thinking space

1/Advertising.csv

@@ -0,0 +1,201 @@
+,TV,radio,newspaper,sales
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1/readme.md

@@ -0,0 +1,76 @@
+# this ass
+
+1. Linear Regression Implementation
+   Download the advertising dataset. This is a dataset that gives us the total sales for different products,
+   after marketing them on Television, Radio and Newspaper.
+
+   - Implement the Linear regression algorithm to predict the sales value, given three inputs
+     (Television, Radio and Newspaper).
+   - Calculate the cost function after each iteration, draw cost function as a function of the iteration
+   - Try the program with various values for the learning rate alpha and number of iteration.’
+
+2. Solve the problem 1 with normal equation method
+3. Redo exercise 1 with regularization
+4. Redo exercise 2 with regularization
+
+## plan
+
+what the fuck is a Linear regression?
+
+it is to my knowledge: fit a thing to a linear equation, with the Minimal Error.
+
+### error function, cost function: the thig we want reduced
+
+this is the cost function, also loss function:
+
+$$
+    E = \frac{1}{2m} \sum^m_{i = 1}\left(h(x_{(i)})- y_{(i)}\right)^2
+$$
+
+with $h(x)$ being our model (we are trying to find a and b and make our guess $h(x)$ as close to $y$ as possible)
+
+this comes from the error function here:
+
+$$e = \frac{1}{2}\left(h(x_{(i)})-y_{(i)}\right)^2$$
+
+and the cost function from the error function:
+
+$$E = \frac{1}{m}\sum^m_{i=1}e_{(i)}$$
+
+as were dealing with linear fitting ($h(x) = ax + b$) the thing turns to this:
+
+$$
+E = \frac{1}{2m} \sum_{i=1}^{m} \left( ax_i + b - y_i \right)^2
+$$
+
+chatgpt-ed this shit it calls this strat Mean Squared Error (MSE)
+
+### gradient descent: we are taking the derivative of this shit
+
+partial derivative of course.
+
+its newton raphson all over again:
+
+you have to change every coefficients so they yk fit the thing every time duh
+
+and how you change goes like this:
+
+$$a:= a - \alpha \frac{\partial E}{\partial a}$$
+
+yes. partial deriv that fucking series wrt a. fucking insane innit.
+
+however they did the calculations:
+
+for our case $h(x) = ax + b$ we have
+
+$$
+\frac{\partial}{\partial a}{E(a, b)}
+\text{ or } \\
+\frac{\partial E}{\partial a} = \frac{1}{m}\sum^m_{i=1}(ax_{(i)}+b - y_{(i)})\cdot x_{(i)}
+$$
+
+yeah also for the case of b:
+
+$$b:= b - \alpha \frac{\partial E}{\partial b}$$
+
+$$\frac{\partial E}{\partial b} = \frac{1}{m}\sum^m_{i=1}(ax_{(i)}+b - y_{(i)})$$

README.md

@@ -1,3 +1,4 @@
 # ml1
 
-machine learning and data mining 1, lab works
+machine learning and data mining 1, lab works
+