# Tabular Data Models for Predicting Art Auction Results
## 3 Results
### Summary of the Results  
In summary, while image-related features in the ColorSVD dataset provide some predictive value, their inclusion does not always result in lower error rates. The analysis indicates that traditional features like TOTAL DIMENSIONS and ARTIST remain consistently powerful across models and datasets. The findings suggest that adding more complex, image-derived features may introduce diminishing returns for the evaluated models, highlighting the need to balance the benefits of added complexity against the risk of reduced model performance.  
Across all datasets analyzed, the RandomForest and XGBoost models consistently emerged as top performers, achieving the lowest sMAPE values. This performance highlights ability to generalize well across a relatively small number of features. These models exhibited some level of resilience in scenarios where color features were included or SVD Entropy was added. The sMAPE values, even with relatively tight error bars indicating some stability, may still be insufficient to reliably capture the complex patterns within art auction datasets.  
Conclusions can be drawn about the higher performance of models that utilize strong or multiple regularization techniques. XGBoost, for example, effectively combines L1 (Lasso) and L2 (Ridge) regularization, which controls model complexity and prevents overfitting. In contrast, while Random Forest does not use explicit regularization, it incorporates several implicit mechanisms. These include bootstrap sampling, where trees are trained on random data subsets and their predictions averaged to reduce variance, as well as feature subsampling, which prevents any one feature from dominating the model. Additionally, limiting tree depth and setting a minimum number of samples per leaf or split help prevent the trees from becoming too complex and overfitting. Together, these techniques act as implicit regularization, enhancing the model's generalization.  
Conversely, the Linear Model consistently exhibited the highest error across all datasets, underscoring its limitations in handling the complex, non-linear relationships likely present in the auction data. Despite being a simpler model, its poor performance indicates that linear assumptions are insufficient for this type of dataset, which likely includes complex interactions and non-linear dependencies that linear regression cannot capture effectively.  
KNN and Decision Trees showed very limited effectiveness, generally ranking in the mid-range of achieved sMAPE scores. The underperformance of these models could be due to the sensitivity of these models to specific characteristics of the data, such as outliers or noisy features. More complex models like Multilayer Perceptron (MLP) and VIME failed to achieve satisfactory results. While these models are theoretically capable of capturing complex, non-linear relationships, they struggled to deliver competitive MSE scores, particularly when compared to the more stable performance of boosting methods like LightGBM and XGBoost. This underperformance could be attributed to the challenges in tuning these deep learning models for specific data applications, which require careful optimization of hyperparameters, architecture, and regularization techniques to prevent overfitting.  
In summary, this analysis highlights the critical need for careful model selection that aligns with the intrinsic characteristics of the art auction dataset. While tree ensembles and boosting models like LightGBM, XGBoost, and CatBoost have shown relative strengths when handling complex features, their performance still falls short of what would be considered robust and reliable. Simpler models and compared deep learning approaches consistently underperform, revealing the persistent challenges of matching model complexity to the specific needs of the dataset. Overall, this analysis suggests that without a precise alignment between model capabilities and data characteristics, achieving satisfactory predictive performance remains difficult.