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Statistical learning has a large assortment of tools for conducting feature selection such as PCA analysis, ridge regression, LASSO, SVM and almost every other machine learning algorithm.

In portfolio optimization, portfolio weights are optimized based on data consisting only of asset return time series, $x$, which line the matrix $X$.

If each asset (each column of $X$) can be thought of as features, then isn't the mean-variance model just a supervised learning model that weights the individual assets based on feature selection philosophy? meaning that pretty much any learning algorithm can be replaced into the traditional model in order to conduct feature selection (the fractional choosing of assets according to each algorithm's own unique criteria)?

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    $\begingroup$ Seen from sufficiently high above, the last 5 billion years of evolution are "just" feature selection aren't they? Seriously, what is your question? That every learning algorithm is just mean-variance optimisation? This is most certainly wrong, although hard to tell if you do not specify how mean and variance are defined. $\endgroup$ – g g Aug 14 '20 at 19:09
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    $\begingroup$ Except for with portfolio optimization we are not trying to minimize variation from a target response but, instead, maximize expected returns -- possibly with a penalty of risk. So $\min (y_i-X_i\beta)^2$ vs (say) $\max w^T r - \lambda w^T\Sigma_r w$, s.t. $||s||_1=1$. Not really the same problem. $\endgroup$ – kurtosis Aug 14 '20 at 19:55
  • $\begingroup$ feature selection can be a stand-alone task, without supervised learning or response variable $\endgroup$ – develarist Aug 14 '20 at 20:34

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