Beginner Explanation
Imagine you have a basket of fruits, and you want to know how much they weigh together. If you weigh each fruit separately and then add them up, you might accidentally count some fruits twice if they are similar. BlockCIR is like a smart scale that recognizes when fruits are similar and weighs them together as one group, so you get the right total weight without any mistakes. This helps in understanding how different features in data relate to each other without overestimating their importance.Technical Explanation
BlockCIR (Block Correlated Input Representation) extends the ExCIR framework by grouping correlated features into blocks. This method effectively evaluates these groups as single entities during model training or evaluation, thus preventing double-counting of information. In practice, this can be implemented by first identifying correlated features using techniques like Pearson correlation or mutual information. Once identified, these features can be grouped, and a representative feature (e.g., the mean or principal component) can be used for modeling. Here’s a simple Python code snippet demonstrating how to group correlated features: “`python import pandas as pd from sklearn.datasets import load_iris from sklearn.correlation import correlation_matrix # Load dataset iris = load_iris() data = pd.DataFrame(iris.data, columns=iris.feature_names) # Calculate correlation matrix corr_matrix = data.corr() # Identify correlated feature groups threshold = 0.8 correlated_features = set() for i in range(len(corr_matrix.columns)): for j in range(i): if abs(corr_matrix.iloc[i, j]) > threshold: colname = corr_matrix.columns[i] correlated_features.add(colname) # Group and reduce features # (Further steps to represent these groups can be implemented) “`Academic Context
BlockCIR is rooted in the need to address feature correlation in machine learning models, particularly in high-dimensional datasets. The mathematical foundation lies in multivariate statistics, where the joint distribution of correlated variables can lead to overfitting if not properly managed. Key papers that discuss the implications of feature correlation include ‘Feature Selection for High-Dimensional Data: A Fast Correlation-Based Filter Solution’ by Hall (1999) and ‘High-Dimensional Statistics: A Non-Asymptotic Viewpoint’ by Vershynin (2018). These works emphasize the importance of understanding feature interactions and the potential pitfalls of ignoring correlated features in predictive modeling.Code Examples
Example 1:
import pandas as pd
from sklearn.datasets import load_iris
from sklearn.correlation import correlation_matrix
# Load dataset
iris = load_iris()
data = pd.DataFrame(iris.data, columns=iris.feature_names)
# Calculate correlation matrix
corr_matrix = data.corr()
# Identify correlated feature groups
threshold = 0.8
correlated_features = set()
for i in range(len(corr_matrix.columns)):
for j in range(i):
if abs(corr_matrix.iloc[i, j]) > threshold:
colname = corr_matrix.columns[i]
correlated_features.add(colname)
# Group and reduce features
# (Further steps to represent these groups can be implemented)Example 2:
for j in range(i):
if abs(corr_matrix.iloc[i, j]) > threshold:
colname = corr_matrix.columns[i]
correlated_features.add(colname)Example 3:
import pandas as pd
from sklearn.datasets import load_iris
from sklearn.correlation import correlation_matrix
# Load datasetExample 4:
from sklearn.datasets import load_iris
from sklearn.correlation import correlation_matrix
# Load dataset
iris = load_iris()Example 5:
from sklearn.correlation import correlation_matrix
# Load dataset
iris = load_iris()
data = pd.DataFrame(iris.data, columns=iris.feature_names)View Source: https://arxiv.org/abs/2511.16482v1