SlowGuess/NeurIPS_2023_OCR huggingface dataset:
$$
\mathbb {E} \left[ \hat {r} _ {H} \left(\mathbf {x} _ {t} ^ {u}, v _ {i}\right) \right] = \frac {K \cdot r _ {H} \left(\mathbf {x} _ {t} ^ {u} , v _ {i}\right)}{| \mathcal {V} |}. \tag {21}
$$
Meanwhile,  $\hat{r}_H(\mathbf{x}_t^u,v_i)$  can also be viewed as the sum of  $K$  i.i.d. Bernoulli random variables  $b_{1},b_{2},\ldots ,b_{k}$ , where  $b_{k} = 1(1\leq k\leq K)$  indicates the  $k$ -th sampled item for  $\mathcal{R}$  is ranked higher than  $v_{i}$ , and  $b_{k} = 0$  otherwise. Hence, by applying Hoeffding's inequality [5], we have:
$$
\mathbb {P} \left[ \left| \frac {1}{K} \sum_ {k = 1} ^ {K} b _ {k} - \mathbb {E} \left[ \frac {1}{K} \sum_ {k = 1} ^ {K} b _ {k} \right] \right| \geq \zeta \right] \leq \exp \left(- 2 K \zeta^ {2}\right). \tag {22}
$$
Then by replacing  $\sum_{k=1}^{K} b_k$  with  $\hat{r}_H(\mathbf{x}_t^u, v_i)$ , we obtain:
$$
\mathbb {P} \left[ \left| \frac {\hat {r} _ {H} \left(\mathbf {x} _ {t} ^ {u} , v _ {i}\right)}{K} - \frac {\mathbb {E} \left[ \hat {r} _ {H} \left(\mathbf {x} _ {t} ^ {u} , v _ {i}\right) \right]}{K} \right| \geq \zeta \right] \leq \exp (- 2 K \zeta^ {2}). \tag {23}
$$
Next, we replace  $\mathbb{E}\big[\hat{r}_H(\mathbf{x}_t^u,v_i)\big]$  with  $\frac{K\cdot r_H(\mathbf{x}_t^u,v_i)}{|\mathcal{V}|}$  according to Eq. 21:
$$
\mathbb {P} \left[ \left| \frac {\hat {r} _ {H} \left(\mathbf {x} _ {t} ^ {u} , v _ {i}\right)}{K} - \frac {r _ {H} \left(\mathbf {x} _ {t} ^ {u} , v _ {i}\right)}{| \mathcal {V} |} \right| \geq \zeta \right] \leq \exp (- 2 K \zeta^ {2}). \tag {24}
$$
C.1 Hyper-parameter Settings for Baselines
For fair comparisons, we implement FPMC with PyTorch. For other baselines, we use the original code provided by the corresponding authors. All the baselines adopt Xavier [6] initializer and Adam [7] optimizer. We empirically find the optimal hyper-parameter setting for each baseline based on the performance on the validation set. The detailed hyper-parameter setting for each baseline is summarized in Table 1.
C.2 More Results on Hyper-parameter Analysis
Figure 2: Effect of key hyper-parameters  $\beta$ ,  $\beta'$ ,  $K$ , and  $\rho$  of BirDRec on Beauty dataset.
Figure 3: Effect of key hyper-parameters  $\beta$ ,  $\beta'$ ,  $K$ , and  $\rho$  of BirDRec on Yelp dataset.
Figure 4: Effect of key hyper-parameters  $\beta$ ,  $\beta'$ ,  $K$ , and  $\rho$  of BirDRec on QK-Vedio dataset.
C.3 More Results on the Percentage of Rectified Instances
(c) Yelp
(d) QK-Video
Figure 5: Testing accuracy (NDCG@10) of our BirDRec and SASRec with increasing epochs. The training stops if the best accuracy does not increase in 25 consecutive epochs.
(c) Yelp
Figure 6: The percentage of instances that are rectified with increasing epochs.
(d) QK-Video
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