machine learning by Andrew NG(2)/Linear Regression with One Variable

2019-11-06 09:19:52

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today we will talk about the following points: - model rePResentation - cost function - gradient descent - gradient descent for linear regression - what’s next

model representation

training set notation: m = number of training examples x’s = input variable / features y’s = output variable / target variable

(x,y) one traing example (x ^i, y ^i) i-th training example

learning algorithmhypothesis

ml model representation

cost function

what ‘s cost function? how it comes? ml cost function

now we have:

why we want to use it ? the less the cost function, the more accuracy of the hypothesis one parameter theta1: ml cost function

two parameter theta0, theta1: ml cost function

gradient descent if we have training set,learning algorithm and hypothesis, then we want to minimize the cost function J of theta. one way of finding the minimum cost function is gradient descent.

methods:

start with some theta0,theta1keep changing theta0,theta1 to reduce J of theta until we end up at a minimum

graphs:

problem: diff start position may lead to diff local optima

definition: simutinously update

intuition: let’s just think about the parameter theta1: the problem of learning rate: why gradient descent can converge without turning learning rate smaller?

gradient descent for linear regression

outcome:

batch Gradient Descent: batch

two extension

solve theta0,theta1 without iterationlearn with larger number of features subscripts to describe features. Ex: x1 x2 x3use linear algebra. Matrix and Vector

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