# Uncertainty Flow Facilitates Zero-Shot Multi-Label Learning in Affective Facial Analysis
## 1 Introduction
### Uncertainty Flow in Zero-Shot Multi-Label Learning  
In combating with the scarcity of multi-label training data, unlike conventional approaches, we resort on inductive transfer learning [7] that allows the knowledge to be distilled from a source task, i.e., a single-label affective learning task, and to be applied on a similar but more complex target task, i.e., a multi-label affective discrimination task. But instead of transferring the mere knowledge, i.e., the model parameters between source and target tasks, we propose the **Uncertainty Flow** framework to transfer the model uncertainty between tasks. The crux of our proposed **Uncertainty Flow** is on the quality of uncertainty quantification. To measure this quantity, instead of non-Bayesian neural networks, Bayesian neural networks are employed in quantification of model uncertainty. Bayesian neural network--a recapitulation of a neural network under the direct probabilistic modelling--replaces the single point estimate of the model parameters with the distribution of the parameter. It allows the production of real probabilistic outputs, i.e., model uncertainty [8]. Contrast with conventional implementations on Bayesian neural networks, we further provide our suggestion on the usage of weakly informative priors, e.g., uniform and Cauchy prior, in perfecting the final production of model uncertainty.  
The article is organised as following: we chiefly introduce the proposed **Uncertainty Flow** framework in sketch along with the description of four core components, e.g., Bayesian neural networks (More precisely, two hierarchical Bayesian neural networks); our suggested weakly informative priors; the quantification of model uncertainty; and three prediction related uncertainty indexes, e.g., **soft-max uncertainty**, **pure uncertainty** and **uncertainty plus**. To demonstrate the effectiveness of our proposed **Uncertainty Flow** framework, we then present the results from a large-scale comparative experiment. This large-scale experiment contains three levels of comparisons, i.e., the comparison among models, the comparison among different priors, and the comparison among three uncertainty indexes. The observed pronounced discriminability, i.e., 20 to 30 percent performance enhancement, proved the effectiveness of the proposed **Uncertainty Flow** framework.  
This pioneer research should be credited under following contributions: (1) We develop a novel inductive transfer learning [3] based computational framework that allows multi-label affective prediction on single evoked source. (2) Unlike conventional inductive transfer learning, the proposed **Uncertainty Flow** focuses on model uncertainty rather than the mere model weights in knowledge distillation. (3) To obtain the model uncertainty, rather than the conventional used informative priors, the usage on weakly informative priors, e.g., uniform and Cauchy prior has also been proposed. (4) To further improve the discriminability of the **Uncertainty Flow**, two advanced prediction related uncertainty indexes, i.e., **pure uncertainty**, and **uncertainty plus** are also suggested in this research.