# Deep Active Learning for Computer Vision Tasks: Methodologies, Applications, and Challenges
## 4 Deep Active Learning Methods
### Deep Active Learning for CNNs
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Type** & **Methodology** & **Equation** \\ \hline \multirow{6}{*}{MC dropout} & \(\rhd\) In practice, the MC dropout usually trains the CNN with the labeled data pool \(L\) with dropout. & \(p(y\mid x,L)=\frac{1}{L}\sum_{t=1}^{T}p(y\mid x,\mathcal{M}_{t})\) \\  & \(\rhd\) After training, it generates a new dropout mask for the model parameters \(\mathcal{M}_{t}\) and performing T forward inference. & \(p(y\mid x,\mathcal{L})=\frac{1}{L}\sum_{t=1}^{T}p(y\mid x,\mathcal{M}_{t})\) \\  & \(\rhd\) The output is the average of T results. & \\ \hline \multirow{6}{*}{Deep Ensembles} & \(\rhd\) The ensemble-based approaches design N neural networks \(\{\mathcal{M}_{1}\cdots\mathcal{M}_{N}\}\) at first. & \\  & \(\rhd\) These networks share same architecture but initialized from different weights. & \(p(y\mid x,L)=\frac{1}{N}\sum_{i=1}^{N}p(y\mid x,\mathcal{M}_{i})\) \\ \cline{1-1}  & \(\rhd\) The average of the outputs of the N networks is the final output. & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of uncertainty estimation methods in deep active learning. difference of CNN-based deep learning (DL) methods and traditional active learning (AL) methods is that AL methods query candidates one by one while DL methods load a batch size of samples at the same time. [PERSON] and [PERSON] [48] conducted experiments on vision tasks with traditional active learning methods and found that previous AL works did not perform well for CNN-based vision tasks due to the batch settings during model training. They attributed this ineffectiveness to batch sampling. In order to solve it, they defined the active learning as a _Core-Set_ selection problem, where the algorithm aims to train on a small mount of labeled samples instead of the whole dataset such that the trained model is able to get competitive performance over the model trained on the whole dataset. They defined the core-set selection problem as the following optimization:  
\[\min_{L^{1}:\left\lvert L^{1}\right\rvert\leq b}\left\lvert\frac{1}{n}\sum_{i \in[n]}loss(\mathbf{x}_{i},y_{i};\mathcal{M}_{L^{0}\cup L^{1}})-\frac{1}{ \left\lvert L^{0}+L^{1}\right\rvert}\sum_{j\in D^{0}\cup L^{1}}loss\left( \mathbf{x}_{j},y_{j};\mathcal{M}_{L^{0}\cup L^{1}}\right)\right\rvert, \tag{2}\]  
where \(L^{0}\) represents the randomly selected samples at the beginning, \(L^{1}\) represents newly selected samples from the entire dataset under budget \(b\). \(n\) is the number of samples in the entire dataset. \(\mathcal{M}_{L^{0}\cup L^{1}}\) denotes the trained model under the subset \(L^{0}\) and \(L^{1}\). _loss_ is the loss function, where the authors suggested the cross-entropy loss for effective training. In order to prove their hypothesis, they conducted experiments on active learning for fully supervised models and weakly supervised models. Specifically, they used dataset CIFAR10/100 [47] for image classification and dataset SVHN [49] for digit classification. Based on the _Core-Set_ strategy, the combination of batch-based active learning and deep learning has been a researcher topic in the community. the goal of batch-based deep active learning is to select the most informative batch or mini-batch \(\mathcal{B}^{*}=\left\{x_{1}^{*},x_{2}^{*},\ldots,x_{n}^{*}\right\}\) from the loaded batches \(\mathcal{B}\), where \(\mathcal{B}\) belongs to unlabeled pool \(\mathcal{U}\), and \(n\) is the batch size. We formulate above process as follows. \[\mathcal{B}^{*}=\operatorname*{arg\,max}_{\mathcal{B}\subseteq U}\Phi( \mathcal{B},\mathcal{M}(L)), \tag{3}\]  
where \(\Phi(\cdot)\) is the score function to measure the informativeness of the batch \(\mathcal{B}\), \(L\) is the labeled data pool, \(\mathcal{M}\) is the trained model. After that, most of the related research was devoted to the innovation of the scoring function \(\Phi(\cdot)\). [PERSON] et al. [50] adopted the idea of Bayesian Active Learning by Disagreement (BALD) [43] into scoring function.