SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Table 11: Summarised performance for the label noise experiments across all generative models. Classification is measured by AUROC, feature selection and model selection by Spearman's Rank Correlation, and statistical fidelity by inverse KL divergence. Numbers show bootstrapped mean and  $95\%$  CI. A value of 'None' in Pre- and postprocessing strategy indicates that the results are for models trained on the real data.
Prop. la-
bel noise	Preprocessing
Strategy	Postprocessing
Strategy	Classification	Feature Selection	Model Selection	Statistical Fidelity
0.0	None	None	0.775 (0.773, 0.777)	-	-	-
baseline	baseline	0.728 (0.717, 0.738)	0.482 (0.398, 0.559)	0.475 (0.365, 0.588)	0.996 (0.994, 0.997)
no-hard	0.739 (0.728, 0.749)	0.481 (0.411, 0.558)	0.657 (0.545, 0.748)	0.996 (0.994, 0.997)
easy-hard	baseline	0.74 (0.733, 0.747)	0.546 (0.46, 0.621)	0.581 (0.474, 0.688)	0.997 (0.995, 0.998)
no-hard	0.749 (0.741, 0.756)	0.546 (0.471, 0.62)	0.703 (0.626, 0.769)	0.997 (0.995, 0.998)
0.02	None	None	0.771 (0.768, 0.774)	-	-	-
baseline	baseline	0.715 (0.705, 0.725)	0.441 (0.344, 0.529)	0.459 (0.387, 0.536)	0.995 (0.993, 0.997)
no-hard	0.727 (0.716, 0.737)	0.489 (0.411, 0.558)	0.503 (0.396, 0.604)	0.995 (0.993, 0.997)
easy-hard	baseline	0.732 (0.724, 0.739)	0.568 (0.492, 0.631)	0.434 (0.346, 0.53)	0.996 (0.994, 0.998)
no-hard	0.746 (0.738, 0.753)	0.557 (0.498, 0.611)	0.607 (0.529, 0.68)	0.996 (0.994, 0.998)
0.04	None	None	0.767 (0.765, 0.77)	-	-	-
baseline	baseline	0.704 (0.691, 0.718)	0.457 (0.37, 0.54)	0.397 (0.321, 0.484)	0.996 (0.994, 0.997)
no-hard	0.714 (0.699, 0.728)	0.447 (0.369, 0.525)	0.432 (0.34, 0.526)	0.995 (0.993, 0.997)
easy-hard	baseline	0.729 (0.723, 0.735)	0.513 (0.447, 0.581)	0.362 (0.276, 0.449)	0.996 (0.993, 0.998)
no-hard	0.738 (0.732, 0.745)	0.485 (0.41, 0.555)	0.599 (0.507, 0.704)	0.996 (0.993, 0.998)
0.06	None	None	0.765 (0.762, 0.767)	-	-	-
baseline	baseline	0.7 (0.688, 0.713)	0.449 (0.367, 0.534)	0.389 (0.303, 0.481)	0.996 (0.993, 0.998)
no-hard	0.71 (0.697, 0.726)	0.443 (0.351, 0.526)	0.536 (0.463, 0.61)	0.995 (0.993, 0.997)
easy-hard	baseline	0.723 (0.712, 0.733)	0.49 (0.418, 0.565)	0.43 (0.355, 0.519)	0.996 (0.993, 0.998)
no-hard	0.733 (0.723, 0.742)	0.468 (0.395, 0.535)	0.597 (0.498, 0.689)	0.996 (0.993, 0.998)
0.08	None	None	0.759 (0.756, 0.762)	-	-	-
baseline	baseline	0.701 (0.686, 0.715)	0.501 (0.428, 0.577)	0.317 (0.232, 0.409)	0.995 (0.993, 0.997)
no-hard	0.709 (0.695, 0.724)	0.463 (0.389, 0.532)	0.343 (0.26, 0.434)	0.995 (0.993, 0.997)
easy-hard	baseline	0.718 (0.709, 0.726)	0.47 (0.376, 0.554)	0.356 (0.262, 0.463)	0.996 (0.994, 0.998)
no-hard	0.729 (0.72, 0.738)	0.48 (0.39, 0.558)	0.351 (0.266, 0.441)	0.996 (0.994, 0.997)
0.1	None	None	0.756 (0.753, 0.76)	-	-	-
baseline	baseline	0.697 (0.68, 0.714)	0.42 (0.329, 0.504)	0.267 (0.19, 0.354)	0.995 (0.993, 0.997)
no-hard	0.703 (0.686, 0.721)	0.455 (0.373, 0.534)	0.296 (0.212, 0.385)	0.995 (0.993, 0.997)
easy-hard	baseline	0.706 (0.697, 0.715)	0.452 (0.387, 0.513)	0.319 (0.238, 0.408)	0.996 (0.994, 0.998)
no-hard	0.713 (0.703, 0.722)	0.42 (0.348, 0.487)	0.326 (0.255, 0.406)	0.996 (0.994, 0.998)
Table 12: Additional measures of statistical fidelity for the main experiment, summarized across all datasets. All numbers have been rounded to 3 decimals. Inv. KL-D = inverse Kullback-Leibler Divergence, WD = Wasserstein Distance, MMD = Maximum Mean Discrepancy.
Generative Model	Preprocessing Strategy	Postprocessing Strategy	Inv. KL-D	WD	MMD
bayesian_network	baseline	baseline	0.998 (0.998, 0.999)	0.041 (0.018, 0.067)	0.001 (0.0, 0.003)
no-hard	0.998 (0.998, 0.999)	0.148 (0.034, 0.34)	0.001 (0.0, 0.003)
easy-hard	baseline	0.998 (0.998, 0.999)	0.04 (0.017, 0.068)	0.001 (0.0, 0.003)
no-hard	0.998 (0.998, 0.999)	0.146 (0.035, 0.332)	0.001 (0.0, 0.003)
ctgan	baseline	baseline	0.979 (0.967, 0.987)	0.022 (0.01, 0.037)	0.001 (0.0, 0.002)
no-hard	0.978 (0.967, 0.986)	0.534 (0.041, 1.481)	0.001 (0.0, 0.002)
easy-hard	baseline	0.979 (0.968, 0.986)	0.022 (0.01, 0.036)	0.001 (0.0, 0.002)
no-hard	0.977 (0.967, 0.985)	0.546 (0.039, 1.518)	0.001 (0.0, 0.002)
ddpm	baseline	baseline	0.846 (0.685, 0.979)	0.717 (0.17, 1.409)	0.0 (0.0, 0.001)
no-hard	0.845 (0.688, 0.971)	1.085 (0.326, 1.966)	0.0 (0.0, 0.001)
easy-hard	baseline	0.849 (0.709, 0.967)	0.744 (0.137, 1.42)	0.0 (0.0, 0.001)
no-hard	0.848 (0.714, 0.967)	1.066 (0.363, 1.874)	0.0 (0.0, 0.001)
nflow	baseline	baseline	0.975 (0.968, 0.981)	0.074 (0.038, 0.115)	0.001 (0.0, 0.002)
no-hard	0.975 (0.968, 0.981)	0.519 (0.079, 1.351)	0.001 (0.0, 0.002)
easy-hard	baseline	0.975 (0.967, 0.981)	0.075 (0.04, 0.113)	0.001 (0.0, 0.003)
no-hard	0.975 (0.967, 0.982)	0.546 (0.076, 1.439)	0.001 (0.0, 0.003)
tvae	baseline	baseline	0.966 (0.952, 0.977)	0.026 (0.012, 0.041)	0.0 (0.0, 0.001)
no-hard	0.965 (0.952, 0.977)	0.531 (0.046, 1.465)	0.0 (0.0, 0.001)
easy-hard	baseline	0.968 (0.957, 0.978)	0.026 (0.012, 0.041)	0.0 (0.0, 0.001)
no-hard	0.968 (0.957, 0.978)	0.483 (0.047, 1.32)	0.0 (0.0, 0.001)
Table 13: Summarised performance across all datasets, with an additional row showing the performance of the real data with data-centric postprocessing.
Generative Model	Preprocessing Strategy	Postprocessing Strategy	Classification	Feature Selection	Model Selection
None	None	None	0.866 (0.856, 0.876)	-	-
no-hard	0.859 (0.837, 0.88)	0.937 (0.926, 0.946)	0.697 (0.647, 0.747)
bayesian_network	baseline	baseline	0.622 (0.588, 0.656)	0.091 (-0.004, 0.188)	0.155 (0.047, 0.263)
no-hard	0.624 (0.59, 0.659)	0.043 (-0.065, 0.143)	0.112 (0.021, 0.207)
easy-hard	baseline	0.624 (0.592, 0.66)	0.1 (-0.015, 0.213)	0.297 (0.202, 0.387)
no-hard	0.627 (0.594, 0.661)	0.082 (-0.033, 0.195)	0.197 (0.104, 0.291)
ctgan	baseline	baseline	0.797 (0.771, 0.822)	0.63 (0.568, 0.699)	0.519 (0.457, 0.581)
no-hard	0.807 (0.782, 0.829)	0.653 (0.592, 0.714)	0.578 (0.512, 0.648)
easy-hard	baseline	0.791 (0.763, 0.818)	0.63 (0.566, 0.692)	0.513 (0.441, 0.576)
no-hard	0.8 (0.772, 0.828)	0.631 (0.566, 0.691)	0.594 (0.531, 0.655)
ddpm	baseline	baseline	0.813 (0.784, 0.842)	0.635 (0.552, 0.718)	0.508 (0.442, 0.571)
no-hard	0.818 (0.787, 0.849)	0.645 (0.569, 0.726)	0.476 (0.406, 0.543)
easy-hard	baseline	0.818 (0.788, 0.844)	0.645 (0.564, 0.723)	0.544 (0.476, 0.61)
no-hard	0.824 (0.796, 0.85)	0.661 (0.584, 0.738)	0.539 (0.466, 0.604)
nflow	baseline	baseline	0.737 (0.713, 0.761)	0.415 (0.342, 0.486)	0.348 (0.275, 0.415)
no-hard	0.745 (0.718, 0.768)	0.439 (0.372, 0.503)	0.357 (0.292, 0.425)
easy-hard	baseline	0.742 (0.718, 0.768)	0.455 (0.384, 0.527)	0.362 (0.297, 0.428)
no-hard	0.749 (0.725, 0.772)	0.445 (0.365, 0.511)	0.371 (0.31, 0.436)
tvae	baseline	baseline	0.792 (0.766, 0.816)	0.675 (0.623, 0.723)	0.506 (0.438, 0.575)
no-hard	0.8 (0.775, 0.828)	0.675 (0.63, 0.721)	0.488 (0.419, 0.561)
easy-hard	baseline	0.79 (0.763, 0.814)	0.687 (0.642, 0.73)	0.477 (0.416, 0.538)
no-hard	0.797 (0.771, 0.822)	0.699 (0.653, 0.742)	0.507 (0.437, 0.578)
C.11 Postprocessing the real data
Tables 13 and 14 investigate the effect of postprocessing the original data (i.e. removing hard examples) on the main experimental benchmark data and on the datasets with added label noise, respectively. The performances for feature and model selection are obtained by comparing the feature and model rankings against the non-postprocessed version of the real data, in a similar manner as the performance of the generative models. The results indicate that postprocessing has a minor impact on classification: a slight negative effect on the purportedly clean benchmark datasets, and a slight positive effect on the datasets with added label noise. Spearman's Rank Correlation for feature selection remains high across both the main benchmark datasets (0.94) and the datasets with label noise (0.88), whereas the ranking of models is lower at approximately 0.7 for both types of data.
Table 14: Summarised performance across all datasets with added label noise, with an additional row showing the performance of the real data with data-centric postprocessing.
Generative Model	Preprocessing Strategy	Postprocessing Strategy	Classification	Feature Selection	Model Selection
None	None	None	0.766 (0.764, 0.767)	-	-
no-hard	0.776 (0.773, 0.779)	0.883 (0.868, 0.896)	0.704 (0.662, 0.744)
bayesian_network	baseline	baseline	0.69 (0.678, 0.703)	0.393 (0.348, 0.439)	0.376 (0.284, 0.47)
no-hard	0.697 (0.685, 0.71)	0.417 (0.371, 0.462)	0.45 (0.359, 0.55)
easy-hard	baseline	0.742 (0.736, 0.747)	0.535 (0.503, 0.565)	0.44 (0.346, 0.54)
no-hard	0.751 (0.745, 0.756)	0.522 (0.485, 0.562)	0.608 (0.533, 0.685)
ctgan	baseline	baseline	0.741 (0.734, 0.746)	0.662 (0.621, 0.7)	0.451 (0.352, 0.565)
no-hard	0.752 (0.747, 0.757)	0.63 (0.6, 0.658)	0.56 (0.463, 0.646)
easy-hard	baseline	0.734 (0.73, 0.738)	0.62 (0.58, 0.665)	0.366 (0.29, 0.443)
no-hard	0.746 (0.74, 0.751)	0.58 (0.539, 0.624)	0.544 (0.46, 0.624)
ddpm	baseline	baseline	0.685 (0.677, 0.693)	0.272 (0.21, 0.333)	0.294 (0.232, 0.357)
no-hard	0.69 (0.682, 0.699)	0.28 (0.203, 0.35)	0.298 (0.228, 0.367)
easy-hard	baseline	0.72 (0.711, 0.73)	0.43 (0.345, 0.518)	0.309 (0.222, 0.404)
no-hard	0.728 (0.717, 0.738)	0.439 (0.365, 0.508)	0.518 (0.417, 0.635)
nflow	baseline	baseline	0.686 (0.675, 0.698)	0.325 (0.266, 0.384)	0.393 (0.328, 0.457)
no-hard	0.699 (0.685, 0.711)	0.344 (0.295, 0.396)	0.467 (0.363, 0.56)
easy-hard	baseline	0.707 (0.699, 0.715)	0.342 (0.279, 0.395)	0.521 (0.449, 0.594)
no-hard	0.717 (0.71, 0.725)	0.324 (0.261, 0.385)	0.577 (0.491, 0.667)
tvae	baseline	baseline	0.735 (0.731, 0.739)	0.64 (0.609, 0.673)	0.41 (0.331, 0.494)
no-hard	0.747 (0.743, 0.752)	0.643 (0.608, 0.676)	0.537 (0.459, 0.621)
easy-hard	baseline	0.722 (0.715, 0.729)	0.608 (0.56, 0.66)	0.437 (0.355, 0.523)
no-hard	0.732 (0.725, 0.738)	0.601 (0.546, 0.653)	0.415 (0.325, 0.521)
D Statistical tests
This appendix provides details on the statistical significance of the effect of data-centric processing on both the datasets in the main experimental benchmark and on the datasets with added noise. Subsection D.1 provides a summary of the insights gained from the tests, and subsections D.2 and D.3 provide details on the main experiment and label noise experiment, respectively.
D.1 Summary
On the label noise experiments, the data-centric processing strategies have a beneficial effect across all tasks (see Table 16), with significant effects of pre- and postprocessing strategies across all tasks, except postprocessing for feature selection. The effect of data-centric processing is not significantly different across varying levels of label noise. There is a slight tendency towards an inverted V shape effect of the processing strategies, i.e., larger benefits with moderate levels of label noise, however, this is not significant.
For the main experimental benchmark data, data-centric processing led to significant improvements in performance for classification (postprocessing only), and model selection (preprocessing only), as shown in Table 15. The diminished effect of data-centric processing in the main experimental benchmark compared to the datasets with added label noise might be caused by the extensive preprocessing of the datasets in the benchmark as mentioned in Sec 4.1. The datasets could therefore be speculated to be too "clean" to receive substantive benefits from data-centric processing.
Measures of model fit  $(R^2)$  of the models in the main benchmark data indicate that the variance in task performance is best explained in the classification task  $(R^2 = 0.98)$ , slightly worse in the feature selection task  $(R^2 = 0.85)$ , and substantially lower in the model selection task  $(R^2 = 0.57)$ . This might be due to the smoothness of the performance metrics. The model ranking score is established by accurately ranking the eight supervised classification models listed in Appendix B.3. Similarly, the feature selection score is determined by correctly ranking the metrics for feature importance across all features within the dataset – a quantity that naturally varies by dataset. In contrast, classification performance relies on AUROC values computed on the test dataset, which encompasses a relatively large number of samples (1,141 in the smallest dataset). Due to the dissimilarity in the number of samples, models, and features, the metrics for model and feature ranking are inevitably more susceptible to larger variance. This occurs because disparities in a single element can lead to more
Table 15: Main effect of the pre- and postprocessing strategies of the main experiment, controlling for the interaction between dataset and generative model. The estimates represent the difference in the corresponding performance metric (AUROC or Spearman's Rank Correlation depending on the task), compared to the baseline strategy, i.e. no processing.
Task	Processing	Estimate	Std. Error	p-value	Significant
Classification	preprocessing_strategy[T.easy-hard]	0.001	0.001	0.526	0
postprocessing_strategy[T.no-hard]	0.007	0.001	<0.000	1
Feature Selection	preprocessing_strategy[T.easy-hard]	0.013	0.008	0.091	0
postprocessing_strategy[T.no-hard]	0.003	0.008	0.706	0
Model Selection	preprocessing_strategy[T.easy-hard]	0.031	0.012	0.008	1
postprocessing_strategy[T.no-hard]	0.003	0.012	0.822	0
substantial effects on the performance metrics in comparison to the impact on classification. In summary, this means that the performance metrics for feature and model selection are more sensitive to minor deviations or random noise than classification.
D.2 Main experiment
Three linear models were constructed to statistically assess the effect of the data-centric processing strategies on the performance of each task (classification, feature selection, model selection). The models controlled for the main effects of the datasets and generative models, as well as the interaction between the two, as the different datasets might have characteristics that make them more or less difficult for specific generative models. The models took the following formula:
$$
\text {m e t r i c} \sim \text {d a s e t} _ {\text {i d}} * \text {g e n e r a t i v e} _ {\text {m o d e l}} + \text {p r e p r o c e s s i n g} _ {\text {s t r a g e y}} + \text {p o s t p r o c e s s i n g} _ {\text {s t r a g e y}}
$$
Where metric represents the performance metric corresponding to the task, i.e., AUROC for classification or Spearman's Rank Correlation for feature and model selection.
Table 15 shows the main effect of the processing strategies for each of the tasks. Tables 17, 18, and 19 show the full output of the models.
D.3 Label noise
Similarly to the main experiment, three linear models were constructed to statistically assess the effect of the data-centric processing strategies on each task's performance with different label noise levels (see Figure 4). The models controlled for the main effects of level of label noise and generative model, and took the following formula:
metric  $\sim$  prop_label_noise + generative_model + preprocessing_strategy + postprocessing_strategy
Table 16 shows the main effect of the processing strategies for each of the tasks. Tables 20, 21, and 22 show the full output of the models.
To assess whether the effectiveness of the data-centric processing strategies is modulated by the level of label noise in the data, we constructed a linear model similar to the one above, but with an interaction effect between the proportion of label noise and the data-centric processing strategies. The models took the following form:
metric  $\sim$  generative_model+prop_label_noise\*(preprocessing_strategy + postprocessing_strategy)
The output of these models is shown in Tables 23, 24, and 25.
Notably, the model with interaction effects had slightly higher Akaike's Information Criteria than the model without, indicating a worse fit to the data.
Table 16: Main effect of the pre- and postprocessing strategies of the label noise experiment, controlling for the effect of the proportion of label noise and generative model. The estimates represent the difference in the corresponding performance metric (AUROC or Spearman's Rank Correlation depending on the task), compared to the baseline strategy, i.e. no processing.
Task	Processing	Estimate	Std. Error	p-value	Significant
Classification	preprocessing_strategy[T,easy-hard]	0.017	0.002	<0.000	1
postprocessing_strategy[T.no-hard]	0.010	0.002	<0.000	1
Feature Selection	preprocessing_strategy[T,easy-hard]	0.039	0.013	0.002	1
postprocessing_strategy[T.no-hard]	-0.005	0.013	0.710	0
Model Selection	preprocessing_strategy[T,easy-hard]	0.050	0.019	0.008	1
postprocessing_strategy[T.no-hard]	0.098	0.019	<0.000	1
Table 20: Full output of the linear model assessing the impact of data-centric processing on the classification task on the label noise data. The model has the following formula: auroc  $\sim$  perc_label_noise + generative_model + preprocessing_strategy + postprocessing_strategy.
coef	std err	t	P-|t|	[0.025, 0.975]
Dep. Variable:	mean	R-squared:	0.450	0.7239	0.003	209.577	0.000	0.717	0.731
Model:	OLS	Adj. R-squared:	0.440	-0.0090	0.003	-2.630	0.009	-0.016	-0.002
Method:	Least Squares	F-statistic:	43.48	-0.0174	0.003	-5.050	0.000	-0.024	-0.011	Omnibus: 9.482	Durbin-Watson: 1.202
Date:	Fri. 11 Aug 2023	Prob (F-statistic):	9.476-69	-0.0223	0.003	-6.482	0.000	-0.029	-0.016	Prob(Omnibus): 0.009	Jargue-Bera (JB): 6.880
Done:	09-19-44	Log-Likelihood:	1376.0	-0.0246	0.003	-7.163	0.000	-0.031	-0.018	Skev: -0.144	Prob(JB): 0.0321
No. Observations:	596	AIC:	-2728.	0.0238	0.003	7.520	0.000	0.018	0.030	Kurtosis: 2.559	Cond. No. 8.98
Dr Residuals:	584	BIC:	-2675.	-0.0139	0.003	-4.398	0.000	-0.020	-0.008
Dr Model:	11	-0.0173	0.003	-5.463	0.000	-0.024	-0.011
Covariance Type:	nonrobust	0.0145	0.003	4.576	0.000	0.008	0.021
0.0175	0.002	8.782	0.000	0.014	0.021
0.0096	0.002	4.834	0.000	0.006	0.014
Table 21: Full output of the linear model assessing the impact of data-centric processing on the feature selection task on the label noise data. The model has the following formula: spearmans_r ~ perc_label_noise + generative_model + preprocessing_strategy + postprocessing_strategy.
Intercept	0.4821	0.022	22.187	0.000	0.439	0.525
Dep, Variable:	spearmans_r	R-squared:	0.424	perlabel_noise[T,T]	-0.0002	0.022	-0.008	0.993	-0.043	0.042
Model:	OLS	Adj.R-squared:	0.413	perlabel Noise[T,T]	-0.0383	0.022	-1.773	0.077	-0.081	0.004
Method:	Least Squares	F-statistic:	39.10	perlabel Noise[T,T]	-0.016	0.022	0.000	0.022	-0.009	0.009
Date:	Fri. 11 Aug 2023	Prob (F-statistic)	5.47e+63	perlabel Noise[T,T]	-0.0355	0.022	-1.643	0.101	-0.078	0.007	Omnibus:	5.130
Time:	09:20:03	Log-Likelihood:	279.90	perlabel Noise[T,T]	-0.0777	0.022	-3.555	0.000	-0.121	-0.035	Sker:	0.172
No. Observations:	596	AIC:	-535.8	synthetic_model_type[Tetgan]	0.1575	0.020	7.912	0.000	0.118	0.197	Kurtosis:	3.299
DF Residuals:	584	BIC:	-483.1	synthetic_model_type[Ttdpm]	-0.1104	0.020	-5.548	0.000	-0.150	-0.071
DF Model:	11	synthetic_model_type[Ttnlow]	-0.1318	0.020	-6.623	0.000	-0.171	-0.093
Covariance Type:	nonrobust	synthetic_model_type[Ttva]	0.1575	0.020	7.914	0.000	0.118	0.197
preprocessingStrategy[Teasy-hard]	0.0391	0.013	3.121	0.002	0.014	0.064
postprocessingStrategy[Ttno-hard]	-0.0047	0.013	-0.372	0.710	-0.029	0.020
Table 22: Full output of the linear model assessing the impact of data-centric processing on the model selection task on the label noise data. The model has the following formula: spearmans_r ~ perc_label_noise + generative_model + preprocessing_strategy + postprocessing_strategy.
coef	std err	t	P> |t|	[0.025, 0.975]
Dep. Variable:	spearmans_r	R-squared:	0.236	Intercept	0.5466	0.032	16.983	0.000	0.483	0.610
Model:	OLS	Adj. R-squared:	0.221	perlabel_noise[T,2]	-0.1033	0.032	-3.228	0.001	-0.166	-0.040
Method:	Least Squares	F-statistic:	16.37	perlabel_noise[T,4]	-0.1564	0.032	-4.886	0.000	-0.219	-0.094
Date:	Fri, 11 Aug 2023	Prob (F-statistic)	3.176-28	perlabel_noise[T,6]	-0.1162	0.032	-3.629	0.000	-0.179	-0.053	Omnibus:	1.523
perlabel_noise[T,8]	-0.2621	0.032	-8.188	0.000	-0.325	-0.199	Prob(Omnibus):	0.467
Time:	09:15:53	Log-Likelihood:	45.755	perlabel_noise[T,10]	-0.238	0.032	-9.12	0.000	-0.238	-0.048	Skew:	0.061
synthetic_model_type[Tctgan]	0.0166	0.029	0.561	0.575	-0.041	0.074	Kurtosis:	2.785
No. Observations:	596	AIC:	-67.51	synthetic_model_type[Ttdpm]	-0.1090	0.029	-3.698	0.000	-0.167	-0.051
Dr Residuals:	584	BIC:	-14.83	synthetic_model_type[Ttaflow]	0.0257	0.029	0.871	0.384	-0.032	0.084
Df Model:	11	synthetic_model_type[Ttavec]	-0.0138	0.029	-0.468	0.640	-0.072	0.044
Covariance Type:	nonrobust	preprocessing_strategy[Teasy-hard]	0.0496	0.019	2.675	0.008	0.013	0.086
postprocessing_strategy[Tno硬]	0.0976	0.019	5.260	0.000	0.061	0.134
Table 23: Full output of the linear model assessing the impact of data-centric processing on the classification task on the label noise data with interaction effects. The model has the following formula: auroc  $\sim$  generative_model + perc_label_noise * (preprocessing_strategy + postprocessing_strategy).
coef	std err	t	P> |t|	[0.025, 0.975]
Intercept	0.7261	0.005	137.188	0.000	0.716	0.736
generative_model[TcTegan]	0.0238	0.003	7.472	0.000	0.018	0.030
generative_model[TdDpm]	-0.0139	0.003	-4.371	0.000	-0.020	-0.008
generative_model[TfTolw]	-0.0173	0.003	-5.428	0.000	-0.011	-0.011
generative_model[TfTvec]	0.0145	0.003	4.547	0.000	0.008	0.021
per_label_name[T2]	-0.0129	0.007	-1.868	0.062	-0.027	0.001
per_label_name[T4]	-0.0233	0.007	-3.364	0.001	-0.037	-0.010
per_label_name[T6]	-0.0272	0.007	-3.933	0.000	-0.041	-0.014
per_label_name[T7]	-0.0266	0.007	-3.843	0.000	-0.043	-0.013
per_label_name[T10]	-0.0305	0.007	-4.370	0.000	-0.044	-0.017
per_post[Tbaseline - no-hard]	0.0116	0.007	1.683	0.093	-0.002	0.025
per_post[Tbase - no-hard]	0.0128	0.007	1.848	0.065	-0.001	0.026	Omnibus: 8.499
per_post[Tbase - no-hard]	0.0211	0.007	3.051	0.002	0.008	0.035	Prob(Omnibus): 0.014
per_label_name[T2][pre post [baseline - no-hard]	0.0007	0.010	0.070	0.020	-0.020	-0.018	Kurtosis: -0.155
per_label_name[T4][pre post [baseline - no-hard]	-0.0016	0.010	-0.167	0.868	-0.021	0.018	Prob(BJ): 2.590
per_label_name[T6][pre post [baseline - no-hard]	-0.0017	0.010	-0.172	0.863	-0.021	0.018	Cond. No. 34.7
per_label_name[T8][pre post [baseline - no-hard]	-0.0033	0.010	-0.333	0.739	-0.022	0.016
per_label_name[T10][pre post [baseline - no-hard]	-0.0061	0.010	-0.619	0.536	-0.026	0.013
per_label_name[T2][pre post [baseline - no-hard]	0.0047	0.010	0.485	0.628	-0.024	0.024
per_label_name[T4][pre post [baseline - no-hard]	0.0122	0.010	1.246	0.213	-0.007	0.031
per_label_name[T6][pre post [baseline - no-hard]	0.0103	0.010	1.050	0.294	-0.009	0.029
per_label_name[T8][pre post [baseline - no-hard]	0.0044	0.010	0.449	0.654	-0.015	0.024
per_label_name[T10][pre post [baseline - baseline]	-0.0034	0.010	-0.349	0.727	-0.023	0.016
per_label_name[T2][pre post [baseline - no-hard]	0.0101	0.010	1.034	0.302	-0.009	0.029
per_label_name[T4][pre post [baseline - no-hard]	0.0131	0.010	1.338	0.182	-0.006	0.032
per_label_name[T6][pre post [baseline - no-hard]	0.0111	0.010	1.137	0.256	-0.008	0.030
per_label_name[T8][pre post [baseline - no-hard]	0.0067	0.010	0.688	0.492	-0.012	0.026
per_label_name[T10][pre post [baseline - no-hard]	-0.0055	0.010	-0.557	0.578	-0.025	0.014