# Neural Network based Explicit Mixture Models and Expectation-maximization based Learning

arXiv: https://arxiv.org/abs/1907.13432 · HTML: https://mlsanity.com/paper/1907.13432/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2019.

## Built on by (most cited first, 3 of 3)

- [Robust Classification using Hidden Markov Models and Mixtures of Normalizing Flows](https://mlsanity.com/paper/2102.07284/) (2021)
- [Normalizing Flow based Hidden Markov Models for Classification of Speech Phones with Explainability](https://mlsanity.com/paper/2107.00730/) (2021)
- [Cohort Organized Learning: Clustering Through Agreement](https://mlsanity.com/paper/2606.21743/) (2026)

## Abstract (arXiv)

We propose two neural network based mixture models in this article. The proposed mixture models are explicit in nature. The explicit models have analytical forms with the advantages of computing likelihood and efficiency of generating samples. Computation of likelihood is an important aspect of our models. Expectation-maximization based algorithms are developed for learning parameters of the proposed models. We provide sufficient conditions to realize the expectation-maximization based learning. The main requirements are invertibility of neural networks that are used as generators and Jacobian computation of functional form of the neural networks. The requirements are practically realized using a flow-based neural network. In our first mixture model, we use multiple flow-based neural networks as generators. Naturally the model is complex. A single latent variable is used as the common input to all the neural networks. The second mixture model uses a single flow-based neural network as a generator to reduce complexity. The single generator has a latent variable input that follows a Gaussian mixture distribution. We demonstrate efficiency of proposed mixture models through extensive experiments for generating samples and maximum likelihood based classification.