A New Modeling to Feature Selection Based on the Fuzzy Rough Set Theory in Normal and Optimistic States on Hybrid Information Systems

Large-scale online marketplaces and recommender systems serve as critical technological support for e-commerce development. In industrial recommender systems, features play vital roles as they carry information for downstream models. Accurate feature importance estimation is critical because it helps identify the most useful feature subsets from thousands of feature candidates for online services. Such selection enables improved online performance while reducing computational cost. To address feature selection problems in deep learning, trainable gate-based and sensitivity-based methods have been proposed and proven effective in industrial practice. However, through the analysis of real-world cases, we identified three bias issues that cause feature importance estimation to rely on partial model layers, samples, or gradients, ultimately leading to inaccurate importance estimation. We refer to these as layer bias, baseline bias, and approximation bias. To mitigate these issues, we propose FairFS, a fair and accurate feature selection algorithm. FairFS regularizes feature importance estimated across all nonlinear transformation layers to address layer bias. It also introduces a smooth baseline feature close to the classifier decision boundary and adopts an aggregated approximation method to alleviate baseline and approximation biases. Extensive experiments demonstrate that FairFS effectively mitigates these biases and achieves state-of-the-art feature selection performance.

Feature selection is crucial for pinpointing relevant features in high-dimensional datasets, mitigating the 'curse of dimensionality,' and enhancing machine learning performance. Traditional feature selection methods for classification use data from all classes to select features for each class. This paper explores feature selection methods that select features for each class separately, using class models based on low-rank generative methods and introducing a signal-to-noise ratio (SNR) feature selection criterion. This novel approach offers a theoretically sound guarantee of feature recovery under specific assumptions and has been demonstrated to outperform some existing feature selection methods on standard classification datasets. Additionally, it can be easily applied in a class-incremental learning setup, yielding performance comparable to that of some current methods.

Sequential subset search -- forward selection with floating backtracking and its descendants -- remains the quality reference in feature selection, but every member of the family sweeps the full pool of remaining candidate features at each step, which excludes it from very-high-dimensional problems; there, only individual-feature ranking remains practical, and it models feature interplay weakly or not at all. We introduce a budgeted sampled step operator pair that replaces the full sweeps by a fixed number of candidate evaluations per step. Candidates are drawn by temperature-controlled softmax sampling from dependency-aware per-feature statistics learned online from every criterion evaluation the search performs, guarded by a uniform exploration floor; per-step cost becomes independent of dimensionality. Substituting the operators turns any sequential method into its stochastic counterpart, defining the Stochastic Sequential Search (SSS) family; we study the stochastic counterpart of floating search, sSFFS. On 500-dimensional madelon, sSFFS retains at least 97% of the full-SFFS criterion value at every subset size at about a quarter of its evaluations, while uniform sampling at the same budget collapses on madelon's synergistic features. On 5,000-dimensional gisette, far beyond full-SFFS reach, sSFFS exceeds the saturated criterion level of DAF and BIF ranking at matched budgets; holdout validation shows that at 500 training samples the binding constraint beyond the sequential frontier becomes the criterion, not the search. On 10,105-dimensional reuters, under a trustworthy multinomial filter criterion, sSFFS dominates BIF and DAF on the search objective and on holdout accuracy at every subset size, in about two minutes of single-core evaluation work. A verified standalone implementation accompanies the paper.