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Flexible covariance requires within-class support.

LinearDiscriminantAnalysis, QuadraticDiscriminantAnalysis, shrinkage and reg_param.

Revisit: QDA allows class-specific shapes · Read cross-validation evidence · Finish once, then report

Compare both assumptions and validation evidence on the same population, then nominate before final testing.

This complete script replaces the editor contents. It includes the input setup and the workflow.

import numpy as np
import pandas as pd
df=pd.read_csv('data/ml-learning/ML-X14.csv')
from sklearn.base import clone
from sklearn.model_selection import train_test_split, StratifiedKFold, cross_validate, cross_val_predict, GridSearchCV
from sklearn.dummy import DummyClassifier
from sklearn.metrics import f1_score, accuracy_score, confusion_matrix

import matplotlib.pyplot as plt
import seaborn as sns
X=df[['bill_length_mm', 'bill_depth_mm', 'flipper_length_mm', 'body_mass_g']]
y=df['species']
X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=.2,random_state=42,stratify=y)
folds=StratifiedKFold(n_splits=5,shuffle=True,random_state=42)
candidates={}
grids={}
# Prepare inputs and construct the candidate pipeline.
preprocessor = 'passthrough'
from sklearn.pipeline import Pipeline
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
model = LinearDiscriminantAnalysis(solver='lsqr')
pipeline = Pipeline([('prepare', preprocessor), ('model', model)])
model = pipeline
candidates['lda']=model
grids['lda']={'model__shrinkage': [None, 'auto']}
# Prepare inputs and construct the candidate pipeline.
preprocessor = 'passthrough'
from sklearn.pipeline import Pipeline
from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis
model = QuadraticDiscriminantAnalysis(reg_param=0.1)
pipeline = Pipeline([('prepare', preprocessor), ('model', model)])
model = pipeline
candidates['qda']=model
grids['qda']={'model__reg_param': [0.1, 0.2, 0.5, 0.9]}
# Validate initial candidates on matching training folds.
initial_results={name:cross_validate(candidate,X_train,y_train,cv=folds,scoring='f1_macro') for name,candidate in candidates.items()}
# Compare with a simple reference before tuning.
reference_results=cross_validate(DummyClassifier(strategy='most_frequent'),X_train,y_train,cv=folds,scoring='f1_macro')
rows=[]
selected={}
for name,candidate in candidates.items():
    initial=initial_results[name]
    grid=grids[name]
    if grid:
        search=GridSearchCV(candidate,grid,cv=folds,scoring='f1_macro',n_jobs=1)
        search.fit(X_train,y_train)
        selected[name]=search.best_estimator_
        validation_score=float(search.best_score_)
        settings=search.best_params_
    else:
        selected[name]=candidate
        validation_score=float(np.mean(initial['test_score']))
        settings='Keep defaults: no production search'
    rows.append({'model':name,'initial_score':float(np.mean(initial['test_score'])),'selected_score':validation_score,'settings':str(settings)})
cv_results=pd.DataFrame(rows).set_index('model')
# This solution nominates by mean training-fold score. Other evidence-based choices can be defensible.
chosen_name=cv_results.selected_score.idxmax()
chosen=selected[chosen_name]
oof_predictions=cross_val_predict(chosen,X_train,y_train,cv=folds)
diagnostic_y=y_train
class_labels=sorted(y_train.unique())
matrix=confusion_matrix(diagnostic_y,oof_predictions,labels=class_labels)
fig,ax=plt.subplots(figsize=(6,4))
sns.heatmap(matrix,annot=True,fmt='d',cmap='Blues',ax=ax,xticklabels=class_labels,yticklabels=class_labels)
ax.set(xlabel='Predicted class',ylabel='Actual class',title='Training-only confusion matrix')
fig.tight_layout()
fig.savefig('diagnostic.png',dpi=150,bbox_inches='tight')
final_model=clone(chosen).fit(X_train,y_train)
final_predictions=final_model.predict(X_test)
final_f1=f1_score(y_test,final_predictions,average='macro')
final_accuracy=accuracy_score(y_test,final_predictions)
print('Final macro F1:',final_f1,'; accuracy:',final_accuracy)

import numpy as np
import pandas as pd
df=pd.read_csv('data/ml-learning/ML-X14.csv')

Why these steps exist

• LDA and QDA share population, features, stratified folds and scoring. Their separate shrinkage/regularisation choices are evaluated before nomination; warnings and class support qualify the more flexible covariance model. The final test evaluates the already chosen workflow.

Another valid approach

Equivalent ordinary Python is welcome. A defensible candidate or grouping need not match the solution’s choice; objective evidence must remain consistent.