which we want to predict a probability distribution by using Mixture Density Network avoiding a NaN problem and other derived problems of the model proposed by [Bishop, C. M. (1994)](http://eprints.aston.ac.uk/373/). The second major objective of this repository is to look for ways to predict uncertainty by using artificial neural networks. The whole code, until 20.1.2017, is the result of a final Master's Thesis of the [Master's Degree in Artificial Intelligence](http://www.upc.edu/master/fitxa_master.php?id_estudi=50&lang=esp) supervised by Jordi Vitrià, PhD. The [Master's Thesis report](https://github.com/axelbrando/Mixture-Density-Networks-for-distribution-and-uncertainty-estimation/blob/master/ABrando-MDN-MasterThesis.pdf) is published in this repository in a PDF format but my idea is to realize a web view of the final master's work in the coming days. To summary all the contents I explained in the report, it is possible to consult the [slides of the presentation](https://github.com/axelbrando/Mixture-Density-Networks-for-distribution-and-uncertainty-estimation/blob/master/ABrando-MDN-Slides.pdf). Any contribution or idea to continue the lines of the proposed work will be very welcome. <p align="center"><img src="https://cdn.rawgit.com/axelbrando/Mixture-Density-Networks-for-distribution-and-uncertainty-estimation/cd4d8e9c/svgs/f442dfcf42c5ca5d6c9b96753cde8768.svg" align=middle width=645.87435pt height=348.58725pt/> </p> <p align="center"> <em>Representation of the Mixture Density Network model. The output of the feed-forward neural network determine the parameters in a mixture density model. Therefore, the mixture density model represents the conditional probability density function of the target variables conditioned on the input vector of the neural network.</em> </p> ## Implemented tricks and techniques > - Log-sum-exp trick. > - ELU+1 representation function for variance scale parameter proposed by us in the Master's Thesis that I will link when it is published. > - Clipping of the mixing coefficient parameter value. > - Mean log Gaussian likelihood proposed by [Bishop](http://eprints.aston.ac.uk/373/). > - Mean log Laplace likelihood proposed by us in the Master's Thesis that I will link when it is published. > - Fast Gradient Sign Method to produce Adversarial Training proposed [by Goodfellow et al](https://arxiv.org/abs/1412.6572). > - Modified version of Adversarial Training proposed by [Nokland](https://arxiv.org/abs/1510.04189). > - Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles implementation proposed by [Lakshminarayanan et a](https://arxiv.org/abs/1612.01474). ## Some Keras algorithms used > - RMSProp optimisation algorithm. > - Adam optimisation algorithm. > - Gradient Clipping > - Batch normalisation ## Implemented visualisation functionalities > - Generic implementation to visualise mean and variance (as errorbar) of the distribution with maximum mixing coefficient of of the MDN. > - Generic implementation to visualise mean and variance (as errorbar) of all the distributions of of the MDN. > - Generic implementation to visualise all the probability density function as a *heat graphic* for 2D problems. > - Generic implementation to visualise the original 3D surface and visualise the mean of the distribution of the mixture through a sampling process. > - Adversarial data set visualisation proposed by us in the Master's Thesis that I will link when it is published. ## Notebooks (Currently tested on Keras (1.1.0) and TensorFlow (0.11.0rc2) #### [Introduction to MDN models and generic implementation of MDN](https://github.com/axelbrando/Mixture-Densit
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matched fp:5819ea8711fc159e, topic:deep-learning, topic:neural-network, topic:tensorflow