Regression with Uncertainty Quantification in Large Scale Complex Data

TL;DR

This paper introduces a simplified Mixture Density Network approach for uncertainty quantification in large-scale regression tasks, demonstrating improved predictive performance and practical applications in finance and age estimation.

Contribution

A novel one-shot MDN-based method for uncertainty quantification that scales to large, complex datasets and outperforms existing techniques in various regression tasks.

Findings

Improved predictive log-likelihood and RMSE on benchmark datasets

Effective anomaly detection in stock price time-series

Successful uncertainty estimation in age prediction from images

Abstract

While several methods for predicting uncertainty on deep networks have been recently proposed, they do not readily translate to large and complex datasets. In this paper we utilize a simplified form of the Mixture Density Networks (MDNs) to produce a one-shot approach to quantify uncertainty in regression problems. We show that our uncertainty bounds are on-par or better than other reported existing methods. When applied to standard regression benchmark datasets, we show an improvement in predictive log-likelihood and root-mean-square-error when compared to existing state-of-the-art methods. We also demonstrate this method's efficacy on stochastic, highly volatile time-series data where stock prices are predicted for the next time interval. The resulting uncertainty graph summarizes significant anomalies in the stock price chart. Furthermore, we apply this method to the task of age estimation from the challenging IMDb-Wiki dataset of half a million face images. We successfully predict the uncertainties associated with the prediction and empirically analyze the underlying causes of the uncertainties. This uncertainty quantification can be used to pre-process low quality datasets and further enable learning.