Mixture Density Networks for Classification with an Application to Product Bundling

While mixture density networks (MDNs) have been extensively used for regression tasks, they have not been used much for classification tasks. One reason for this is that the usability of MDNs for classification is not clear and straightforward. In this paper, we propose two MDN-based models for classification tasks. Both models fit mixtures of Gaussians to the the data and use the fitted distributions to classify a given sample by evaluating the learnt cumulative distribution function for the given input features. While the proposed MDN-based models perform slightly better than, or on par with, five baseline classification models on three publicly available datasets, the real utility of our models comes out through a real-world product bundling application. Specifically, we use our MDN-based models to learn the willingness-to-pay (WTP) distributions for two products from synthetic sales data of the individual products. The Gaussian mixture representation of the learnt WTP distributions is then exploited to obtain the WTP distribution of the bundle consisting of both the products. The proposed MDN-based models are able to approximate the true WTP distributions of both products and the bundle well.

Predicting Remaining Useful Life using Time Series Embeddings based on Recurrent Neural Networks

We consider the problem of estimating the remaining useful life (RUL) of a system or a machine from sensor data. Many approaches for RUL estimation based on sensor data make assumptions about how machines degrade. Additionally, sensor data from machines is noisy and often suffers from missing values in many practical settings. We propose Embed-RUL: a novel approach for RUL estimation from sensor data that does not rely on any degradation-trend assumptions, is robust to noise, and handles missing values. Embed-RUL utilizes a sequence-to-sequence model based on Recurrent Neural Networks (RNNs) to generate embeddings for multivariate time series subsequences. The embeddings for normal and degraded machines tend to be different, and are therefore found to be useful for RUL estimation. We show that the embeddings capture the overall pattern in the time series while filtering out the noise, so that the embeddings of two machines with similar operational behavior are close to each other, even when their sensor readings have significant and varying levels of noise content. We perform experiments on publicly available turbofan engine dataset and a proprietary real-world dataset, and demonstrate that Embed-RUL outperforms the previously reported state-of-the-art on several metrics.