this is for holding javascript data
Vadim Kosoy added We_are_now_ready_to__.tex
about 8 years ago
Commit id: 450fc870082c94ad9db7219a3f8762ee0c4941d8
deletions | additions
diff --git a/We_are_now_ready_to__.tex b/We_are_now_ready_to__.tex
new file mode 100644
index 0000000..3b4b9fb
--- /dev/null
+++ b/We_are_now_ready_to__.tex
...
We are now ready to give our central definition, which corresponds to a notion of "expected value" for distributional estimation problems.
\begin{definition}
Fix $\Gamma$ a growth space of type $(2,2)$ and $\mathcal{E}$ and error space of rank 2. Consider $(\mu,f)$ a distributional estimation problem and $P: \Words \xrightarrow{\Gamma} \Rats$ with bounded range. $P$ is called an \emph{\mathcal{E}(\Gamma)-optimal predictor for $(\mu,f)$} when for any $Q: \Words \xrightarrow{\Gamma} \Rats$ there is $\varepsilon \in \mathcal{E}$ s.t.
\begin{equation}
\E_{(x,y) \sim \mu^k \times U^{\R_P(K)}}[(P^{kj}(x,y) - f(x))^2] \leq \E_{(x,y) \sim \mu^k \times U^{\R_Q(K)}}[(Q^{kj}(x,y) - f(x))^2] + \varepsilon^{kj}
\end{equation}
\end{definition}
