ipss 1.0.1

Python implementation of integrated path stability selection (IPSS)

Integrated path stability selection (IPSS)

Integrated path stability selection (IPSS) is a general method for improving feature selection algorithms. Given an n-by-p data matrix X (n = number of samples, p = number of features), and an n-dimensional response variable y, IPSS applies a base selection algorithm to subsamples of the data to select features (columns of X) that are most related to y. This package includes IPSS for gradient boosting (IPSSGB), random forests (IPSSRF), and L1-regularized linear models (IPSSL). The final outputs are efp scores and q-values for each feature in X.

• The efp score of feature j is the expected number of false positives selected when j is selected.
• The q-value of feature j is the false discovery rate (FDR) when feature j is selected.

Key attributes

• Error control: IPSS controls the number of false positives and the FDR.
• Generality: IPSSGB and IPSSRF are nonlinear, nonparametric methods. IPSSL is linear.
• Speed: IPSS is efficient. For example, IPSSGB runs in <20 seconds when n = 500 and p = 5000.
• Simplicity: The only required inputs are X and y. Users can also specify the base method (IPSSGB, IPSSRF, or IPSSL), and the target number of false positives or the target FDR.

Associated papers

IPSSL: https://arxiv.org/abs/2403.15877
IPSSGB and IPSSRF:

Installation

To install from PyPI:

pip install ipss

Examples

Examples are available in the examples folder. These include

• A simple example, simple_example.py (Open in Google Colab).
• Various simulation experiments, simulation.py (Open in Google Colab).
• IPSS applied to cancer data, cancer.py (Open in Google Colab).

Usage

from ipss import ipss

# load data X and y

# run ipss:
ipss_output = ipss(X, y)

# select features based on target number of false positives
target_fp = 1
efp_scores = ipss_output['efp_scores']
selected_features = []
for feature_index, efp_score in efp_scores:
	if efp_score <= target_fp:
		selected_features.append(feature_index)
print(f'Selected features (target E(FP) = {target_fp}): {selected_features}')

# select features based on target FDR
target_fdr = 0.1
q_values = ipss_output['q_values']
selected_features = []
for feature_index, q_value in q_values:
	if q_value <= target_fdr:
		selected_features.append(feature_index)
print(f'Selected features (target FDR = {target_fdr}): {selected_features}')

Results

ipss_output = ipss(X, y) is a dictionary containing:

• efp_scores: List of tuples (feature_index, efp_score) with features ordered by their efp scores from smallest to largest (list of length p).
• q_values: List of tuples (feature_index, q_value) with features ordered by their q-values from smallest to largest (list of length p).
• runtime: Runtime of the algorithm in seconds (float).
• selected_features: List of indices of features selected by IPSS; empty list if target_fp and target_fdr are not specified (list of ints).
• stability_paths: Estimated selection probabilities at each parameter value (array of shape (n_alphas, p))

Full list of ipss arguments

Required arguments:

• X: Features (array of shape (n, p)), where n is the number of samples and p is the number of features.
• y: Response (array of shape (n,) or (n, 1)). ipss automatically detects if y is continuous or binary.

Optional arguments:

• selector: Base algorithm to use (str; default 'gb'). Options are:
  • 'gb': Gradient boosting with XGBoost.
  • 'l1': L1-regularized linear or logistic regression.
  • 'rf': Random forest with sci-kit learn.
• selector_args: Arguments for the base algorithm (dict; default None).
• target_fp: Target number of false positives to control (positive float; default None).
• target_fdr: Target false discovery rate (FDR) (positive float; default None).
• B: Number of subsampling steps (int; default 100 for IPSSGB, 50 otherwise).
• n_alphas: Number of values in the regularization or threshold grid (int; default 100).
• ipss_function: Function to apply to selection probabilities (str; default 'h3'). Options are:
  • 'h1': Linear function, h1(x) = 2x - 1 if x >= 0.5 else 0.
  • 'h2': Quadratic function, h2(x) = (2x - 1)**2 if x >= 0.5 else 0.
  • 'h3': Cubic function, h3(x) = (2x - 1)**3 if x >= 0.5 else 0.
• preselect: Number (if int) or percentage (if float) of features to preselect. False for no preselection (default 0.05).
• preselect_min: Minimum number of features to keep in the preselection step (int; default 200).
• preselect_args: Arguments for the preselection algorithm (dict; default None).
• cutoff: Maximum value of the theoretical integral bound I(Lambda) (positive float; default 0.05).
• delta: Defines probability measure; see Associated papers (float; default 1).
• standardize_X: Scale features to have mean 0, standard deviation 1 (bool; default None).
• center_y: Center response to have mean 0 (bool; default None).
• true_features: List of true feature indices when known, e.g., in simulations (list; default None).
• n_jobs: Number of jobs to run in parallel (int; default 1).

General observations/recommendations:

• IPSSGB is usually best for capturing nonlinear relationships between features and response
• IPSSL is usually best for capturing linear relationships between features and response
• target_fp or target_fdr (at most one is specified) are problem specific/left to the user
• In general, all other parameters should not changed
  • selector_args include, e.g., decision tree parameters for tree-based models
  • Results are robust to B provided it is bigger than 25
  • Results are robust to n_alphas provided it is bigger than 50
  • 'h3' yields the most true positives. 'h2' is more conservative, and 'h1' even more so.
  • Preselection can significantly reduce computation time. Results are robust otherwise.
  • Results are robust to cutoff provided it is between 0.025 and 0.1.
  • Results are robust to delta provided it is between 0 and 1.5.
  • Standardization is automatically applied for IPSSL. IPSSGB and IPSSRF are unaffected by this.
  • Centering y is automatically applied for IPSSL. IPSSGB and IPSSRF are unaffected by this.