An uncertainty based incremental learning for identifying the severity of bug report

Abstract

To ensure the reliability of software system, software developers have to keep track of the severity of bug reports, and fix critical bugs as soon as possible. Recently, automatic methods to identify the severity of bug reports have emerged as a promising tool to lessen the work burden of software developers. However, most of such methods are supervised and data-driven models which fail to provide favorable performance in the presence of insufficient labeled sample or limited training data. In order to tackle with these issues, we propose an incremental learning for bug reports recognition. According to this framework of incremental learning, one active learning method is developed for tagging unlabeled bug reports, meanwhile, a sample augmentation method is utilized for sufficient training data. Both of these methods are based on uncertainty which is correlated to the informativeness and the classification risk of samples. Moreover, different types of connectionist models are employed to identify bug reports, and comprehensive experiments on real bug report datasets demonstrate that the generalization abilities of these models can be improved by this proposed incremental learning.

Appendix

Given a RBM, we set the hidden vector without $h_k$ as $\mathbf{h }_{\tilde{k}}=(h_1,h_2, ..., h_{k-1}, h_{k+1}, ..., h_{n_h})^T$, where $h_i$ is the ith hidden node. When the $h_k$ is 1, the energy function (9) can be split into two items as follows (Fig. 7):

$$\begin{aligned} \alpha (\mathbf{v })= & {} b_k+\sum _{i=1}^{n_v}w_{k, i}v_i \end{aligned}$$

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$$\begin{aligned} \beta (\mathbf{v }, \mathbf{h }_{\tilde{k}})= & {} \sum _{i=1}^{n_v}a_iv_i+\sum _{j=1,j \ne k}^{n_h}b_jh_j+\sum _{i=1}^{n_v}\sum _{j=1, j\ne k}^{n_h}h_jw_{j,i}v_i. \end{aligned}$$

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Then, the derivation process of conditional probability $P(h_k=1|\mathbf{v })$ is shown below

$$\begin{aligned} \begin{aligned} p(h_k=1|\mathbf{v })&= p(h_k=1|\mathbf{h }_{\tilde{k}}, \mathbf{v }) \\&= \frac{p(h_k=1, \mathbf{h }_{\tilde{k}}, \mathbf{v })}{p(\mathbf{h }_{\tilde{k}}, \mathbf{v })} \\&= \frac{p(h_k=1, \mathbf{h }_{\tilde{k}}, \mathbf{v })}{p(h_k=1, \mathbf{h }_{\tilde{k}}, \mathbf{v })+p(h_k=0, \mathbf{h }_{\tilde{k}}, \mathbf{v })} \\&= \frac{\frac{1}{Z}e^{-E(h_k=1, \mathbf{h }_{\tilde{k}}, \mathbf{v })}}{\frac{1}{Z}e^{-E(h_k=1, \mathbf{h }_{\tilde{k}}, \mathbf{v })}+\frac{1}{Z}e^{-E(h_k=0, \mathbf{h }_{\tilde{k}}, \mathbf{v })}} \\&= \frac{e^{-E(h_k=1, \mathbf{h }_{\tilde{k}}, \mathbf{v })}}{e^{-E(h_k=1, \mathbf{h }_{\tilde{k}}, \mathbf{v })}+e^{-E(h_k=0, \mathbf{h }_{\tilde{k}}, \mathbf{v })}}\\&= \frac{1}{1+e^{-E(h_k=0,\mathbf{h }_{\tilde{k}},\mathbf{v })+E(h_k=1,\mathbf{h }_{\tilde{k}},\mathbf{v })}}\\&= \frac{1}{1+e^{[\beta (\mathbf{h }_{\tilde{k}},\mathbf{v }+0 \cdot \alpha _{k}(\mathbf{v }))]+[-\beta (\mathbf{h }_{\tilde{k}},\mathbf{v })+1 \cdot \alpha _{k}(\mathbf{v })]}}\\&= \frac{1}{1+e^{-\alpha _{k}(\mathbf{v })}} = sigmoid(\alpha _{k}(\mathbf{v })) \end{aligned} \end{aligned}$$

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The derivation process of $p(v_k=1|\mathbf{h })$ is the same way as shown above.

Fig. 7

The overall results of incremental learning. The blue lines are the results of CELM, and the green lines are the results of BLS