AI News, Python Implementation of Andrew Ng’s Machine Learning Course (Part 1)
Python Implementation of Andrew Ng’s Machine Learning Course (Part 1)
The file ex1data1.txt (available under week 2's assignment material) contains the dataset for our linear regression exercise.
Adding the intercept term In the following lines, we add another dimension to our data to accommodate the intercept term (the reason for doing this is explained in the videos).
np.newaxis is used if you want to convert 1-D array (shape: N elements) into row vector (shape: N rows, 1 column) or column vector (shape: 1 row, N columns).
It should give you a value of 4.483 which is much better than 32.07 Plot showing the best fit line Lets extend the idea of linear regression to work with multiple independent variables.
The file ex1data2.txt((available under week 2’s assignment material)) contains a training set of housing prices in Portland, Oregon.
The first column is the size of the house (in square feet), the second column is the number of bedrooms, and the third column is the price of the house.
As can be seen above we are dealing with more than one independent variables here (but the concepts you have learnt in the previous section applies here as well).
When features differ by orders of magnitude, first performing feature scaling can make gradient descent converge much more quickly.
Our task here is to: Adding the intercept term and initializing parameters (the below code is similar to what we did in the previous section) Computing the cost You should expect to see a cost of 65591548106.45744.
BSCI 1510L Literature and Stats Guide: 6 Scatter plot, trendline, and linear regression
A regression analysis can provide three forms of descriptive information about the data included in the analysis: the equation of the best fit line, an R2 value, and a P-value.
A regression analysis of these data calculates that the equation of the best fit line is y = 6x + 55 .
Right: R2=0.16, P=0.029 There are other patterns of data for which the best fit line would also be y = 6x + 55 .
Its value ranges from 0 (essentially a random cloud of points) to 1 (the points fall perfectly on a straight line).
An R2 of 0.94 means that 94% of the variance in the data is explained by the line and 6% of the variance is due to unexplained effects.
The value of P is accordingly high, indicating that it is probable that the slope could deviate from zero by this amount based solely on chance.
How to run Linear regression in Python scikit-Learn
You know that linear regression is a popular technique and you might as well seen the mathematical equation of linear regression.
There are several ways in which you can do that, you can do linear regression using numpy, scipy, stats model and sckit learn.
It contains function for regression, classification, clustering, model selection and dimensionality reduction. Today, I will explore the sklearn.linear_model module which contains “methods intended for regression in which the target value is expected to be a linear combination of the input variables”.
In this post, I will use Boston Housing data set, the data set contains information about the housing values in suburbs of Boston.
The goal of this exercise is to predict the housing prices in boston region using the features given.
Y = boston housing price(also called “target” data in Python) and X = all the other features (or independent variables) First, I am going to import linear regression from sci-kit learn module.
fits a linear model lm.predict() -> Predict Y using the linear model with estimated coefficients lm.score() -> Returns the coefficient of determination (R^2). A measure of how well observed outcomes are replicated by the model, as the proportion of total variation of outcomes explained by the model. You can also explore the functions inside lm object by pressing lm.<tab>
Training and validation data sets In practice you wont implement linear regression on the entire data set, you will have to split the data sets into training and test data sets.
You can create training and test data sets manually, but this is not the right way to do, because you may be training your model on less expensive houses and testing on expensive houses.
am going to build a linear regression model using my train-test data sets.
“Fit a model X_train, and calculate MSE with X_test, Y_test:”, np.mean((Y_test – lm.predict(X_test)) ** 2) Output: Fit a model X_train, and calculate MSE with Y_train: 19.5467584735 Fit a model X_train, and calculate MSE with X_test, Y_test: 28.5413672756 Residual Plots Residual plots are a good way to visualize the errors in your data. If you have done a good job then your data should be randomly scattered around line zero.
- On Monday, March 25, 2019
Scatter Plot for Multiple Regression
I demonstrate how to create a scatter plot to depict the model R results associated with a multiple regression/correlation analysis.
Gradient descent, how neural networks learn | Deep learning, chapter 2
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