Supervised Feature Selection via Dependence Estimation (0704.2668v1)

Abstract: We introduce a framework for filtering features that employs the Hilbert-Schmidt Independence Criterion (HSIC) as a measure of dependence between the features and the labels. The key idea is that good features should maximise such dependence. Feature selection for various supervised learning problems (including classification and regression) is unified under this framework, and the solutions can be approximated using a backward-elimination algorithm. We demonstrate the usefulness of our method on both artificial and real world datasets.

• The paper introduces HSIC as a novel dependence measure to evaluate the relationship between features and labels without density estimation.
• It employs a backward elimination strategy (BAHSIC) that reliably assesses each feature's contribution within a joint context.
• BAHSIC demonstrates versatile performance across binary, multiclass, and regression tasks, matching state-of-the-art methods.

Supervised Feature Selection via Dependence Estimation

The paper "Supervised Feature Selection via Dependence Estimation" presents a systematic approach for selecting informative features in supervised learning using the Hilbert-Schmidt Independence Criterion (HSIC) as a measure of dependence between features and labels. This approach attempts to maximize this dependence, thus identifying robust feature sets for a variety of supervised tasks including classification and regression. The paper proposes the use of a backward-elimination algorithm to approximate solutions for feature selection tasks.

Core Contributions

1. Hilbert-Schmidt Independence Criterion (HSIC): The main innovation presented revolves around the utilization of HSIC for feature selection, which, unlike many feature selection criteria, does not require density estimation. This independence criterion evaluates the correlation between the input features and the associated labels using kernel methods without the need for estimating probability densities. HSIC is shown to have desirable uniform convergence guarantees, making it a powerful tool for identifying dependencies.
2. Backward Elimination Algorithm: The authors focus on a backward elimination strategy, named BAHSIC, to filter features, arguing that it is generally superior to forward selection strategies. The backward elimination is computationally intensive compared to forward selection but provides a more reliable feature appraisal since each feature's contribution is evaluated in the context of other features.
3. Unified Framework and Practical Versatility: By employing HSIC, this method accommodates binary classification, multiclass classification, and regression tasks. The broad applicability is achieved by altering the kernel functions according to the task requirements, thus providing a generalized framework that subsumes many traditional feature selection methods as special cases.

Theoretical and Practical Implications

The paper confirms that HSIC satisfies key criteria for a competent feature selection metric: it can detect both linear and non-linear dependencies, and it is concentrated concerning the underlying data distribution. The authors prove that the empirical estimates of HSIC are unbiased and converge towards the population counterpart, employing U-statistics to ensure solid statistical foundations.

In practical settings, BAHSIC demonstrates effectiveness across synthetic and real-world datasets. Through comprehensive experiments, including artificial scenarios involving binary, multiclass, and regression challenges, BAHSIC consistently identified relevant features effectively compared to traditional methods like mutual information, RELIEF, and Pearson’s correlation.

For real-world datasets, the method's performance is comparable to state-of-the-art feature selectors like SVM Recursive Feature Elimination (RFE) and $\ell_0$-norm SVM while demonstrating computational efficiency. Additionally, through extensive testing across diverse datasets, it is shown that the algorithm maintains robust performance without the necessity of embedded regularization techniques, further validating the method's potential for scalable applications.

Future Directions

The prospects for this research stretch into refining the computational aspects of HSIC for feature selection, especially concerning large-scale datasets or streaming data where computational efficiency remains a pivotal challenge. There is also potential in exploring more advanced kernel methods tailored to specific types of data beyond traditional feature vectors, such as graphs or sequences, which constitute an increasingly critical area in real-world applications.

Moreover, given the adaptability of the HSIC framework, future investigations might orient towards incorporating multi-view datasets where multiple HSIC evaluations can be used to discern cross-domain feature relations. Exploring HSIC's ability in active learning scenarios where data labels are scarce could also provide substantial utility considering the criterion’s capacity to operate under semi-supervised conditions.

Conclusion

Overall, this paper presents an innovative perspective on using dependence estimation for feature selection, introducing HSIC as a potent criterion. The backward selection strategy embedded within the BAHSIC algorithm offers a promising avenue for identifying informative features across a multitude of supervised learning tasks. This approach not only balances theoretical robustness with empirical efficacy but also underscores the flexibility necessary to tackle modern machine learning challenges.