Mutual Information Calculation for Feature Selection Accuracy
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Solution Overview
Problem
Existing methods for determining mutual information between random variables can produce contradictory results due to the cancellation of positive and negative values in the log term, leading to inaccurate representation of the true mutual information and suboptimal feature selection in machine learning models.
Innovation Solution
The method involves determining mutual information with absolute dependency, where both positive and negative values of the log term are considered to accurately reflect the correlation between variables, using formulas such as I(X,Y)=∑x∈X∑y∈Y p(x,y)·log(p(x,y)/p(x)p(y)) and I(X,Y)=∑x∈X∑y∈Y p(y)·log(p(x,y)/p(x)p(y)), and optimizing for accuracy by using marginal distribution functions, to enhance feature selection in machine learning systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If standard mutual information formula is used, then calculation is simple, but positive and negative log term values cancel each other out resulting in inaccurate mutual information representation
Solution Approach 1:
The patent converts the harmful cancellation effect of negative log term values into a beneficial measure by taking the absolute value. This transforms the problem where negative values reduced mutual information accuracy into a solution where absolute values preserve and emphasize the true dependency relationship between variables, accurately representing feature importance for selection.
2Measurement precision
If mutual information values are optimized for accuracy using absolute dependency, then feature selection accuracy improves, but calculation complexity increases
Solution Approach 1:
The patent changes the parameter of the log term from its standard signed value to its absolute value. This parameter transformation maintains the computational structure of mutual information while fundamentally altering how the dependency relationship is measured, thereby improving feature selection accuracy without requiring complex additional calculations or system changes.
Data Source
AI summary
Systems and techniques are provided for determining mutual information with absolute dependency for feature selection. Items may be received from a dataset. Each item may include two random variables. A first random variable may be associated with a first range of discrete values, and a second random variable may be associated with a second range of discrete values. Mutual information between the two random variables may be determined according to one of:I(X,Y)=∑x∈X∑y∈Yp(x,y)·log(p(x,y)p(x)·p(y))andI(X,Y)=∑x∈X∑y∈Yp(y)·log(p(x,y)p(x)·p(y)),I(X,Y) may be the mutual information between X and Y, x may be a value for X, y may be a value for Y, p(x,y) may be a joint probability distribution function of x and y, p(x) may be a marginal probability distribution function of x, and p(y) may be a marginal probability distribution function of y. The mutual information may be used in a machine learning system to predict a value for one of the random variables for an item for which the value is unknown.