Python, Machine Learning and Linear Regression

Question

I'm new to Python and Machine Learning and I have an homework to deliver next week. This is the code I have until now:

# to get in-line plots
%matplotlib inline
import matplotlib.pyplot as plt

import numpy as np
import scipy as sp
from scipy import stats

# Load the data
IDnumber = 0000001
np.random.seed(IDnumber)

filename = "ccpp_Data_clean2018.csv"

Data = np.genfromtxt(filename, delimiter=';',skip_header=1)
dataDescription = stats.describe(Data)
print(dataDescription)

Data.shape

#get number of total samples
num_total_samples = Data.shape[0]

print("Total number of samples: "+str(num_total_samples))

#size of each chunk of data for training, validation, testing
size_chunk = int(num_total_samples/3.)

print("Size of each chunk of data: "+str(size_chunk))

#shuffle the data
np.random.shuffle(Data)

#training data
X_training = np.delete(Data[:size_chunk], 4, 1)
Y_training = Data[:size_chunk, 4]
print("Training data input size: "+str(X_training.shape))
print("Training data output size: "+str(Y_training.shape))

#validation data, to be used to choose among different models
X_validation = np.delete(Data[size_chunk:size_chunk*2], 4, 1)
Y_validation = Data[size_chunk:size_chunk*2, 4]
print("Validation data input size: "+str(X_validation.shape))
print("Validation data ouput size: "+str(Y_validation.shape))

#test data, to be used to estimate the true loss of the final model(s)
X_test = np.delete(Data[size_chunk*2:num_total_samples], 4, 1)
Y_test = Data[size_chunk*2: num_total_samples, 4]
print("Test data input size: "+str(X_test.shape))
print("Test data output size: "+str(Y_test.shape))
#scale the data

# standardize the input matrix
from sklearn import preprocessing
scaler = preprocessing.StandardScaler().fit(X_training)
X_training = scaler.transform(X_training)
print("Mean of the training input data:"+str(X_training.mean(axis=0)))
print("Std of the training input data:"+str(X_training.std(axis=0)))
X_validation = scaler.transform(X_validation) # use the same transformation on validation data
print("Mean of the validation input data:"+str(X_validation.mean(axis=0)))
print("Std of the validation input data:"+str(X_validation.std(axis=0)))
X_test = scaler.transform(X_test) # use the same transformation on test data
print("Mean of the test input data:"+str(X_test.mean(axis=0)))
print("Std of the test input data:"+str(X_test.std(axis=0)))
#compute linear regression coefficients for training data

#add a 1 at the beginning of each sample for training, validation, and testing
m_training = # COMPLETE: NUMBER OF POINTS IN THE TRAINING SET
X_training = np.hstack((np.ones((m_training,1)),X_training))

m_validation = # COMPLETE: NUMBER OF POINTS IN THE VALIDATION SET
X_validation = np.hstack((np.ones((m_validation,1)),X_validation))

m_test = # COMPLETE: NUMBER OF POINTS IN THE TEST SET
X_test = np.hstack((np.ones((m_test,1)),X_test))

# Compute the coefficients for linear regression (LR) using linalg.lstsq
w_np, RSStr_np, rank_X_tr, sv_X_tr = #COMPLETE

print("LR coefficients with numpy lstsq: "+ str(w_np))

# compute Residual sums of squares by hand
print("RSS with numpy lstsq: "+str(RSStr_np))
print("Empirical risk with numpy lstsq:"+str(RSStr_np/m_training))

The way I split the set was part of the assignment, the data I have to predict is in the last column and this is the dataset: http://archive.ics.uci.edu/ml/datasets/Combined+Cycle+Power+Plant .

My question is: in the last part of the code (where are the "complete" line) the m_training, m_validation and m_test are simply the shape of the corresponding X? I mean:

m_training = X_training.shape

and so on. I am not sure about that. Finally what are the parameters that I have to pass in input to the linalg.lstsq function?

UPDATE I'm going forward with the code but I'm stuck again, this time I have to:

#compute predictions on training set, validation set, and test set
prediction_training = # COMPLETE
prediction_validation = # COMPLETE
prediction_test = # COMPLETE

#what about the RSS and loss for points in the validation data?
RSS_validation =# COMPLETE
RSS_test = # COMPLETE

print("RSS on validation data: "+str(RSS_validation))
print("Loss estimated from validation data:"+str(RSS_validation/m_validation))


#another measure of how good our linear fit is given by the following (that is 1 - R^2)
#compute 1 -R^2 for training, validation, and test set
Rmeasure_training = #COMPLETE
Rmeasure_validation = #COMPLETE 
Rmeasure_test = #COMPLETE

I am finding many difficulties so if you have some good suggestion on where I can find and learn what I need I would appreciate so much. I have a text book but there isn't programming, only theory.

Answer 1

You can use

 m_training=len(X_training)

but a better way is indeed to use shape

X_training.shape

that will return a tuple (m, n), where m is the number of rows, and n is the number of columns. Then

m_training = X_training.shape[0]

is what you are looking for. Indeed in order to add a column of 1 in the fist row of your data you need to indicate the number of rows.

For the function linalg.lstsq you can look at the examples in: https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.linalg.lstsq.html

In your case it should be:

linalg.lstsq(X_training,y_training)