Algorithm 4 The Uncertainty of Sampling Second Variant (UoS-2) Querying Method

Input: A dataset $\mathcal{D}=(x_i,y_i)$, an exploitation active learning strategy S, the number of simulation iterations n and a scaling parameter K. Output: A query sample $x^{*}$. Train the regression model using the training samples $\mathcal{D}$ to obtain the mean ${\mu }_{\beta |\mathcal{D}}$ and the covariance ${\Sigma }_{\beta |\mathcal{D}}$ of the model parameters’ vector $\beta$ and the posterior estimates of $a_{\sigma |\mathcal{D}}$ and $b_{\sigma |\mathcal{D}}$. for$i=1$ to n do Sample ${\beta }_i$ from $t_{2a_{\sigma |\mathcal{D}}}({\mu }_{\beta |\mathcal{D}},\frac{b_{\sigma |\mathcal{D}}}{a_{\sigma |\mathcal{D}}}{\Sigma }_{\beta |\mathcal{D}})$. ${x_s}_i\leftarrow$ the query sample returned after applying exploitation strategy S, using the sampled model parameters ${\beta }_i$. end for Evaluate the average query sample ${\overline{x}}_s$: ${\overline{x}}_s=\frac{1}{n}\sum _{i=1}^n{x_s}_i$ ${{\sigma }_s}^2\leftarrow \frac{K}{n-1}\sum _{i=1}^n{({x_s}_i-{\overline{x}}_s)}^2$. $x^{*}\leftarrow$ Generate a query sample according to a Gaussian distribution as follows: $\mathcal{N}({\overline{x}}_s,{{\sigma }_s}^2)$.