Calculating the Best Performance Achievable in a Regression 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 Yacht Hydrodynamics dataset.

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

# Required imports
import pandas as pd
import kxy

df = pd.read_csv('http://archive.ics.uci.edu/ml/machine-learning-databases/'\
                 '00243/yacht_hydrodynamics.data', sep='[ ]{1,2}',\
                 names=['Longitudinal Position', 'Prismatic Coeefficient',\
                        'Length-Displacement', 'Beam-Draught Ratio',\
                        'Length-Beam Ratio', 'Froude Number',\
                        'Residuary Resistance'])
df.rename(columns={col: col.title() for col in df.columns}, inplace=True)

How To Generate The Achievable Performance Analysis

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

performance_analysis

Achievable R^2	Achievable True Log-Likelihood Per Sample
0.996555	0.798462

Note: the same syntax is used for classification 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.

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