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@ -71,11 +71,11 @@
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</section>
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<section>
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<img src="graphics/yingyang.jpg" style="float: right; margin-left: 20px;" />
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<img src="graphics/yingyang.jpg" style="float: right; margin-left: 20px; padding-top: 20px" />
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<h3>Disclaimer</h3>
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<p>Ying could not be here today. If you like her ideas, get in touch with her. </p>
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<p class="fragment">(she's on the job market)</p>
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<p class="fragment">(If you don't, blame my presentation)</p>
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<p class="fragment">(Also, Ying is on the job market)</p>
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</section>
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</section>
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@ -93,9 +93,9 @@
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<h2>Graphical Models</h2>
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<p>Joint probability distributions are expensive to store<br/>
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$$p(D, I, G, S, J)$$</p>
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<p>Bayes rule lets us break apart the distribution<br/>
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<p class="fragment">Bayes rule lets us break apart the distribution<br/>
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$$= p(D, I, G, S) \cdot p(J | D, I, G, S)$$</p>
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<p>And conditional independence lets us further simplify<br/>
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<p class="fragment">And conditional independence lets us further simplify<br/>
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$$= p(D, I, G, S) \cdot p(J | G, S)$$</p>
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<p class="fragment">This is basis for a type of graphical model called a "Bayes Net"</p>
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</section>
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@ -136,6 +136,7 @@
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<span class="fragment" data-fragment-index="3">$\cdot\;0.95$</span>
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<span class="fragment" data-fragment-index="4">$\cdot\;0.25$</span>
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<span class="fragment" data-fragment-index="5">$\cdot\;0.8$</span>
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<span class="fragment" data-fragment-index="6">$=\;0.0665$</span>
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</p>
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</section>
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<section>
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@ -178,7 +179,7 @@
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</section>
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<section>
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<h2>Idea: Use OLA</h2>
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<h2>Idea: Online Aggregation</h2>
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</section>
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<section>
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<h2>Online Aggregation (OLA)</h2>
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@ -260,17 +261,6 @@
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</ol>
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</section>
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<section>
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<h2>Cyclic Sampling</h2>
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<dl>
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<dt>Advantages</dt>
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<dd>Progressively better estimates over time.</dd>
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<dd>Converges in bounded time.</dd>
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<dt>Disadvantages</dt>
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<dd>Exponential time in the number of variables.</dd>
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</dl>
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</section>
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<section>
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<h2>Accuracy</h2>
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<dl>
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@ -281,6 +271,17 @@
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</dl>
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<p></p>
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</section>
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<section>
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<h2>Cyclic Sampling</h2>
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<dl>
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<dt>Advantages</dt>
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<dd>Progressively better estimates over time.</dd>
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<dd>Converges in bounded time.</dd>
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<dt>Disadvantages</dt>
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<dd>Exponential time in the number of variables.</dd>
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</dl>
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</section>
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</section>
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<section>
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@ -293,18 +294,18 @@
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<img src="graphics/JoinGraph.svg" height="400" style="float:left"/>
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<table style="float:right">
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<tr><th>$G$</th><th>#</th><th>$\sum p_{\psi_2}$</th></tr>
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<tr class="fragment" data-fragment-index="2"><td>1</td><td>3</td><td>0.348</td></tr>
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<tr class="fragment" data-fragment-index="3"><td>2</td><td>4</td><td>0.288</td></tr>
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<tr class="fragment" data-fragment-index="3"><td>3</td><td>4</td><td>0.350</td></tr>
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<tr class="fragment" data-fragment-index="2"><td>1</td><td>1</td><td>0.126</td></tr>
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<tr><td> </td><td> </td><td> </td></tr>
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<tr><td> </td><td> </td><td> </td></tr>
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</table>
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<table>
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<tr><th>$D$</th><th>$G$</th><th>#</th><th>$\sum p_{\psi_1}$</th></tr>
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<tr class="fragment" data-fragment-index="1"><td>0</td><td>1</td><td>1</td><td>0.126</td></tr>
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<tr class="fragment" data-fragment-index="3"><td>1</td><td>1</td><td>2</td><td>0.222</td></tr>
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<tr class="fragment" data-fragment-index="3"><td>0</td><td>2</td><td>2</td><td>0.238</td></tr>
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<tr class="fragment" data-fragment-index="3"><td>1</td><td>2</td><td>2</td><td>0.050</td></tr>
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<tr class="fragment" data-fragment-index="3"><td>0</td><td>3</td><td>2</td><td>0.322</td></tr>
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<tr class="fragment" data-fragment-index="3"><td>1</td><td>3</td><td>2</td><td>0.028</td></tr>
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<tr><th>$I$</th><th>$G$</th><th>#</th><th>$\sum p_{\psi_1}$</th></tr>
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<tr class="fragment" data-fragment-index="1"><td>0</td><td>1</td><td>1</td><td>0.18</td></tr>
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<tr><td> </td><td> </td><td> </td><td> </td></tr>
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<tr><td> </td><td> </td><td> </td><td> </td></tr>
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<tr><td> </td><td> </td><td> </td><td> </td></tr>
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<tr><td> </td><td> </td><td> </td><td> </td></tr>
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<tr><td> </td><td> </td><td> </td><td> </td></tr>
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</table>
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</section>
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@ -317,7 +318,7 @@
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<tr><td>3</td><td>4</td><td>0.350</td></tr>
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</table>
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<table>
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<tr><th>$D$</th><th>$G$</th><th>#</th><th>$\sum p_{\psi_1}$</th></tr>
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<tr><th>$I$</th><th>$G$</th><th>#</th><th>$\sum p_{\psi_1}$</th></tr>
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<tr><td>0</td><td>1</td><td>2</td><td>0.140</td></tr>
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<tr><td>1</td><td>1</td><td>2</td><td>0.222</td></tr>
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<tr><td>0</td><td>2</td><td>2</td><td>0.238</td></tr>
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@ -336,7 +337,7 @@
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<tr><td>3</td><td>4</td><td>0.350</td></tr>
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</table>
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<table>
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<tr><th>$D$</th><th>$G$</th><th>#</th><th>$\sum p_{\psi_1}$</th></tr>
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<tr><th>$I$</th><th>$G$</th><th>#</th><th>$\sum p_{\psi_1}$</th></tr>
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<tr><td>0</td><td>1</td><td>2</td><td>0.140</td></tr>
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<tr><td>1</td><td>1</td><td>2</td><td>0.222</td></tr>
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<tr><td>0</td><td>2</td><td>2</td><td>0.238</td></tr>
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@ -429,6 +430,7 @@
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<li><b>Idea 2</b>: "Leak" samples through a normal join graph.</li>
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<li>Compared to both Variable Elim. and Gibbs Sampling, Leaky Joins are often better and never drastically worse.</li>
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</ul>
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<p class="fragment" style="font-weight: bold">Questions?</p>
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</section>
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</div></div>
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