Feature selection is a critical step in regression problems where a large number of continuous explanatory variables explain the same target through different dependency structures. Classical filters may remain sensitive to a single form of dependence, a single scale, or a specific discretization scheme; generalized entropy measures, on the other hand, typically require the parameters to be fixed at a single point. This study proposes a framework that evaluates the Sharma–Mittal entropy volumetrically across a two-dimensional parameter region rather than for a single parameter pair. For the continuous target and explanatory variables, the marginal, joint, and conditional densities are obtained using a Gaussian kernel density estimation; the conditional entropy and information gain surfaces are integrated across the region Ω = [0.05, 0.95]² in the α-β plane to define three indices: PICSME, which measures the conditional uncertainty volume; PIGSME, which measures the gain volume; and NIGSME, which is the ratio of this gain to the total entropy volume of the target. The method is supported by bandwidth consistency and the renormalization of conditional densities; thus, the issue of negative gain that can occur in the continuous variables is resolved, yielding positive and interpretable scores across all six datasets. It is formally demonstrated that the fact that the three indices produce the same ranking is not an empirical observation but rather the result of a monotonicity relationship valid under a fixed target entropy volume. The method is compared with Pearson and Spearman correlations, the Shannon information gain, mutual information, and random forest variable importance across six regression datasets (Airfoil Self-Noise, AirQualityUCI, BodyFat, Meteorology, Concrete, and WineQualityWhite) that differ in their sample size, dimensions, and application domain. The evaluation is not limited to ranking consistency; the out-of-sample prediction performance is measured using least-squares models on the top-k subsets, with rankings calculated from the training partition. The findings show that NIGSME exhibits a performance comparable to that of built-in filters, outperforms them on the Concrete and Meteorology datasets, and never ranks as the weakest method on any dataset. The results demonstrate that volumetric entropy metrics defined across the entire parameter space provide a feature-ranking tool that is independent of parameter selection for continuous variables.

Feature selection is one of the fundamental steps in producing simpler, more interpretable, and computationally efficient models while maintaining predictive power. In this study, rather than fixing the uncertainty relationship between the target variable and each candidate feature to a single entropy parameter, three volume-based indices are proposed that integrate the two-parameter structure of the Sharma-Mittal entropy over a defined parameter region. The indices, named Parameter-Integrated Conditional Sharma-Mittal Entropy, Parameter-Integrated Sharma-Mittal Entropy Information Gain, and Normalized Parameter-Integrated Sharma-Mittal Entropy Information Gain, represent, respectively, the conditional entropy volume, the information gain volume, and the form of this volume normalized relative to the total entropy volume of the target, respectively. Densities were estimated using Gaussian kernel density estimation; the alpha and beta parameters were numerically integrated over the range [0.05; 0.95] × [0.05; 0.95]. The methods were compared across six different regression datasets-Airfoil Self-Noise, AirQualityUCI, BodyFat, meteorology-based reference evapotranspiration, Concrete, and WineQualityWhite-using absolute Pearson correlation, absolute Spearman rank correlation, Shannon information gain, mutual information, and random forest variable importance. The comparison was conducted using raw importance scores, derived feature rankings, Spearman’s rho and Kendall’s tau rank correlations, bivariate rank scatter plots, and Mann–Whitney U test results. The results show that the proposed indices produced high or very high rank agreement with correlation- and information-based reference methods in the Airfoil Self-Noise, AirQualityUCI, BodyFat, and meteorological datasets. Specifically, the absolute Pearson correlation, absolute Spearman rank correlation, Shannon information gain, and mutual information, along with the average Spearman rho values across all datasets, were obtained as 0.884, 0.874, 0.883, and 0.903, respectively; the average agreement with random forest importance scores remained at 0.538. The findings reveal that the parameter-integrated Sharma–Mittal framework offers a density-based and discretization-independent filtering perspective for continuous data; however, they also highlight the need for additional sensitivity and out-of-sample prediction performance evaluations regarding absolute score scales, negative information-gain values, and the rank equivalence of the three proposed indices.