# Uncertainty Estimation in Deep Speech Enhancement Using Complex Gaussian Mixture Models

arXiv: https://arxiv.org/abs/2212.04831 · HTML: https://mlsanity.com/paper/2212.04831/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 34 references that are in the map.
- First posted on arXiv 9 Dec 2022.

## Builds on (most cited first, 16 of 16)

- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Supervised Speech Separation Based on Deep Learning: An Overview](https://mlsanity.com/paper/1708.07524/) (2017)
- [Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow](https://mlsanity.com/paper/1802.07095/) (2018)
- [The INTERSPEECH 2020 Deep Noise Suppression Challenge: Datasets, Subjective Testing Framework, and Challenge Results](https://mlsanity.com/paper/2005.13981/) (2020)
- [On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks](https://mlsanity.com/paper/2203.09168/) (2022)
- [Overcoming Limitations of Mixture Density Networks: A Sampling and Fitting Framework for Multimodal Future Prediction](https://mlsanity.com/paper/1906.03631/) (2019)
- [Stochastic Multiple Choice Learning for Training Diverse Deep Ensembles](https://mlsanity.com/paper/1606.07839/) (2016)
- [Unsupervised Domain Adaptation for Speech Recognition via Uncertainty Driven Self-Training](https://mlsanity.com/paper/2011.13439/) (2020)
- [Uncertainty-Aware Learning from Demonstration using Mixture Density Networks with Sampling-Free Variance Modeling](https://mlsanity.com/paper/1709.02249/) (2017)
- [ProbFlow: Joint Optical Flow and Uncertainty Estimation](https://mlsanity.com/paper/1708.06509/) (2017)
- [COLD Fusion: Calibrated and Ordinal Latent Distribution Fusion for Uncertainty-Aware Multimodal Emotion Recognition](https://mlsanity.com/paper/2206.05833/) (2022)
- [A consolidated view of loss functions for supervised deep learning-based speech enhancement](https://mlsanity.com/paper/2009.12286/) (2020)
- [Nonparametric Bayesian Deep Networks with Local Competition](https://mlsanity.com/paper/1805.07624/) (2018)
- [Integrating Statistical Uncertainty into Neural Network-Based Speech Enhancement](https://mlsanity.com/paper/2203.02288/) (2022)

## Built on by (most cited first, 1 of 1)

- [Hinge-Wasserstein: Estimating Multimodal Aleatoric Uncertainty in Regression Tasks](https://mlsanity.com/paper/2306.00560/) (2023)

## Abstract (arXiv)

Single-channel deep speech enhancement approaches often estimate a single multiplicative mask to extract clean speech without a measure of its accuracy. Instead, in this work, we propose to quantify the uncertainty associated with clean speech estimates in neural network-based speech enhancement. Predictive uncertainty is typically categorized into aleatoric uncertainty and epistemic uncertainty. The former accounts for the inherent uncertainty in data and the latter corresponds to the model uncertainty. Aiming for robust clean speech estimation and efficient predictive uncertainty quantification, we propose to integrate statistical complex Gaussian mixture models (CGMMs) into a deep speech enhancement framework. More specifically, we model the dependency between input and output stochastically by means of a conditional probability density and train a neural network to map the noisy input to the full posterior distribution of clean speech, modeled as a mixture of multiple complex Gaussian components. Experimental results on different datasets show that the proposed algorithm effectively captures predictive uncertainty and that combining powerful statistical models and deep learning also delivers a superior speech enhancement performance.