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Okay, well in summary,
we've really learned a lot this module.

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We've thought about this task
of feature selection and

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we've described ways searching over first,
all possible

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sets of features that we might want to
include to come up with the best model.

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Talked about the challenges
of that computationally, and

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then we turned to thinking about greedy
algorithms and then discuss these

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radialized regression approach of lasso
for addressing the feature selection task.

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So really it's covering a lot of ground.

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That's really important
concepts in machine learning.

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And this lasso regularized regression
approach, although really, really simple,

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has dramatically transformed the field
of machine learning statistics and

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engineering.

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It's shown its utility in a variety
of different applied domains.

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But I wanna mention a really important
issue, which we kind of alluded to,

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which is that for feature selection,
not just lasso, but

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in general when you're thinking about
feature selection, you have to be really

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careful about interpreting
the features that you selected.

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And some reasons for
this include the fact that

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the features you selected
are always just in the context of

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what you provided as the set of possible
features to choose from to begin with.

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And likewise, the set of selected
features are really sensitive to

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correlations between features and,
in those cases,

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small changes in the data can lead to
different features being included, too.

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So to say that one feature is
important and the other isn't,

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you have to be careful
with statements like that.

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And also of course,

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the set of selective features
depends on which algorithm you use.

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We especially saw this when we talked
about those greedy algorithms,

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like the forward stepwise procedure.

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But I did want to mention that there
are some nice theoretical guarantees for

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lasso under very specific conditions.

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So in conclusion,
here's a very long list of things that you

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can do now that you've
completed this module.

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Everywhere from thinking about searching
over the discrete set of possible

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models to do future selection using
all subsets with these 3D algorithms.

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To formulating a regularized
regression approach,

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lasso, to implicitly do
this feature selection,

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searching over a continuous space,
this tuning parameter lambda.

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We talked about formulating the objective,

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geometric interpretations of why
the lasso objective leads to sparsity.

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And we talked about using coordinate
descent as an algorithm for solving lasso.

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And so coordinate descent itself was
an algorithm that generalizes well beyond

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lasso, so that was an important concept
that we got out of this module as well.

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And finally,
if you watch the optional video,

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we talked about some really technical
concepts relating to subgradients.

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And to conclude this module we
talked about some of the challenges

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associated with lasso.

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But, as well as some of the potential
impact that this method has,

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because it's really
quite an important tool.

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And like I've mentioned,

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it's really shown a lot of promise
in many different domains.

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