Probabilistic Regression with Huber Distributions

TL;DR

This paper introduces a robust probabilistic regression method using Huber-inspired distributions and a novel matrix parameterization, improving object position estimation in neural networks with outlier resistance.

Contribution

It presents a new Huber-inspired probability distribution and a matrix parameterization technique for robust, invariant object position regression with neural networks.

Findings

Achieves performance comparable or better than non-heatmap methods on pose datasets.

Demonstrates robustness to outliers and bounded gradients.

Provides publicly available code for reproducibility.

Abstract

In this paper we describe a probabilistic method for estimating the position of an object along with its covariance matrix using neural networks. Our method is designed to be robust to outliers, have bounded gradients with respect to the network outputs, among other desirable properties. To achieve this we introduce a novel probability distribution inspired by the Huber loss. We also introduce a new way to parameterize positive definite matrices to ensure invariance to the choice of orientation for the coordinate system we regress over. We evaluate our method on popular body pose and facial landmark datasets and get performance on par or exceeding the performance of non-heatmap methods. Our code is available at github.com/Davmo049/Public_prob_regression_with_huber_distributions