Develop Reference

How to train data with LOOCV approach and OVO?

I'm new in this field and I'm currently working with gene expression data. I have to do a classification where my data are Counts under matrix form. The features are the genes and the Samples to classify are the patients (7 types of cancer and healthy donors). The book from which I'm replicating the experiment says the following :
For the multi-class SVM classification algorithm, a One-Versus-One (OVO) approach was used. To cross validate the algorithm for all samples in the training cohort, the SVM algorithm was trained by all samples in the training cohort minus one, while the remaining sample was used for (blind) classification. This process was repeated for all samples until each sample was predicted once (leave-one-out cross-validation [LOOCV] procedure).
Now I actually know how to use Loocv on Python as I know how to use OVO by looking online. But I dont get what is mneant to be done here. I tried an attempt and results came out quite similar but im pretty sure I'm doing a horrible mistake somewhere. Please dont flame me I need help , here down below my interpretation (I copied this from internet and added Ovo instead of only svm):
#Function for training
def loocv(train_X,train_y):
# define X and y
X = train_X
y = train_y
# define LOOCV
loo = LeaveOneOut()
loo.get_n_splits(X)
# define true and predict list
y_true,y_pred = [],[]
# run
for train_index, test_index in loo.split(X):
X_train, X_test = X[train_index], X[test_index]
y_train, y_test = y[train_index], y[test_index]
model = SVC(kernel='linear',random_state=0)
ovo_classifier = OneVsOneClassifier(model)
ovo_classifier.fit(X_train,y_train)
yhat = ovo_classifier.predict(X_test)
y_true.append(y_test[0])
y_pred.append(yhat[0])
return y_true,y_pred,ovo_classifier
Validation :
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3,random_state=0)
y_true,y_pred,model = loocv(X_train,y_train)
pred_y = model.predict(X_test)
training_accuracy = accuracy_score(y_true,y_pred)
accuracy = accuracy_score(y_test,pred_y)
print(accuracy)
print(training_accuracy)
Results :
0.6918604651162791
0.6658291457286432

Evaluate Polynomial regression using cross_val_score

I am trying to use cross_val_score to evaluate my regression model (with PolymonialFeatures(degree = 2)). As I noted from different blog posts that I should use cross_val_score with original X, y values, not the X_train and y_train.
r_squareds = cross_val_score(pipe, X, y, cv=10)
r_squareds
>>> array([ 0.74285583, 0.78710331, -1.67690578, 0.68890253, 0.63120873,
0.74753825, 0.13937611, 0.18794756, -0.12916661, 0.29576638])
which indicates my model doesn't perform really well with the mean r2 of only 0.241. Is this supposed to be a correct interpretation?
However, I came across a Kaggle code working on the same data and the guy performed cross_val_score on X_train and y_train. I gave this a try and the average r2 was better.
r_squareds = cross_val_score(pipe, X_train, y_train, cv=10)
r_squareds.mean()
>>> 0.673
Is this supposed to be a problem?
Here is the code for my model:
X = df[['CHAS', 'RM', 'LSTAT']]
y = df['MEDV']
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=0)
pipe = Pipeline(
steps=[('poly_feature', PolynomialFeatures(degree=2)),
('model', LinearRegression())]
)
## fit the model
pipe.fit(X_train, y_train)

You first interpretation is correct. The first cross_val_score is training 10 models with 90% of your data as train and 10 as a validation dataset. We can see from these results that the estimator's r_square variance is quite high. Sometimes the model performs even worse than a straight line.
From this result we can safely say that the model is not performing well on this dataset.
It is possible that the obtained result using only the train set on your cross_val_score is higher but this score is most likely not representative of your model performance as the dataset might be to small to capture all its variance. (The train set for the second cross_val_score is only 54% of your dataset 90% of 60% of the original dataset)

Regarding increase in MSE of Cross-Validation model with increasing dataset for regression

I have the following experimental setup for a regression problem.
Using the following routine, a data set of about 1800 entries is separated into three groups, validation, test, and training.
X_train, X_test, y_train, y_test = train_test_split(inputs, targets, test_size=0.2,
random_state=42, shuffle=True)
X_train, X_val, y_train, y_val = train_test_split(X_train, y_train, test_size=0.25,
random_state=42, shuffle=True)
So in essence, training size ~ 1100, validation and test size ~ 350, and each subset is then having unique set of data points, that which is not seen in the other subsets.
With these subsets, I can preform a fitting using any number of the regression models available from scikit-learn, using the following routine:
model = LinearRegression()
clf = make_pipeline(StandardScaler(), model)
clf.fit(X_train, y_train)
predictions = clf.predict(X_test)
Doing this I then calculate the RMSE of the predictions, which in the case of the linear regressor, is about ~ 0.948.
Now, I could instead use cross-validation and not worry about splitting the data instead, using the following routine:
model = LinearRegression()
clf = make_pipeline(StandardScaler(), model)
predictions2 = cross_val_predict(clf, X, y, cv=KFold(n_splits=10, shuffle=True, random_state=42))
However, when I calculate the RMSE of these predictions, it is about ~2.4! To compare, I tried using a similar routine, but switched X for X_train, and y for y_train, i.e.,
model = LinearRegression()
clf = make_pipeline(StandardScaler(), model)
predictions3 = cross_val_predict(clf, X_train, y_train, cv=KFold(n_splits=10, shuffle=True, random_state=42))
and received a RMSE of about ~ 0.956.
I really do not understand why that when using the entire data set, the RMSE for the cross-validation is so much higher, and that the predictions are terrible in comparison to that with reduced data set.
Additional Notes
Additionally, I have tried out running the above routine, this time using the reduced subset X_val, y_val as inputs for the cross validation, and still receive small RMSE. Additionally, when I simply fit a model on the reduced subset X_val, y_val, and then make predictions on X_train, y_train, the RMSE is still better (lower) than that of the cross-validation RMSE!
This does not only happen for LinearRegressor, but also for RandomForrestRegressor, and others. I have additionally tried to change the random state in the splitting, as well as completely shuffling the data around before handing it to the train_test_split, but still, the same outcome occurs.
Edit 1.)
I tested out this on a make_regression data set from scikit and did not get the same results, but rather all the RMSE are small and similar. My guess is that is has to do with my data set.
If anyone could help me out in understanding this, I would greatly appreciate it.
Edit 2.)
Hi thank you (#desertnaut) for the suggestions, the solution was actually quite easy, and the fact was that in my routine to process the data, I was using (targets, inputs) = (X, y), which is really wrong. I swapped that with (targets, inputs) = (y, X), and now the RMSE is about the same as the other profiles. I made a histogram profile of the data and found that problem. Thanks! I'll save the question for about 1 hour, then delete it.

You're overfitting.
Imagine you had 10 data points and 10 parameters, then RMSE would be zero because the model could perfectly fit the data, now increase the data points to 100 and the RMSE will increase (assuming there is some variance in the data you are adding of course) because your model is not perfectly fitting the data anymore.
RMSE being low (or R-squared high) more often than not doesn't mean jack, you need to consider the standard errors of your parameter estimates . . . If you are just increasing the number of parameters (or conversely, in your case, decreasing the number of observations) you are just chewing away your degrees of freedom.
I'd wager that your standard error estimates for the X model's parameter estimates are smaller than your standard error estimates in the X_train model, even though RMSE is "lower" in the X_train model.
Edit: I'll add that your dataset exhibits high multicollinearity.

Should Cross Validation Score be performed on original or split data?

When I want to evaluate my model with cross validation, should I perform cross validation on original (data thats not split on train and test) or on train / test data?
I know that training data is used for fitting the model, and testing for evaluating. If I use cross validation, should I still split the data into train and test, or not?
features = df.iloc[:,4:-1]
results = df.iloc[:,-1]
x_train, x_test, y_train, y_test = train_test_split(features, results, test_size=0.3, random_state=0)
clf = LogisticRegression()
model = clf.fit(x_train, y_train)
accuracy_test = cross_val_score(clf, x_test, y_test, cv = 5)
Or should I do like this:
features = df.iloc[:,4:-1]
results = df.iloc[:,-1]
clf = LogisticRegression()
model = clf.fit(features, results)
accuracy_test = cross_val_score(clf, features, results, cv = 5)), 2)
Or maybe something different?

Both your approaches are wrong.
In the first one, you apply cross validation to the test set, which is meaningless
In the second one, you first fit the model with your whole data, and then you perform cross validation, which is again meaningless. Moreover, the approach is redundant (your fitted clf is not used by the cross_val_score method, which does its own fitting)
Since you are not doing any hyperparameter tuning (i.e. you seem to be interested only in performance assessment), there are two ways:
Either with a separate test set
Or with cross validation
First way (test set):
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score
x_train, x_test, y_train, y_test = train_test_split(features, results, test_size=0.3, random_state=0)
clf = LogisticRegression()
model = clf.fit(x_train, y_train)
y_pred = clf.predict(x_test)
accuracy_test = accuracy_score(y_test, y_pred)
Second way (cross validation):
from sklearn.model_selection import cross_val_score
from sklearn.metrics import accuracy_score
from sklearn.utils import shuffle
clf = LogisticRegression()
# shuffle data first:
features_s, results_s = shuffle(features, results)
accuracy_cv = cross_val_score(clf, features_s, results_s, cv = 5, scoring='accuracy')
# fit the model afterwards with the whole data, if satisfied with the performance:
model = clf.fit(features, results)

I will try to summarize the "best practice" here:
1) If you want to train your model, fine-tune parameters, and do final evaluation, I recommend you to split your data into training|val|test.
You fit your model using the training part, and then you check different parameter combinations on the val part. Finally, when you're sure which classifier/parameter obtains the best result on the val part, you evaluate on the test to get the final rest.
Once you evaluate on the test part, you shouldn't change the parameters any more.
2) On the other hand, some people follow another way, they split their data into training and test, and they finetune their model using cross-validation on the training part and at the end they evaluate it on the test part.
If your data is quite large, I recommend you to use the first way, but if your data is small, the 2.

SKLearn Predicting using new Data

I've tried out Linear Regression using SKLearn. I have data something along the lines of: Calories Eaten | Weight.
150 | 150
300 | 190
350 | 200
Basically made up numbers but I've fit the dataset into the linear regression model.
What I'm confused on is, how would I go about predicting with new data, say I got 10 new numbers of Calories Eaten, and I want it to predict Weight?
regressor = LinearRegression()
regressor.fit(x_train, y_train)
y_pred = regressor.predict(x_test) ??
But how would I go about making only my 10 new data numbers of Calories Eaten and make it the Test Set I want the regressor to predict?

You are correct, you simply call the predict method of your model and pass in the new unseen data for prediction. Now it also depends on what you mean by new data. Are you referencing data that you do not know the outcome of (i.e. you do not know the weight value), or is this data being used to test the performance of your model?
For new data (to predict on):
Your approach is correct. You can access all predictions by simply printing the y_pred variable.
You know the respective weight values and you want to evaluate model:
Make sure that you have two separate data sets: x_test (containing the features) and y_test (containing the labels). Generate the predictions as you are doing with the y_pred variable, then you can calculate its performance using a number of performance metrics. Most common one is the root mean square, and you simply pass the y_test and y_pred as parameters. Here is a list of all the regression performance metrics supplied by sklearn.
If you do not know the weight value of the 10 new data points:
Use train_test_split to split your initial data set into 2 parts: training and testing. You would have 4 datasets: x_train, y_train, x_test, y_test.
from sklearn.model_selection import train_test_split
# random state can be any number (to ensure same split), and test_size indicates a 25% cut
x_train, y_train, x_test, y_test = train_test_split(calories_eaten, weight, test_size = 0.25, random_state = 42)
Train model by fitting x_train and y_train. Then evaluate model's training performance by predicting on x_test and comparing these predictions with the actual results from y_test. This way you would have an idea of how the model performs. Furthermore, you can then predict the weight values for the 10 new data points accordingly.
It is also worth reading further on the topic as a beginner. This is a simple tutorial to follow.

You have to select the model using model_selection in sklearn then train and fit the dataset.
from sklearn.model_selection import train_test_split
X_train, y_train, X_test, y_test = train_test_split(eaten, weight)
regressor.fit(X_train, y_train)
y_pred = regressor.predict(X_test)

What I'm confused on is, how would I go about predicting with new
data, say I got 10 new numbers of Calories Eaten, and I want it to
predict Weight?
Yes, Calories Eaten represents the independent variable while Weight represent dependent variable.
After you split the data into training set and test set the next step is to fit the regressor using X_train and y_train data.
After the model is trained you can predict the results for X_test method and so we got the y_pred.
Now you can compare y_pred (predicted data) with y_test which is real data.
You can also use score method for your created linear model in order to get the performance of your model.
score is calculated using R^2(R squared) metric or Coefficient of determination.
score = regressor.score(x_test, y_test)
For splitting the data you can use train_test_split method.
from sklearn.model_selection import train_test_split
X_train, y_train, X_test, y_test = train_test_split(eaten, weight, test_size = 0.2, random_state = 0)