案例学习：预测房价

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From the course by University of Washington

机器学习：回归

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案例学习：预测房价

From the lesson

Feature Selection & Lasso

A fundamental machine learning task is to select amongst a set of features to include in a model. In this module, you will explore this idea in the context of multiple regression, and describe how such feature selection is important for both interpretability and efficiency of forming predictions. <p> To start, you will examine methods that search over an enumeration of models including different subsets of features. You will analyze both exhaustive search and greedy algorithms. Then, instead of an explicit enumeration, we turn to Lasso regression, which implicitly performs feature selection in a manner akin to ridge regression: A complex model is fit based on a measure of fit to the training data plus a measure of overfitting different than that used in ridge. This lasso method has had impact in numerous applied domains, and the ideas behind the method have fundamentally changed machine learning and statistics. You will also implement a coordinate descent algorithm for fitting a Lasso model. <p>Coordinate descent is another, general, optimization technique, which is useful in many areas of machine learning.

- Emily FoxAmazon Professor of Machine Learning

Statistics - Carlos GuestrinAmazon Professor of Machine Learning

Computer Science and Engineering

>> [MUSIC]

Now that we've described our lasso objective and

we've given some intuition for why it leads to sparse solutions,

now let's turn to how we're going to optimize our objective and

actually solve for our lasso solution, for a specific value of lambda, this tuning

parameter that's weighing how much we're Including this L1 term in our objective.

So, in our machine learning workflow for

regression, we're talking about this gray box here, our machine learning algorithm.

And let's first remember what we've done for

past objectives when we talked about least squares and ridge regression.

What we did was, we took the gradient of our total cost and then we

either looked at a closed-form solution, setting that gradient equal to zero, or

we used the gradient within an iterative procedure called gradient descent.

Well here's our lasso objective.

And let's think about taking the gradient.

Well, we know how to take the gradient to the residual sum of squares term, but

then we get to this L1 objective.

And we have some issues.

In particular, what's the derivative of the absolute value?

Because remember our L1 objective is the sum over

j equals zero to d of the absolute value of wj.

So we're gonna have to take derivatives of this absolute value of wj.

And when I think about this absolute value function.

So this is wj, absolute value of wj,

well, what's the derivative here?

The derivative any point along this side is gonna be minus one.

The slope of this line is minus one.

And the derivative anywhere on this half of the plain

Is plus one because the slope is plus one.

And then I get to this critical zero point.

And what's the derivative there?

There's actually no derivative that exists at that point.

So instead of thinking about gradients defined by these derivatives,

we can talk about something called subgradients.

And we're gonna discuss the concept of subgradients

in a more advanced, optional video.

But just know that they exist, and they're crucial to

the derivation of the algorithms we're gonna talk about for the lasso objective.

And if you're interested in learning more, stay tuned for

our optional advanced video.

But even if you could compute this derivative that we're saying

doesn't exist for this absolute value function,

there's still no closed-form solution for our lasso objective.

So we can't do the closed-form option, but

we could do our gradient descent algorithm.

But again not using gradients, using subgradients.

[MUSIC]

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