Calculating the Best Performance Achievable in a Classification Problem

In this tutorial we show how to run to use the kxy package to estimate the best performance that can be achieved when using a specific set of variables in a regression problem.

We use the UCI bank note classification dataset.

%load_ext autoreload
%autoreload 2
import warnings
warnings.filterwarnings('ignore')

# Required imports
import pandas as pd
import kxy

url = 'http://archive.ics.uci.edu/ml/machine-learning-databases/00267/' \
    'data_banknote_authentication.txt'
df = pd.read_csv(url, names=['Variance', 'Skewness', 'Kurtosis', 'Entropy', 'Is Fake'])

How To Generate The Achievable Performance Analysis

performance_analysis = df.kxy.achievable_performance_analysis('Is Fake', \
    input_columns=()) # Use all columns but the label column as inputs

performance_analysis

Achievable R^2	Achievable Log-Likelihood Per Sample	Achievable Accuracy
0.684734	-0.115977	0.975

Note: the same syntax is used for regression problems. The type of supervised learning problem is inferred based on the label column.

Column Meaning

• Achievable R^2: The highest \(R^2\) that can be achieved by a model using the inputs to predict the label.

• Achievable True Log-Likelihood Per Sample: The highest true log-likelihood per sample that can be achieved by a model using the inputs to predict the label.

• Achievable Accuracy: The highest classification accuracy that can be achieved by a model using the inputs to predict the label.

These performances are not mere upper bounds, they are attainable.