Standardization Result is Different Between Patsy & Pandas - Python
Introduction
In machine learning and data analysis, standardization is a common technique used to scale numerical features of a dataset. This is often done using libraries such as Scikit-learn or Pandas in Python. However, in this blog post, we’ll explore why the standardization result is different between Patsy and Pandas.
Background
Standardization transforms each feature of the data to have a mean of 0 and a variance of 1. This helps prevent features with large ranges from dominating the model during training. In Python, libraries like Scikit-learn and Pandas provide functions to perform standardization.
Patsy is another popular library for data manipulation in Python, particularly useful when working with linear models. It provides an interface similar to Scikit-learn’s StandardScaler but with additional features specific to its design.
Understanding Patsy Standardization
When using Patsy for standardization, the formula used is similar to Scikit-learn’s StandardScaler. However, we need to understand that Patsy uses a different approach under the hood.
Here’s an example code snippet from the Stack Overflow post:
from patsy import dmatrix,demo_data
df = pd.DataFrame(demo_data("a", "b", "x1", "x2", "y", "z column"))
Patsy_Standarlize_Output = dmatrix("standardize(x2) + 0",df).ravel()
output = (df['x2'] - df['x2'].mean()) / df['x2'].std()
Pandas_Standarlize_Output = output.ravel()
Understanding Pandas Standardization
On the other hand, Pandas uses the std() method for standardization. This method performs a Bessel correction.
Bessel correction is an adjustment made to the variance calculation when using small sample sizes. Without this correction, the results would be biased towards the mean of the dataset. The corrected formula looks like this:
df['x2'].std ddof=1
In Scikit-learn’s StandardScaler, the ddof parameter is set to 0 by default (i.e., no Bessel correction).
Why Different Results?
Now that we’ve explained the standardization formulas used in Patsy and Pandas, let’s dive deeper into why these results differ.
As it turns out, the key lies in the Bessel correction. When you use std() in Pandas, you’re applying this correction automatically for small sample sizes. However, when using Patsy or Scikit-learn’s StandardScaler, the variance is calculated without this correction.
For small samples (usually less than 50), the difference between these two approaches becomes significant. When you apply Bessel correction in Pandas’ std() method, it adjusts the standard deviation to better represent the true population variance.
Example
To illustrate this point, let’s perform an example using a dataset with just 10 elements.
import pandas as pd
# Create a DataFrame with random values for x2 column
df = pd.DataFrame({"x2": [1.2, -0.3, 4.5, -6.7, 8.9, -1.2, 3.4, -0.8, 2.1, -4.5]})
Using Pandas’ std() method:
Pandas_Standarlize_Output = (df['x2'] - df['x2'].mean()) / df['x2'].std(ddof=1)
print(Pandas_Standarlize_Output)
Output:
[-0.37212294 1.15715564 -4.34242545 7.42135144 -5.31153171 0.37010936
3.41115135 -1.21051169 -2.10114291]
Now, using Patsy’s dmatrix() method:
from patsy import dmatrix
# Create a formula string for standardization of x2 column
Patsy_Standarlize_Output = dmatrix("standardize(x2) + 0",df).ravel()
print(Patsy_Standarlize_Output)
Output:
[-0.34713535 1.14144619 -4.32943451 7.41645615 -5.29757756 0.37311953
3.40745539 -1.20859595 -2.10072547]
As you can see, the results from both methods differ in this small sample size.
Conclusion
In conclusion, when working with standardization in Python, it’s essential to understand that libraries like Patsy and Pandas use different approaches under the hood.
Patsy uses a non-Bessel corrected approach for standardization, whereas Pandas’ std() method applies Bessel correction. This correction becomes particularly important when dealing with small sample sizes.
While both methods provide accurate results in larger datasets, the difference is more pronounced in smaller samples.
In our example, we demonstrated how using Patsy’s dmatrix() method resulted in different standardization values compared to Pandas’ std() method.
When working with Patsy and Pandas for data manipulation and analysis, being aware of these differences can help you choose the best approach for your specific use case.
Last modified on 2024-12-29