Slight typo

chapters/highdimensional.tex

@@ -1,7 +1,7 @@
 %!TEX root = ../main.tex
 \chapter{High-Dimensional Linear Regression}
 \section{Introduction}
-So far we've looked at model selection. For example, we considered the problem of choosing the ``best'' set of regressors for a forecasting problem. Here, the idea was to consider dropping regressors with small coefficients to get a favorable bias-variance tradeoff. There are several problems with this approach. First, variable selection can be unstable because of the discrete nature of the problem: small changes in the underlying data could lead to large changes in the selected set of regressors. Second, it is only computationally infeasible to consider all possible subsets of regressors when $p < 30$. Our colleague Andy Postelwaite actually has a microeconomic theory paper about this called ``Fact Free Learning.'' You should check it out: it's very interesting!
+So far we've looked at model selection. For example, we considered the problem of choosing the ``best'' set of regressors for a forecasting problem. Here, the idea was to consider dropping regressors with small coefficients to get a favorable bias-variance tradeoff. There are several problems with this approach. First, variable selection can be unstable because of the discrete nature of the problem: small changes in the underlying data could lead to large changes in the selected set of regressors. Second, it is only computationally infeasible to consider all possible subsets of regressors when $p < 30$. Our colleague Andy Postlewaite actually has a microeconomic theory paper about this called ``Fact Free Learning.'' You should check it out: it's very interesting!
 
 In this lecture we'll consider an alternative to model selection called ``shrinkage.'' The idea is roughly as follows: rather than making a discrete choice of which variables are ``in'' and which are ``out,'' it might make more sense to leave everything in the model but ``regularize'' or ``shrink'' the estimated coefficients away from the maximum likelihood estimator, much as a Bayesian prior does. Rather than attempting to incorporate prior beliefs, however, here the idea is merely to find a clever way of adding bias that buys us a large decrease in variance. There will still be a model selection component here, but it will involve a single, continuous ``tuning'' or ``smoothing'' parameter.