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Stable Feature Selection for Biomarker Discovery
Zengyou He, Weichuan Yu
TL;DR
Feature-selection stability under sampling variation has been under-considered in biomarker discovery, and different algorithms may identify different features. This review organizes existing stable feature-selection methods and stability measures within a general hierarchical framework, while identifying stability as an important research problem and outlining an expandable basis for further work.
Problem
Feature-selection algorithms do not necessarily identify the same features, while stability under sampling variation has been under-considered in biomarker discovery.
Method
The review summarizes existing stable feature-selection methods and stability measures using a general hierarchical framework.
Results
The review identifies stable feature selection as an important research problem from both theoretical and practical perspectives.
Takeaways & Limitations
The expandable framework provides an overview and categorization intended to support future research and development on stable feature selection.
Takeaways & Limitations
No available method and measure is identified for handling stability issues when correlated features make feature selection harder than finding a minimal optimal feature set.
Abstract
from arXiv · showhide
Feature selection techniques have been used as the workhorse in biomarker discovery applications for a long time. Surprisingly, the stability of feature selection with respect to sampling variations has long been under-considered. It is only until recently that this issue has received more and more attention. In this article, we review existing stable feature selection methods for biomarker discovery using a generic hierarchal framework. We have two objectives: (1) providing an overview on this new yet fast growing topic for a convenient reference; (2) categorizing existing methods under an expandable framework for future research and development.
1 Introduction
Biomarker discovery commonly uses feature selection to identify discriminating variables, but sampling variation can produce different feature subsets with similar accuracy. This review focuses on stable feature-selection methods and organizes them in a unified framework.
- Feature selection in omics data selects discriminating features for classification, such as distinguishing healthy from diseased samples or tumor stages.
- Repeated biomarker-discovery procedures may identify different candidate subsets, even when the data and feature-selection method are unchanged.
- Different feature subsets can achieve the same or similar predictive accuracy, making reproducibility as important as classification accuracy.
- Instability in feature-selection results reduces confidence in discovered markers.
- The review covers methods that incorporate stability into algorithmic design, emphasizing reliable-marker methods rather than stability metrics.Stability metrics are listed for completeness, while the main focus remains on methods.
2 Causes of Instability
Feature-selection instability arises from algorithms that ignore stability, multiple possible marker sets, and few samples relative to feature dimensionality. The review notes that these sources matter for understanding and designing stable methods.
- Classic feature-selection algorithms optimize predictive accuracy with a minimal feature subset but often omit stability from their design.
- Multiple valid marker sets can arise because correlated features or distinct non-correlated marker sets may be selected under different settings.
- Biomarker datasets typically contain hundreds of samples but thousands of features, creating a small-sample, high-dimensional setting.
- At least thousands of samples were concluded to be necessary for stable feature selection in one mathematical model.
- The listed causes may not be exhaustive, so identifying additional sources remains important for future research and method design.
3 Existing Methods
Existing stable feature-selection methods are organized by how they address different instability sources. The framework includes ensemble, prior-relevance, group-selection, and sample-injection approaches.
- The review aims to cover stable feature-selection methods systematically in an expandable framework based on how they treat instability sources.
- Ensemble feature selection and prior-feature-relevance methods incorporate stability considerations during algorithm design.
- Group feature selection treats feature clusters as the selection unit to improve robustness when features are highly correlated.
- Sample injection methods increase the sample size to address the small-sample versus large-feature-size problem.
3.1 Ensemble Feature Selection
Ensemble feature selection creates multiple selectors and aggregates their outputs to improve robustness to sampling or algorithmic variation. Data perturbation varies sample subsets, whereas function perturbation combines different selection algorithms but is limited by their availability.
- Ensemble feature selection creates different feature selectors, then aggregates their results into a consensus output.The second step is typically formulated as rank aggregation.
- Data Perturbation: Data perturbation constructs selectors from different samples of the original data and distinguishes methods by sampling, selection algorithm, and rank aggregation.Several methods fall into this category and are classified in Table 1.
- Data Perturbation: Data sampling combined with ensemble learning is an intuitive strategy for handling selection instability caused by sampling variation.Its superiority has been verified experimentally and theoretically.
- Function Perturbation: Function perturbation uses different feature selection algorithms on the original data rather than repeatedly sampling data.Its component learners capitalize on different algorithmic strengths to obtain robust feature subsets.
- Function Perturbation: Function perturbation is less flexible than data perturbation because its ensemble size is constrained by the number of available feature selection algorithms.The reviewed methods use no more than four component selectors.
3.2 Feature Selection with Prior Feature Relevance
Prior feature relevance can be incorporated into biomarker feature selection through expert knowledge, publications, relevant datasets, or pathway-based methods. Such prior information improves stability and classification performance, but may conflict with biomarker discovery’s goal of finding new features.
- Prior knowledge can bias feature selection toward features assumed to be more relevant before selection.Its use has been associated with a large gain in stability and improved classification performance.
- Prior relevance can come from domain experts, relevant publications, or markers identified in related datasets through transfer learning.Transfer learning applies knowledge from a source task to a different but related task.
- In transfer learning, features previously identified as markers in other datasets are treated as more relevant in the new selection task.
- Using prior information has a limitation because biomarker discovery aims to find new features rather than known ones.
3.3 Group Feature Selection
Group feature selection forms groups of associated features, transforms each group into a coherent representation, and then selects features in the transformed space. Groups may be formed from biological knowledge or directly from the data, with pathway-based methods offering interpretability but possible grouping errors.
- Generic framework: Group feature selection consists of group formation followed by group transformation and feature selection in the transformed space.Groups are first identified, each group is converted into a single entity, and selection is performed on those transformed features.
- Knowledge-Driven Group Formation: Knowledge-driven formation uses domain information such as pathways, where co-regulated genes can be grouped for biomarker discovery.Genes in the same pathway may be searched as a group because they commonly function in co-regulated groups.
- Data-Driven Group Formation: Data-driven formation identifies feature clusters using only information contained in the input data.Clustering-based approaches include hierarchical clustering and k-means, while density estimation uses stable dense core regions.
- Group Transformation: Group transformation creates one coherent representation per group, ranging from feature-value means to principal components.Pathway information can guide correlated-gene or protein grouping, after which each group becomes a new feature for analysis.
- Knowledge-Driven Group Formation: Pathway-guided transformations are biologically interpretable and may approximate disease processes more closely than gene-based models, but uncertain PPI interactions can group unrelated features.Knowledge-based methods have also been applied to proteomics, although the passage notes that further research is desired in that direction.
- Data-Driven Group Formation: Data-driven group selection is widely applicable because it exploits target-data characteristics, but its selected groups are difficult to interpret and validate biologically.A hybrid strategy combining data-driven and knowledge-driven formation is identified as one possible remedy.
3.4 Feature Selection with Sample Injection
Feature selection is unstable in high-dimensional biomarker data because sample sizes are small, while generating real patient samples is costly and time-consuming. The reviewed alternatives augment data by using unlabeled test samples or generating artificial training samples, which can support selection or evaluation.
- Motivation: Biomarker datasets commonly contain hundreds of samples but thousands of features, making the small-sample, high-dimensional setting a major source of instability.This setting is typical in gene-expression and proteomics analyses.
- Motivation: Real patient and healthy-person samples are expensive and time-consuming to generate, motivating alternative ways to increase effective sample size.The passage frames data augmentation as an alternative to collecting more real samples.
- Data Augmentation Strategies: Transductive augmentation incorporates unlabeled test data into feature selection and classification, whereas inductive learning uses training data to build a general hypothesis.Transductive learning targets labels for a given test set and can use both training and testing data during learning.
- Data Augmentation Strategies: Artificial-sample augmentation generates training points according to the distribution of available samples and combines them with original data for subset assessment.The injected samples may be treated as training data or used only during evaluation.
- Artificial Training Samples: One generation scheme samples x_i, draws z from a standard normal distribution, and constructs y = x_i + hz, where h is constant.This procedure produces artificial points around randomly selected training samples.
4 Stability Measure
Stability measures quantify how sensitive feature-selection outputs are to training-set variation, using feature subsets, rankings, or weighting-score vectors as representations.
- Stability measures are used to evaluate algorithms and internally validate feature-selection methods that explicitly account for stability.
- Feature-selection outputs can be represented as subsets, ranking vectors, or weighting-score vectors, which determine the applicable similarity measure.
- Most stability measures compare two subsets or rankings for simplified notation, although general formulations can average pairwise measures or consider all outputs simultaneously.
- Feature Subset: Subset measures include overlap and distance-based comparisons, with percentage of overlapping features related incorporating correlations among features.
- Ranking List: Ranking measures include Spearman correlation, Canberra distance, and overlap scores that can emphasize highly ranked features.
- Weighting Score Vector: Weighting-score stability can be measured with Pearson correlation, whose values range from -1 to 1.
5 Discussions
The discussion identifies unresolved stability challenges in high-dimensional biomarker discovery and reviews the scope and promise of existing strategies.
- Small sample sizes in high-dimensional feature spaces are identified as the most difficult instability source in biomarker discovery.
- Group feature selection is extensively studied because high-dimensional data contain correlated features, but grouping only partially alleviates instability.
- Ensemble feature selection is described as more promising, and a hybrid strategy can group features before applying ensemble selection.
- Group selection helps when redundant features produce multiple true-marker sets, but does not address multiple true-marker sets without shared correlations.
- No available method or measure is identified for stability when true-marker sets share no correlated features; the general problem remains open.
- There is no consensus on the best stability measure, motivating comprehensive comparisons of existing measures.
- The review discusses stable feature-selection techniques for biomarker identification, not biomarker classifier development.
- The discussion raises questions about measuring stability without resampling, explicitly controlling reported-feature stability, and biomarker-specific requirements.
6 Conclusions
The review frames stable feature selection as an important theoretical and practical problem and calls for further research on reproducible biomarker discovery.
- Stable feature-selection methods and stability measures have recently received increased attention for discovering reproducible markers from omics data.
- The review summarizes existing stable feature-selection methods and stability measures within this research area.
- Stable feature selection is characterized as important from both theoretical and practical perspectives, with further research encouraged.