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| author | Stratis Ioannidis <stratis@stratis-Latitude-E6320.(none)> | 2013-07-08 13:18:24 -0700 |
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| committer | Stratis Ioannidis <stratis@stratis-Latitude-E6320.(none)> | 2013-07-08 13:18:24 -0700 |
| commit | 8360348b640a56c004730036025b0f3f9f9ed9a2 (patch) | |
| tree | 64f9f16a7bc058630fdb56c8c59d3bc9694570a6 /intro.tex | |
| parent | ca7140f58fc666ae5b05a5cf4e3bf8ad09352b82 (diff) | |
| download | recommendation-8360348b640a56c004730036025b0f3f9f9ed9a2.tar.gz | |
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@@ -8,7 +8,7 @@ Typically, \E\ has a hypothesis on the relationship between $x_i$'s and $y_i$'s. $$y_i = \T{\beta} x_i+\varepsilon_i,$$ for all $i\in \{1,\ldots,n\},$ where $\varepsilon_i$ are zero-mean, i.i.d.~random variables. Conducting the experiments and obtaining the measurements $y_i$ lets \E\ estimate $\beta$, \emph{e.g.}, through linear regression. %, \emph{i.e.}, the model underlying the data, and the experimenter's goal is to obtain such an estimate as accurately as possible. %The goal of experimental design amounts to determining which subjects to experiment upon to produce the best possible such estimate. The above experimental design scenario has many applications. Regression over personal data collected through surveys or experimentation is the cornerstone of marketing research, as well as research in a variety of experimental sciences such as medicine and sociology. Crucially, statistical analysis of user data is also a widely spread practice among Internet companies, which routinely use machine learning techniques over vast records of user data to perform inference and classification tasks integral to their daily operations. -Beyond linear regression, there is a rich literature about estimation procedures, as well as for means of quantifying the quality of the produced estimate~\cite{pukelsheim2006optimal}. There is also an extensive theory on how to select subjects +Beyond linear regression, there is a rich literature about estimation procedures, as well as about means of quantifying the quality of the produced estimate~\cite{pukelsheim2006optimal}. There is also an extensive theory on how to select subjects if \E\ can conduct only a limited number of experiments, so the estimation process returns a $\beta$ that approximates the true parameter of the underlying population \cite{ginebra2007measure,le1996comparison,chaloner1995bayesian,boyd2004convex}. |
