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Feature Importance Ranking for Deep Learning

Maksymilian Wojtas, Ke Chen

arXiv:2010.08973v1cs.LGcs.AIcs.CV

TL;DR

Populationwise deep-learning FIR must find a fixed-size optimal feature subset and rank its selected features despite a combinatorial, generally NP-hard search problem. The paper introduces jointly trained operator and selector networks with stochastic local search, and reports stronger performance than several state-of-the-art FIR and supervised feature-selection methods across synthetic, benchmark, and real datasets.

  • Problem

    Populationwise deep-learning FIR requires simultaneously finding a fixed-size optimal feature subset and ranking its selected features, while subset selection is generally NP-hard.

  • Method

    The paper jointly trains an operator network for supervised prediction and a selector network using operator-performance feedback, with stochastic local search addressing subset search.

  • Results

    The approach outperforms several state-of-the-art feature-importance-ranking and supervised-feature-selection methods on synthetic, benchmark, and real datasets.

  • Takeaways & Limitations

    The method supports populationwise feature selection and FIR with deep-learning models, while the paper identifies extensions to instancewise, group, and unsupervised settings as ongoing work.

  • Takeaways & Limitations

    Training has a high computational burden because the approach uses a dual-net architecture and alternate learning procedure involving two deep-learning models.

Abstract

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Feature importance ranking has become a powerful tool for explainable AI. However, its nature of combinatorial optimization poses a great challenge for deep learning. In this paper, we propose a novel dual-net architecture consisting of operator and selector for discovery of an optimal feature subset of a fixed size and ranking the importance of those features in the optimal subset simultaneously. During learning, the operator is trained for a supervised learning task via optimal feature subset candidates generated by the selector that learns predicting the learning performance of the operator working on different optimal subset candidates. We develop an alternate learning algorithm that trains two nets jointly and incorporates a stochastic local search procedure into learning to address the combinatorial optimization challenge. In deployment, the selector generates an optimal feature subset and ranks feature importance, while the operator makes predictions based on the optimal subset for test data. A thorough evaluation on synthetic, benchmark and real data sets suggests that our approach outperforms several state-of-the-art feature importance ranking and supervised feature selection methods. (Our source code is available: https://github.com/maksym33/FeatureImportanceDL)

1 Introduction

Feature importance ranking measures how individual input features contribute to supervised-learning performance, supporting explainability and domain insight. In deep learning, populationwise ranking and feature selection are difficult because subset search is generally NP-hard and nonlinear models intensify the combinatorial challenge.

  • Motivation: Feature importance ranking measures individual input features’ contributions to supervised-learning performance.It is used in explainable AI to understand model decisions and identify important domain factors.
  • Motivation: Feature selection addresses correlated, dependent, and irrelevant features by selecting a subset that optimizes a predefined learning criterion.The supplied passage frames this as a response to the curse of dimensionality and a way to improve generalization.
  • Challenge: Populationwise feature selection is generally NP-hard, and deep-learning nonlinearity intensifies its combinatorial optimization challenge.The problem concerns finding one feature subset for a population rather than separate subsets for individual instances.
  • Paper objective: The paper targets fixed-size populationwise subsets that maximize deep-network performance while simultaneously ranking selected-feature importance.Its dual-net approach jointly addresses subset discovery and ranking, followed by comparative evaluation across synthetic, benchmark, and real datasets.

2 Related Work

Prior deep-learning feature-importance methods include regularization, greedy search, and averaged input gradients, while conventional methods include LASSO, random forests, SVM-based RFE, and BAHSIC. The paper motivates a deep-learning approach because existing methods can face computational, gradient, capacity, or complex-dependence limitations.

  • Deep-learning FIR: Deep-learning FIR methods include regularization, greedy search, and averaged input gradients.Deep feature selection is described as a regularization-based method but can require costly hyperparameter search and suffer vanishing gradients.
  • Existing methods: LASSO and random forests are off-the-shelf FIR methods, while SVM-based RFE and BAHSIC are additional strong alternatives.The passage contrasts these methods with deep learning for complex tasks and dependencies.
  • Motivation: Existing FIR and feature-selection methods may have limited capacity for complex tasks or may not capture complex dependence between inputs and targets.The paper positions its formulation as a supervised feature-selection subproblem when subset size is fixed.

3 Method

The method represents fixed-size feature subsets with binary masks and uses dual operator and selector networks. Alternate training combines operator feedback, selector-based candidate generation, stochastic local search, exploration, exploitation, and perturbation to address combinatorial search.

  • Problem formulation: A binary mask m with ||m||0 = s represents a subset of s features from d available features.Applying the mask elementwise to each input yields the selected feature subset used for supervised learning.
  • Problem formulation: The FIR objective selects an optimal subset and assigns importance scores to all features within that subset.The formulation treats the optimal mask as the subset indicator and Score(m*) as the importance of selected features.
  • Model description: The dual-net architecture uses an operator for supervised prediction and a selector that learns subset quality from operator-performance feedback.The two networks are trained jointly in an alternate manner.
  • Model description: The trained operator predicts on test data using the selector-generated optimal subset.The operator can be instantiated with deep models such as MLPs or CNNs.
  • Learning algorithm: Stochastic local search with injected noise explores a small candidate set instead of exhaustively searching the combinatorial subset space.The algorithm uses an exploration-exploitation strategy to update selector parameters and generate candidate masks.
  • Learning algorithm: The selector generates an optimal mask by ranking gradients, validating swaps, and perturbing the result to create additional candidates.The operator then trains on candidates supplied by the selector, with the two nets updated jointly until a stopping condition.

4 Experiments

Experiments on synthetic, benchmark, and real-world datasets evaluate the method’s feature-ranking and supervised feature-selection performance. The approach consistently identifies relevant features and performs strongly against established alternatives, while converging to local optima empirically.

  • Experimental setup: The evaluation uses 5-fold cross-validation on synthetic, benchmark, and real-world datasets, reporting mean and standard deviation across folds.Synthetic experiments cover regression, binary classification, and multiclass classification, while benchmark experiments assess explainability and supervised feature selection.
  • Synthetic Data: With s = 5 selected from d = 10 features, the method identifies relevant synthetic-data features in all 5 folds and assigns negative scores to irrelevant features.The synthetic setup deliberately selects more features than the number relevant to the target.
  • Synthetic Data: On synthetic tasks, the method outperforms all other 9 methods on XOR classification, achieves the least MSE on nonlinear regression, and remains comparable on binary classification.Its feature-importance ranking is consistent with random forest on relevant features while performing significantly better overall across the three datasets.
  • Benchmark Data: On MNIST “3” versus “8”, the method reaches 99.31 ± 0.08% accuracy using 85 features and produces maps highlighting discriminative pixels.DFS, AvGrad, and random forest reach 97.42 ± 0.30%, 99.27 ± 0.04%, and 98.84 ± 0.03%, respectively; AvGrad and random forest use all 784 features.
  • Benchmark Data: On four benchmark datasets, the method substantially outperforms RFE, BAHSIC, mRMR, and CCM on glass, vowel, and yale, while matching CCM on TOX-171.TOX-171 contains 5,700+ features but only 109 training examples per fold, making deep learning particularly challenging.
  • Real-world Data: On GM12878 enhancer–promoter data, the method’s accuracy is comparable to DFS and slightly better than random forest and RFE, while its alternate learning algorithm generally converges to a local optimum.The comparison uses top s = 35 of d = 102 features for the method and RFE, whereas random forest and DFS use more features.

5 Discussion

The approach combines a dual-net architecture with alternate learning to address populationwise feature-selection combinatorial optimization, while remaining extensible but computationally demanding.

  • Learning strategy: An exploration-exploitation strategy enables simultaneous use of multiple feature subsets and random input-node dropout during learning.The authors relate this design to random forests and dropout regularization.
  • Connections: The approach uses one operator net across different feature masks, paralleling a population of models in evolutionary computation.This connects the method to evolutionary feature selection while using a single deep learning model.
  • Scope: The method is scalable to big data and can incorporate state-of-the-art deep learning techniques as component models.The paper presents this as a scalability and model-flexibility property.
  • Limitation: Training has a high computational burden because it uses two deep learning models and alternate learning.The paper notes that newer deep learning developments such as EfficientNet could alleviate this load.
  • Extensions: The approach can address generic populationwise feature selection and extend to group-based and unsupervised feature selection.Group constraints can be added to stochastic local search, while an autoencoder-like operator can support unsupervised selection.
  • Conclusion: The evaluation reports that the approach outperforms several state-of-the-art feature-importance-ranking and supervised-feature-selection methods.The authors identify instancewise FIR, group selection, unsupervised selection, and challenging applications as future extensions.

Broader Impact

The study reports no direct ethical or societal-consequence issues, while noting that future applications in domains such as medicine and life science may require consideration of them.

  • Current study: The research does not directly involve ethical aspects or future societal consequences.The authors distinguish the current study from possible future applications.
  • Future applications: Future applications in medicine and life science might require attention to ethical aspects and societal consequences.The passage frames this as a future possibility rather than a current issue.

Supplementary Materials of Feature Importance

The supplementary materials document the experimental setup and implementation details, including the operator architecture, selector loss weighting, validation procedure, and optimization settings.

  • Supplementary contents: The supplementary document contains the detailed experimental setup, additional results, alternate-learning behavior, and algorithm pseudocode.It organizes these materials across Sections A–D.
  • Experimental setup: The experiments use grid search with 5-fold cross-validation to select optimal hyperparameters for the compared learning methods.This procedure is stated for the training setup across the experiments.
  • Operator architecture: The operator concatenates selected features x ⊗m with mask m to distinguish zero-valued selected features from removed features.This concatenated representation is fed to the first hidden layer.
  • Selector training: The selector uses a weighted loss that assigns weights 10, 5, and 1 to the best previous subset, the current optimal subset, and other subsets, respectively.The weighting uses information learned so far to support stochastic local search.
  • Validation: The subset-validation procedure is capped at five repetitions so that it terminates even when its exit condition is not satisfied.The cap preserves a bounded validation process in the experiments.
  • Optimization: The dual-net experiments use MLPs or CNNs for the operator and sigmoid-MLPs for the selector, trained with Adam-based stochastic gradient descent and early stopping.The operator uses Nesterov momentum with Adam in the reported setup.

A.2 Optimal Hyperparameters in Other Methods

The comparative study uses established implementations and tuned settings for competing methods, with filtering methods evaluated through additional learning models and experiments conducted across multiple datasets.

  • Implementation: The study implements deep learning methods with TensorFlow 2.0 and Keras, while using existing code for the other comparison methods.The authors state that original settings were followed for the comparative methods.
  • Random Forest: Random Forest hyperparameters are selected by grid search over tree counts from 50 to 220 and depths from 7 to 24.The optimal values found using five folds are reported in Table IV.
  • RFE: RFE uses one step for most datasets and five steps for TOX-171 and Yale, with a linear-SVM estimator.The estimator uses the reported default values C = 1 and γ = 1 nfeatures∗var(X).
  • BAHSIC: BAHSIC removes 0.1 of the features per iteration and uses the inverse kernels recommended in its original materials.The passage describes these as the default experimental settings.
  • mRMR: mRMR requires no tuned hyperparameter in these experiments and uses the MIQ option from the PyMRMR library.The choice follows the library recommendation.
  • Datasets: The comparative experiments cover synthetic classification, nonlinear regression, benchmark, and additional datasets using the stated method-specific settings.The experimental section reports learning behavior and benchmark-dataset information across these evaluations.
  • Evaluation models: CCM, RFE, BAHSIC, and mRMR are evaluated with SVM or SVR using Gaussian kernels, whereas LASSO uses the same MLPs as the deep learning models.These filtering methods require another learning model to measure selected-feature performance.

B.1 Learning Behavior

The alternate learning algorithm jointly trains operator and selector nets, producing dataset-dependent learning behavior during Phase II. Loss trends generally improve, but stochastic search and limited data can create fluctuations that affect early-stopping choices.

  • Learning procedure: Phase II alternates operator and selector updates so each model’s learning behavior affects the other during every batch.The procedure differs from typical deep-learning training because it jointly trains two mutually interacting models.
  • Synthetic nonlinear regression: On synthetic nonlinear regression, selector loss decreases monotonically while operator training and validation losses steadily decrease as the selector supplies better subsets.The reported behavior is shown across five folds.
  • MNIST: On MNIST, selector loss trends downward but can sharply increase when stochastic local search discovers a mask that sharply reduces operator loss.The increase reflects newly encountered training examples rather than a uniformly monotonic optimization path.
  • Yale: On Yale, limited examples and subset exploration produce fluctuating operator validation loss, especially while comparing different subset sizes.The operator uses a convolutional neural network for this facial-image classification task.
  • Early stopping: Early stopping usually uses validation loss with the optimal mask, but some atypical behavior requires validation accuracy or validation MSE instead.The authors identify investigation of this atypical behavior as ongoing work.

B.2 Detailed Information on Benchmark Data

The benchmark appendix describes challenging datasets and highlights important data-setting effects. In particular, Glass performance depends strongly on whether the ID feature is included, while TOX-171 exposes a limitation associated with very few samples and many features.

  • Benchmark scope: The comparative study uses four challenging benchmark datasets because existing state-of-the-art feature-selection methods perform poorly on them.The listed datasets include Glass, Vowel, TOX-171, and Yale.
  • Glass dataset: Including the non-shuffled Glass instance ID makes it highly important and yields 90%+ accuracy for the proposed approach under the reported experimental setting.The ID feature aligns with class ordering in the data file.
  • Glass dataset: Without the Glass ID feature, all methods perform considerably worse; the proposed approach reaches 75%-80% in 5-fold cross-validation, near the known 80% OpenML accuracy.The reported comparison therefore depends on the data preprocessing and feature-inclusion setting.
  • TOX-171 dataset: TOX-171 contains only 43 instances per class but 5,784 features, making deep-learning models particularly prone to overfitting.The appendix reports that the proposed approach does not generally outperform CCM on this dataset.
  • Yale dataset: Randomly splitting Yale images can create covariate shift because training and validation/test sets may have different feature distributions conditional on the same labels.This creates difficulty for models without covariate-shift adaptation.

B.3 Feature Importance Map

The appendix visualizes feature-importance maps across folds and mask sizes. MNIST maps are reported as consistent across folds, while Yale visualizations become less clear with larger masks and are most meaningful at mask size 30.

  • Map construction: The visualization method encodes normalized nonnegative FIR scores by hue over a mean background image in HSV color space.Unselected features are not shown with negative FIR scores.
  • MNIST maps: MNIST feature-importance maps from different folds are reported to be very consistent, and input gradients allow a full map covering selected and unselected features.The method computes FIR scores from input gradients for all features.
  • Yale maps: Yale visualizations compare mask sizes s = 10, 30, 50, 70, 90, with a second row superimposing maps on mean face images.The images contain d = 32 × 32 features.
  • Yale maps: Increasing Yale mask size makes feature importance less visually clear, whereas s = 30 highlights meaningful pixels near the lips, nose, and eyes.The appendix identifies s = 30 as the best-performing mask size for this dataset.

C.1 Results on Enhance-Promoter Dataset

On the Enhancer-Promoter dataset, the dual-net approach was evaluated for classification and feature-importance ranking across subset sizes, with results compared against several established methods.

  • Dataset and setup: The dataset contains seven classes and 102 features, then preprocessing merges four classes into an imbalanced three-class classification problem.The three classes are active promoter, active enhancer, and background; down-sampling balances them to 2,878 samples each.
  • Learning behavior: The approach evaluates dual-net learning behavior through selector and operator losses, classification accuracy, and training, validation, and test performance across five folds.The selector loss reflects stochastic local search, while operator overfitting appears after the optimal subset is identified around 10.5k batches.
  • Classification results: The method yields slightly higher classification accuracy than DFS for subset sizes above 15 and outperforms RFE, RF, and instancewise-FIR aggregation methods across sizes 15–55.The comparison includes LIME- and SAN-based populationwise FIR approaches as well as DFS, RFE, and RF.
  • Limitations: The populationwise FIR comparison lacks ground truth, so the differing rankings do not support an affirmative conclusion about real-world feature importance.The authors characterize populationwise FIR on real-world data as extremely challenging.
  • Feature-importance ranking: Across subset sizes, the method produces relatively consistent rankings and repeatedly places RNA, ATF2, and ATF3 among the most important features.The importance order of top features varies by only one or two positions, while DFS, RFE, and RF emphasize different features.
  • Efficiency: Training takes about 1,100 seconds, reflecting the computational load of the dual-net architecture and alternate learning algorithm.RF, SAN, DFS, LIME, and RFE take approximately 2.5, 35, 90, 540, and 1,700 seconds, respectively.

C.2 Results on RNA-seq Data

On the RNA-seq cancer dataset, the approach is tested with many features and compared with existing feature-selection results, showing strong performance while leaving scalability as future work.

  • Dataset and setup: The RNA-seq experiment uses 20,264 standardized features after removing 267 constant features, with 600 training and 201 test samples.The data are randomly split, and four-fold cross-validation is applied to the training subset.
  • Comparative results: Under the same settings, the approach outperforms the best performer among existing feature-selection methods reported for this dataset.Most existing methods do not operate on the entire dataset.
  • Interpretation: The authors conclude that the approach works well on a many-feature real-world dataset when enough training examples are available for deep learning.They identify applicability to very large datasets such as images as a belief, while explicitly reserving scalability for ongoing work.
  • Overall result: The paper reports that its approach outperforms several state-of-the-art FIR and feature-selection methods on two biological datasets.This is presented as evidence that the method is a strong candidate for real-world biological feature selection and importance ranking.
  • Learning algorithm: The implementation uses an alternate learning algorithm for the dual-net architecture, generating optimal subset candidates and updating selector weights during training.The algorithm includes operator and selector losses, random masks, generated optimal masks, perturbed candidates, and recorded best masks.
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