63 lines
2.0 KiB
Plaintext
63 lines
2.0 KiB
Plaintext
---
|
|
template: templates/cse4562_2019_slides.erb
|
|
title: Incomplete and Probabilistic Databases
|
|
date: May 6, 2019
|
|
textbook: "<a href='https://github.com/UBOdin/mimir/wiki/Concepts-CTables'>PDB Concepts and C-Tables</a>"
|
|
dependencies:
|
|
- lib/slide_utils.rb
|
|
---
|
|
<%
|
|
require "slide_utils.rb"
|
|
%>
|
|
<section>
|
|
<section>
|
|
<p><b>Idea: </b> Make $\texttt{bob}$ and $\texttt{carol}$ random variables.</p>
|
|
</section>
|
|
|
|
<section>
|
|
<p>$$\texttt{bob} = \begin{cases} 4 & p = 0.8 \\ 9 & p = 0.2\end{cases}$$</p>
|
|
<p>$$\texttt{carol} = \begin{cases} 3 & p = 0.4 \\ 8 & p = 0.6\end{cases}$$</p>
|
|
</section>
|
|
|
|
<section>
|
|
<p style="font-size: 70%">
|
|
$$Q(\mathcal D) = \begin{cases}
|
|
1 & \textbf{if } \texttt{bob} = 9 \wedge \texttt{carol} = 8\\
|
|
2 & \textbf{if } \texttt{bob} = 4 \wedge \texttt{carol} = 8 \\&\; \vee\; \texttt{bob} = 9 \wedge \texttt{carol} = 3\\
|
|
3 & \textbf{if } \texttt{bob} = 4 \wedge \texttt{carol} = 3
|
|
\end{cases}$$</p>
|
|
<p style="font-size: 90%" class="fragment">
|
|
$$ = \begin{cases}
|
|
1 & p = 0.2 \times 0.6\\
|
|
2 & p = 0.8 \times 0.6 + 0.2 \times 0.4\\
|
|
3 & p = 0.8 \times 0.4 \end{cases}$$
|
|
</p>
|
|
<p class="fragment">
|
|
$$ = \begin{cases}
|
|
1 & p = 0.12\\
|
|
2 & p = 0.56\\
|
|
3 & p = 0.32\end{cases}$$
|
|
</p>
|
|
</section>
|
|
|
|
<section>
|
|
<p>
|
|
$$Q(\mathcal D) = \begin{cases}
|
|
1 & p = 0.12\\
|
|
2 & p = 0.56\\
|
|
3 & p = 0.32\end{cases}$$
|
|
</p>
|
|
<p class="fragment" style="margin-top: 50px;">$E\left[Q(\mathcal D)\right] = 0.12+1.12+0.96 = 2.20$</p>
|
|
<p class="fragment" style="margin-top: 50px;">$P\left[Q(\mathcal D) \geq 2\right] = 0.56+0.32 = 0.88$</p>
|
|
</section>
|
|
|
|
<section>
|
|
<p>In general, computing probabilities exactly is <code>#P</code></p>
|
|
|
|
<p style="margin-top: 50px;" class="fragment">... so we approximate</p>
|
|
</section>
|
|
|
|
<section>
|
|
<p><b>Idea 1</b>: Sample. Pick 10 random possible worlds and compute results for each.</p>
|
|
</section>
|
|
</section> |