# Robust Classification using Hidden Markov Models and Mixtures of Normalizing Flows

arXiv: https://arxiv.org/abs/2102.07284 · HTML: https://mlsanity.com/paper/2102.07284/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 18 references that are in the map.
- First posted on arXiv 15 Feb 2021.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Attention-Based Models for Speech Recognition](https://mlsanity.com/paper/1506.07503/) (2015)
- [Light Gated Recurrent Units for Speech Recognition](https://mlsanity.com/paper/1803.10225/) (2018)
- [The PyTorch-Kaldi Speech Recognition Toolkit](https://mlsanity.com/paper/1811.07453/) (2018)
- [Normalizing Flows: An Introduction and Review of Current Methods](https://mlsanity.com/paper/1908.09257/) (2019)
- [Powering Hidden Markov Model by Neural Network based Generative Models](https://mlsanity.com/paper/1910.05744/) (2019)
- [Neural Network based Explicit Mixture Models and Expectation-maximization based Learning](https://mlsanity.com/paper/1907.13432/) (2019)

## Built on by (most cited first, 4 of 4)

- [Listen, Denoise, Action! Audio-Driven Motion Synthesis with Diffusion Models](https://mlsanity.com/paper/2211.09707/) (2022)
- [Constructing Neural Network-Based Models for Simulating Dynamical Systems](https://mlsanity.com/paper/2111.01495/) (2021)
- [OverFlow: Putting flows on top of neural transducers for better TTS](https://mlsanity.com/paper/2211.06892/) (2022)
- [Normalizing Flow based Hidden Markov Models for Classification of Speech Phones with Explainability](https://mlsanity.com/paper/2107.00730/) (2021)

## Abstract (arXiv)

We test the robustness of a maximum-likelihood (ML) based classifier where sequential data as observation is corrupted by noise. The hypothesis is that a generative model, that combines the state transitions of a hidden Markov model (HMM) and the neural network based probability distributions for the hidden states of the HMM, can provide a robust classification performance. The combined model is called normalizing-flow mixture model based HMM (NMM-HMM). It can be trained using a combination of expectation-maximization (EM) and backpropagation. We verify the improved robustness of NMM-HMM classifiers in an application to speech recognition.