Multi-output is essential in machine learning that it might suffer from nonconforming residual distributions, i.e., the multi-output residual distributions are not conforming to the expected distribution. In this paper, we propose "Wrapped Loss Function" to wrap the original loss function to alleviate the problem. This wrapped loss function acts just like the original loss function that its gradient can be used for backpropagation optimization. Empirical evaluations show wrapped loss function has advanced properties of faster convergence, better accuracy, and improving imbalanced data.
@cite_4: Numerous deep learning applications benefit from multitask learning with multiple regression and classification objectives. In this paper we make the observation that the performance of such systems is strongly dependent on the relative weighting between each task's loss. Tuning these weights by hand is a difficult and expensive process, making multi-task learning prohibitive in practice. We propose a principled approach to multi-task deep learning which weighs multiple loss functions by considering the homoscedastic uncertainty of each task. This allows us to simultaneously learn various quantities with different units or scales in both classification and regression settings. We demonstrate our model learning per-pixel depth regression, semantic and instance segmentation from a monocular input image. Perhaps surprisingly, we show our model can learn multi-task weightings and outperform separate models trained individually on each task.
@cite_1: 
@cite_7: This report presents our audio event detection system submitted for Task 2, "Detection of rare sound events", of DCASE 2017 challenge. The proposed system is based on convolutional neural networks (CNNs) and deep neural networks (DNNs) coupled with novel weighted and multi-task loss functions and state-of-the-art phase-aware signal enhancement. The loss functions are tailored for audio event detection in audio streams. The weighted loss is designed to tackle the common issue of imbalanced data in background foreground classification while the multi-task loss enables the networks to simultaneously model the class distribution and the temporal structures of the target events for recognition. Our proposed systems significantly outperform the challenge baseline, improving F-score from 72.7 to 90.0 and reducing detection error rate from 0.53 to 0.18 on average on the development data. On the evaluation data, our submission obtains an average F1-score of 88.3 and an error rate of 0.22 which are significantly better than those obtained by the DCASE baseline (i.e. an F1-score of 64.1 and an error rate of 0.64).
For the multi-task learning, there are two or more related tasks jointly learned, and their loss functions are combined into a loss function. Then the weights can be added to each tasks to generate a loss function. Huy @cite_7 uses convolutional neural networks and deep neural network coupled with weighted loss function to solve audio event detection, and Sankaran @cite_1 shows that the combination of 3 techniques: LSCSR-initialization, Multi-task training and Class-weighted cross entropy training gives the best results on keyword spotting. Unlike above cases use pre-set weights, Kendall @cite_4 applies IRLS to find maximum likelihood estimates of multi-task learning model for scene geometry and semantics.