Question: How is DIRL evaluated?
Evidence: Through the experiments, we empirically studied our analysis on DIRL and the effectiveness of our proposed solution in dealing with the problem it suffered from. In addition, we studied the impact of each step described in §SECREF10 and §SECREF14 to our proposed solution, respectively. To performe the study, we carried out performance comparison between the following models:
SO: the source-only model trained using source domain labeled data without any domain adaptation.
CMD: the centre-momentum-based domain adaptation model BIBREF3 of the original DIRL framework that implements $\mathcal {L}_{inv}$ with $\text{CMD}_K$.
DANN: the adversarial-learning-based domain adaptation model BIBREF2 of the original DIRL framework that implements $\mathcal {L}_{inv}$ with $\text{JSD}(\rm {P}_S, \rm {P}_T)$.
$\text{CMD}^\dagger $: the weighted version of the CMD model that only applies the first step (described in §SECREF10) of our proposed method.
$\text{DANN}^\dagger $: the weighted version of the DANN model that only applies the first step of our proposed method.
$\text{CMD}^{\dagger \dagger }$: the weighted version of the CMD model that applies both the first and second (described in §SECREF14) steps of our proposed method.
$\text{DANN}^{\dagger \dagger }$: the weighted version of the DANN model that applies both the first and second steps of our proposed method.
$\text{CMD}^{*}$: a variant of $\text{CMD}^{\dagger \dagger }$ that assigns $\mathbf {w}^*$ (estimate from target labeled data) to $\mathbf {w}$ and fixes this value during model training.
$\text{DANN}^{*}$: a variant of $\text{DANN}^{\dagger \dagger }$ that assigns $\mathbf {w}^*$ to $\mathbf {w}$ and fixes this value during model training.
We conducted experiments on the Amazon reviews dataset BIBREF9, which is a benchmark dataset in the cross-domain sentiment analysis field. This dataset contains Amazon product reviews of four different product domains: Books (B), DVD (D), Electronics (E), and Kitchen (K) appliances. Each review is originally associated with a rating of 1-5 stars and is encoded in 5,000 dimensional feature vectors of bag-of-words unigrams and bigrams.
From this dataset, we constructed 12 binary-class cross-domain sentiment analysis tasks: B$\rightarrow $D, B$\rightarrow $E, B$\rightarrow $K, D$\rightarrow $B, D$\rightarrow $E, D$\rightarrow $K, E$\rightarrow $B, E$\rightarrow $D, E$\rightarrow $K, K$\rightarrow $B, K$\rightarrow $D, K$\rightarrow $E. Following the setting of previous works, we treated a reviews as class `1' if it was ranked up to 3 stars, and as class `2' if it was ranked 4 or 5 stars. For each task, $\mathcal {D}_S$ consisted of 1,000 examples of each class, and $\mathcal {D}_T$ consists of 1500 examples of class `1' and 500 examples of class `2'. In addition, since it is reasonable to assume that $\mathcal {D}_T$ can reveal the distribution of target domain data, we controlled the target domain testing dataset to have the same class ratio as $\mathcal {D}_T$. Using the same label assigning mechanism, we also studied model performance over different degrees of $\rm {P}(\rm {Y})$ shift, which was evaluated by the max value of $\rm {P}_S(\rm {Y}=i)/\rm {P}_T(\rm {Y}=i), \forall i=1, \cdots , L$. Please refer to Appendix C for more detail about the task design for this study.
We additionally constructed 12 multi-class cross-domain sentiment classification tasks. Tasks were designed to distinguish reviews of 1 or 2 stars (class 1) from those of 4 stars (class 2) and those of 5 stars (class 3). For each task, $\mathcal {D}_S$ contained 1000 examples of each class, and $\mathcal {D}_T$ consisted of 500 examples of class 1, 1500 examples of class 2, and 1000 examples of class 3. Similarly, we also controlled the target domain testing dataset to have the same class ratio as $\mathcal {D}_T$.
Table TABREF27 shows model performance on the 12 binary-class cross-domain tasks. From this table, we can obtain the following observations. First, CMD and DANN underperform the source-only model (SO) on all of the 12 tested tasks, indicating that DIRL in the studied situation will degrade the domain adaptation performance rather than improve it. This observation confirms our analysis. Second, $\text{CMD}^{\dagger \dagger }$ consistently outperformed CMD and SO. This observation shows the effectiveness of our proposed method for addressing the problem of the DIRL framework in the studied situation. Similar conclusion can also be obtained by comparing performance of $\text{DANN}^{\dagger \dagger }$ with that of DANN and SO. Third, $\text{CMD}^{\dagger }$ and $\text{DANN}^{\dagger }$ consistently outperformed $\text{CMD}$ and DANN, respectively, which shows the effectiveness of the first step of our proposed method. Finally, on most of the tested tasks, $\text{CMD}^{\dagger \dagger }$ and $\text{DANN}^{\dagger \dagger }$ outperforms $\text{CMD}^{\dagger }$ and $\text{DANN}^{\dagger }$, respectively. Figure FIGREF35 depicts the relative improvement, e.g., $(\text{Acc}(\text{CMD})-\text{Acc}(\text{SO}))/\text{Acc}(\text{SO})$, of the domain adaptation methods over the SO baseline under different degrees of $\rm {P}(\rm {Y})$ shift, on two binary-class domain adaptation tasks (You can refer to Appendix C for results of the other models on other tasks). From the figure, we can see that the performance of CMD generally got worse as the increase of $\rm {P}(\rm {Y})$ shift. In contrast, our proposed model $\text{CMD}^{\dagger \dagger }$ performed robustly to the varying of $\rm {P}(\rm {Y})$ shift degree. Moreover, it can achieve the near upbound performance characterized by $\text{CMD}^{*}$. This again verified the effectiveness of our solution.
Through the experiments, we empirically studied our analysis on DIRL and the effectiveness of our proposed solution in dealing with the problem it suffered from. In addition, we studied the impact of each step described in §SECREF10 and §SECREF14 to our proposed solution, respectively. To performe the study, we carried out performance comparison between the following models:

SO: the source-only model trained using source domain labeled data without any domain adaptation.

CMD: the centre-momentum-based domain adaptation model BIBREF3 of the original DIRL framework that implements $\mathcal {L}_{inv}$ with $\text{CMD}_K$.

DANN: the adversarial-learning-based domain adaptation model BIBREF2 of the original DIRL framework that implements $\mathcal {L}_{inv}$ with $\text{JSD}(\rm {P}_S, \rm {P}_T)$.

$\text{CMD}^\dagger $: the weighted version of the CMD model that only applies the first step (described in §SECREF10) of our proposed method.

$\text{DANN}^\dagger $: the weighted version of the DANN model that only applies the first step of our proposed method.

$\text{CMD}^{\dagger \dagger }$: the weighted version of the CMD model that applies both the first and second (described in §SECREF14) steps of our proposed method.

$\text{DANN}^{\dagger \dagger }$: the weighted version of the DANN model that applies both the first and second steps of our proposed method.

$\text{CMD}^{*}$: a variant of $\text{CMD}^{\dagger \dagger }$ that assigns $\mathbf {w}^*$ (estimate from target labeled data) to $\mathbf {w}$ and fixes this value during model training.

$\text{DANN}^{*}$: a variant of $\text{DANN}^{\dagger \dagger }$ that assigns $\mathbf {w}^*$ to $\mathbf {w}$ and fixes this value during model training.
We conducted experiments on the Amazon reviews dataset BIBREF9, which is a benchmark dataset in the cross-domain sentiment analysis field. 
From this dataset, we constructed 12 binary-class cross-domain sentiment analysis tasks: B$\rightarrow $D, B$\rightarrow $E, B$\rightarrow $K, D$\rightarrow $B, D$\rightarrow $E, D$\rightarrow $K, E$\rightarrow $B, E$\rightarrow $D, E$\rightarrow $K, K$\rightarrow $B, K$\rightarrow $D, K$\rightarrow $E. 
We additionally constructed 12 multi-class cross-domain sentiment classification tasks. Tasks were designed to distinguish reviews of 1 or 2 stars (class 1) from those of 4 stars (class 2) and those of 5 stars (class 3). 
Table TABREF27 shows model performance on the 12 binary-class cross-domain tasks. From this table, we can obtain the following observations. 
Answer: The answers are shown as follows:
* Through the experiments, we empirically studied our analysis on DIRL and the effectiveness of our proposed solution in dealing with the problem it suffered from.