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week 37

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Morten Hjorth-Jensen
2022-08-23 10:41:54 +02:00
parent 3b8fc53c1c
commit a64e06d984
57 changed files with 3260 additions and 3441 deletions
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doc/src/week37/olscode.py~
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import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import KFold
from sklearn.linear_model import Ridge, LinearRegression
from sklearn.model_selection import cross_val_score
from sklearn.preprocessing import PolynomialFeatures
# A seed just to ensure that the random numbers are the same for every run.
# Useful for eventual debugging.
np.random.seed(3155)
# Generate the data.
nsamples = 1000
x = np.random.randn(nsamples)
y = 3*x**2 + np.random.randn(nsamples)
## Cross-validation on Ridge regression using KFold only
# Decide degree on polynomial to fit
poly = PolynomialFeatures(degree = 6)
# Initialize a KFold instance
k = 10
kfold = KFold(n_splits = k)
# Perform the cross-validation to estimate MSE using OLS
scores_KFold = np.zeros((k))
model = LinearRegression()
j = 0
for train_inds, test_inds in kfold.split(x):
xtrain = x[train_inds]
ytrain = y[train_inds]
xtest = x[test_inds]
ytest = y[test_inds]
Xtrain = poly.fit_transform(xtrain[:, np.newaxis])
model.fit(Xtrain, ytrain[:, np.newaxis])
Xtest = poly.fit_transform(xtest[:, np.newaxis])
ypred = model.predict(Xtest)
scores_KFold[j] = np.sum((ypred - ytest[:, np.newaxis])**2)/np.size(ypred)
print(f"Score for each fold:{scores_KFold[j]}")
j += 1
estimated_mse_KFold = np.mean(scores_KFold)
print(f"Average OLS score:{estimated_mse_KFold}")
doc/src/week37/week37.do.txt
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@@ -5,11 +5,9 @@ DATE: today
!split
===== Plans for week 37 =====
* Thursday September 16: Summary of Ridge and Lasso with examples and start resampling techniques
o "Video of Lecture, first part":"https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember16Firstpart.mp4?vrtx=view-as-webpage"
o "Video of Lecture, second part":"https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember16SecondPart.mp4?vrtx=view-as-webpage"
* Friday September 17: Resampling methods, Cross-validation, Bootstrapping and jackknife
o "Video of Lecture":"https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember17.mp4?vrtx=view-as-webpage"
* Thursday September 15: Summary of Ridge and Lasso with examples and start resampling techniques
* Friday September 16: Resampling methods, Cross-validation, Bootstrapping and jackknife
Recommended Reading:
o Lectures on Resampling methods (these lectures)
o Bishop 1.3 (cross-validation) and 3.2 (bias-variance tradeoff)
@@ -18,7 +16,7 @@ o Hastie et al Chapter 7, here we recommend 7.1-7.5 and 7.10 (cross-validation)
!split
===== Thursday September 16, Summary of Ridge and Lasso Regression and start Resampling methods =====
===== Thursday September 15, Summary of Ridge and Lasso Regression and start Resampling methods =====
!split