Polynom

polynom

Sometimes there's more than one, right?

And the reason is, what we've done is, we've fit this extra the parameter d, that is this degree of polynomial, and we'll fit that parameter d using the test set.

So the easiest way to approximate it is to say, well, the simplest polynomial is just a constant, right?

That's because I've fit my parameters to the test set.

Now let's plot the following figure.

So they give us a function, f of x.

So that's the area and it's a monomial.

left corresponds to a high bias problem, that is, if you are fitting an overly

And what we did in this with the repeated factor is true if we went to a higher degree term.

So this checks out.

So let me just draw a little bit of a graph.

What can I do with this?

And we showed it in the beginning.

Let's keep going.

I have something shifted here.

Now let's consider the model selection problem.

Let's start with the training error.

In this case, in all of the examples we'll do, it'll be x.

So x is equal to r3.

In this video, I want to focus on a few more techniques for factoring polynomials.

It could be that NP is equal to x. It could also that P is equal to NP.

lambda, such as if lambda were equal to 0.

We know the exponential function.

So let's see if we can make some headway on this.

Consider the following graph where the horizontal axis graphs complexity of the solution.

It could be the case that the class NP is actually equal to the class EXP.

Okay, so you have a sense that these are considered to be pretty good algorithms.

Oh. We're not good enough?

So if we viewed a squared as kind of the independent variable or the x term, so now this kind of has the shape of polynomials that hopefully you're used to factoring a

This is true.

One thing I could do is

This might not be completely obvious.

That's y minus 1 squared.

The sum of two binomials is 5x squared minus 6x.

After every step we're canceling out the largest degree of the polynomial we're dividing into.

We have a graph of a given size that from that we generate a formula and the formula has given size and that size is polynomial.

Then we would have this equaling 0 and then you could say the roots of this polynomial or the solutions to the equation are what makes this true.

Or we could write this as x minus 7 squared is equal to 0.

The y terms become 4 times y minus 2 squared. y minus 2 squared.

Let's say this is my polynomial, let me call my polynomial p of x.

Let me draw my axes.

And, if you include enough polynomial terms then, you know, maybe you can get a hypotheses that separates the positive and negative examples.

Simplify the rational expression and state the domain.