function that returns the input that maximizes the expression.

finding argmax

direct optimization

Typical maximization system. Take derivative, set it to 0, solve, plug in, solve. THis is pretty bad during times are not differentiable.

gradient ascent

We take steps following the direction

\begin{equation} \theta_{1j} = \theta_{0j} + \eta \pdv{LL(\theta_{0})}{\theta_{0j}} \end{equation}

additional information

argmax of log

see argmax of log

• When you make an array, you are making space for each element
• When you create a pointer, you are making space for 64 bit address
• arrays “decay to pointers”: when you identify an array by name, you are sharing the location of the leading element
• &arr gets an address to the FIRST element — don’t do this, &ptr gets the pointers’ address

Array is a special type that represent a segment of contiguously allocated memory. You can’t reassign an array to be equal to a new array.

Artificial Intelligence is defined as the act of parameter estimation.

Toy example for Linear Regression

• Imagine if we want to predict the price of a choclate bar
• We feed in a bunch of bar weight vs. chocolate price data; that’s the training data
• Then, we come up with a model of the training data
• We then throw away the training data

Therefore, we can think of the model as a COMPRESSION of the training data; estimating parameters.