[MUSIC] Okay, well in summary,
we've really learned a lot this module. We've thought about this task
of feature selection and we've described ways searching over first,
all possible sets of features that we might want to
include to come up with the best model. Talked about the challenges
of that computationally, and then we turned to thinking about greedy
algorithms and then discuss these radialized regression approach of lasso
for addressing the feature selection task. So really it's covering a lot of ground. That's really important
concepts in machine learning. And this lasso regularized regression
approach, although really, really simple, has dramatically transformed the field
of machine learning statistics and engineering. It's shown its utility in a variety
of different applied domains. But I wanna mention a really important
issue, which we kind of alluded to, which is that for feature selection,
not just lasso, but in general when you're thinking about
feature selection, you have to be really careful about interpreting
the features that you selected. And some reasons for
this include the fact that the features you selected
are always just in the context of what you provided as the set of possible
features to choose from to begin with. And likewise, the set of selected
features are really sensitive to correlations between features and,
in those cases, small changes in the data can lead to
different features being included, too. So to say that one feature is
important and the other isn't, you have to be careful
with statements like that. And also of course, the set of selective features
depends on which algorithm you use. We especially saw this when we talked
about those greedy algorithms, like the forward stepwise procedure. But I did want to mention that there
are some nice theoretical guarantees for lasso under very specific conditions. So in conclusion,
here's a very long list of things that you can do now that you've
completed this module. Everywhere from thinking about searching
over the discrete set of possible models to do future selection using
all subsets with these 3D algorithms. To formulating a regularized
regression approach, lasso, to implicitly do
this feature selection, searching over a continuous space,
this tuning parameter lambda. We talked about formulating the objective, geometric interpretations of why
the lasso objective leads to sparsity. And we talked about using coordinate
descent as an algorithm for solving lasso. And so coordinate descent itself was
an algorithm that generalizes well beyond lasso, so that was an important concept
that we got out of this module as well. And finally,
if you watch the optional video, we talked about some really technical
concepts relating to subgradients. And to conclude this module we
talked about some of the challenges associated with lasso. But, as well as some of the potential
impact that this method has, because it's really
quite an important tool. And like I've mentioned, it's really shown a lot of promise
in many different domains. [MUSIC]