Quantifying Spuriousness of Biased Datasets Using Partial Information Decomposition (2407.00482v1)

Abstract: Spurious patterns refer to a mathematical association between two or more variables in a dataset that are not causally related. However, this notion of spuriousness, which is usually introduced due to sampling biases in the dataset, has classically lacked a formal definition. To address this gap, this work presents the first information-theoretic formalization of spuriousness in a dataset (given a split of spurious and core features) using a mathematical framework called Partial Information Decomposition (PID). Specifically, we disentangle the joint information content that the spurious and core features share about another target variable (e.g., the prediction label) into distinct components, namely unique, redundant, and synergistic information. We propose the use of unique information, with roots in Blackwell Sufficiency, as a novel metric to formally quantify dataset spuriousness and derive its desirable properties. We empirically demonstrate how higher unique information in the spurious features in a dataset could lead a model into choosing the spurious features over the core features for inference, often having low worst-group-accuracy. We also propose a novel autoencoder-based estimator for computing unique information that is able to handle high-dimensional image data. Finally, we also show how this unique information in the spurious feature is reduced across several dataset-based spurious-pattern-mitigation techniques such as data reweighting and varying levels of background mixing, demonstrating a novel tradeoff between unique information (spuriousness) and worst-group-accuracy.

• The paper introduces a novel PID-based metric that uses unique information to quantify spurious correlations in biased datasets.
• It develops the 'Spuriousness Disentangler' autoencoder for practical PID estimation in high-dimensional, real-world data.
• Empirical results show that reducing unique spurious information correlates with improved worst-group accuracy and overall model performance.

Quantifying Spuriousness of Biased Datasets Using Partial Information Decomposition

In the presented paper, the authors introduce a novel information-theoretic approach to defining and quantifying spuriousness in biased datasets using Partial Information Decomposition (PID). Specifically, the paper proposes a metric based on unique information derived from PID to measure the extent of spurious correlations between features in a dataset.

Information-Theoretic Formalization

The core idea behind the paper is the use of PID to disentangle the information shared between spurious and core features regarding a target variable (such as a prediction label). Through this decomposition, the joint information content is split into distinct components: unique information, redundant information, and synergistic information. Unique information, in particular, is posited as a metric for spuriousness. The motivations and theoretical justifications for this measure derive from concepts in statistical decision theory, such as Blackwell Sufficiency, which provides a partial ordering when one random variable can be more "informative" than another for inference.

Proposition and Theoretical Justifications

The primary proposition is that the unique information contained in spurious features, not shared by core features, quantifies the spuriousness of a dataset. This is mathematically formalized and justified through Theorem 1, where it is shown that the condition of having zero unique information equates to Blackwell Sufficiency — a scenario where the core features are entirely informative about the target variable, rendering spurious features redundant.

The desirable properties of the proposed measure include:

• Unique information is bounded by the mutual information of spurious features and the target variable.
• The measure increases as more spurious features are added, and decreases as more core features are added.

Practical Estimation and Empirical Validation

To make this theoretical framework applicable to high-dimensional data, the authors introduce a novel autoencoder-based estimator termed the "Spuriousness Disentangler." This estimator facilitates the practical estimation of PID values by reducing dimensionality and discretizing features, thereby handling the complexity of real-world, continuous image data.

Empirical Insights

The empirical section demonstrates the application of this measure on two datasets: the Waterbird dataset and a synthetic dataset called Dominoes. The results showcase how unique information in spurious features diminishes significantly when bias in datasets is mitigated through balanced sampling or background mixing techniques. Additionally, the empirical evaluation highlights a novel tradeoff where lower unique information in spurious features correlates with higher worst-group-accuracy — demonstrating the measure's utility in predicting model performance nuances in biased datasets.

Practical and Theoretical Implications

The practical implications of this work are substantial. The proposed metric can be used to quantitatively assess dataset quality before model training, potentially saving considerable computational resources. Theoretically, it offers a new lens to understand and address spurious correlations through the rigorous lens of information theory.

Future Directions

Potential future directions include refining the Spuriousness Disentangler for broader dataset types, improving computational efficiency, and extending this framework to dynamic and adaptive datasets. Further exploration into more sophisticated techniques for dataset de-biasing and their impact on the unique information metric could also be pursued.

In conclusion, this paper presents a well-founded, novel approach to quantifying spuriousness in biased datasets, providing both a theoretical framework and practical tools for understanding and mitigating the spurious correlations that degrade model performance. The integration of information-theoretic principles with modern machine learning practices opens new avenues for research and application in the domain of unbiased dataset generation and model training.