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>> Okay, let's talk about this in the context of the bias variance trade-off.
And what we saw is when we had very large lambda,
we had a solution with very high bias, but low variance.
And one way to see this is that, is thinking about when we're cranking lambda
all the way up to infinity, in that limit, we get coefficients shrunk to be zero,
and clearly that's a model with high bias but low variance.
It's completely low variance, it doesn't change no matter what data you give me.
On the other hand, when we had very small lambda,
we have a model that is low bias, but high variance.
And to see this think about setting lambda to zero, in which case, we get out just
our old solution, our old lee squares or minimizing residual sum of squares fit.
And there we see that for
higher complexity models clearly you're gonna have low bias but high variance.
So what we see is this lambda tuning parameter controls our model
complexity and controls this bias variance trade-off.
Okay, so let's return to our polynomial regression demo, but
now using ridge regression and see if we can ameliorate the issues of
over-fitting as we vary the choice of lambda.
And so we're going to explore this ridge regression solution for
a couple different choices of this lambda tuning parameter.
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