Slides
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<section>
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<h3>Uniform Prior</h3>
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<p style="text-align: left; margin-bottom: 0px; font-weight: bold;">We assume that for $\sigma_c(Q)$...</p>
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<p style="text-align: left; margin-bottom: 0px; font-weight: bold;">We assume that for $\sigma_c(Q)$ or $\delta_A(Q)$...</p>
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<ol>
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<li>Basic statistics are known about $Q$: <ul>
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<li style="margin-top: 0px;"><code>COUNT(*)</code></li>
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</section>
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<section>
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<h3>Some Conditions</h3>
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<p>Estimating $\delta_A(Q)$ requires only <code>COUNT(DISTINCT A)</code></p>
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</section>
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<section>
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<h3>Estimating Selectivity</h3>
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<p>Selectivity is a probability ($\texttt{SEL}(c, Q) = P(c)$)</p>
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<table style="font-size: 85%">
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<section>
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<p><b>Idea 1:</b> Pick 100 tuples at random from each input table.</p>
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</section>
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<section>
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<svg data-src="graphics/2018-03-05-JoinIssue.svg" />
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</section>
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<section>
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<h3>The Birthday Paradox</h3>
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<p style="margin-top: 50px;">
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Assume: $\texttt{UNIQ}(A, R) = \texttt{UNIQ}(A, S) = N$
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</p>
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<p style="margin-top: 50px;">
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It takes $O(\sqrt{N})$ samples from both $R$ and $S$ <br/> to get even <b>one match.</b>
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</p>
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</section>
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<section>
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<p>To be resumed later in the term when we talk about AQP</p>
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</section>
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<section>
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<p><b>How DBs Do It</b>: Instrument queries while running them.<ul>
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<li class="fragment">The first time you run a query it <i>might</i> be slow.</li>
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<li class="fragment">The second, third, fourth, etc... times it'll be fast.</li>
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</ul></p>
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</section>
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</section>
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<section>
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<section>
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<h3>Limitations</h3>
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<dl>
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<div class="fragment highlight-grey">
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<dt>Don't always have statistics for $Q$</dt>
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<dd>For example, $\pi_{A \leftarrow (B \times C)}(R)$</dd>
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</div>
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<div class="fragment highlight-grey">
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<dt>Don't always have clear rules for $c$</dt>
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<dd>For example, $\sigma_{\texttt{FitsModel}(A, B, C)}(R)$</dd>
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</div>
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<div class="fragment highlight-blue">
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<dt>Attribute values are not always uniformly distributed.</dt>
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<dd>For example, <span style="font-size: 60%"> $|\sigma_{SPC\_COMMON = 'pin\ oak'}(T)|$ vs $|\sigma_{SPC\_COMMON = 'honeylocust'}(T)|$</span></dd>
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</div>
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<div class="fragment highlight-grey">
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<dt>Attribute values are sometimes correlated.</dt>
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<dd>For example, $\sigma_{(stump < 5) \wedge (diam > 3)}(T)$</dd>
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</div>
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</dl>
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</section>
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<section>
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<h3>(Some) Estimation Techniques</h3>
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<dd style="color: grey;">Using rules about the data for improved guesses.</dd>
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</dl>
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</section>
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<section>
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<h3>Limitations of Uniform Prior</h3>
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<dl>
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<div class="fragment highlight-grey" data-fragment-index="1">
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<dt>Don't always have statistics for $Q$</dt>
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<dd>For example, $\pi_{A \leftarrow (B \times C)}(R)$</dd>
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</div>
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<div class="fragment highlight-grey" data-fragment-index="1">
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<dt>Don't always have clear rules for $c$</dt>
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<dd>For example, $\sigma_{\texttt{FitsModel}(A, B, C)}(R)$</dd>
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</div>
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<div class="fragment highlight-blue" data-fragment-index="1">
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<dt>Attribute values are not always uniformly distributed.</dt>
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<dd>For example, <span style="font-size: 60%"> $|\sigma_{SPC\_COMMON = 'pin\ oak'}(T)|$ vs $|\sigma_{SPC\_COMMON = 'honeylocust'}(T)|$</span></dd>
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</div>
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<div class="fragment highlight-grey" data-fragment-index="1">
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<dt>Attribute values are sometimes correlated.</dt>
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<dd>For example, $\sigma_{(stump < 5) \wedge (diam > 3)}(T)$</dd>
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</div>
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</dl>
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</section>
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<section>
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<p class="fragment highlight-grey" data-fragment-index="1">
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<b>Ideal Case:</b> You have some
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$$f(x) = \left(\texttt{SELECT COUNT(*) WHERE A = x}\right)$$
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(and similarly for the other aggregates)
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</p>
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<p class="fragment" data-fragment-index="1">
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<b>Slightly Less Ideal Case:</b> You have some
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$$f(x) \approx \left(\texttt{SELECT COUNT(*) WHERE A = x}\right)$$
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</p>
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</section>
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<section>
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<p>If this sounds like CDF-based indexing... you're right!</p>
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<p class="fragment">... but we're not going to talk about NNs today</p>
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</section>
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</section>
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<section>
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<section>
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<p>
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<b>Simpler/Faster Idea: </b> Break $f(x)$ into chunks
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</p>
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</section>
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<section>
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<h3>Example Data</h3>
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<table style="font-size: 80%">
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<tr><th>Name</th> <th>YearsEmployed</th> <th>Role</th></tr>
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<tr><td>'Alice'</td> <td>3</td> <td>1</td></tr>
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<tr><td>'Bob'</td> <td>2</td> <td>2</td></tr>
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<tr><td>'Carol'</td> <td>3</td> <td>1</td></tr>
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<tr><td>'Dave'</td> <td>1</td> <td>3</td></tr>
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<tr><td>'Eve'</td> <td>2</td> <td>2</td></tr>
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<tr><td>'Fred'</td> <td>2</td> <td>3</td></tr>
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<tr><td>'Gwen'</td> <td>4</td> <td>1</td></tr>
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<tr><td>'Harry'</td> <td>2</td> <td>3</td></tr>
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</table>
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</section>
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<section>
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<h3>Histograms</h3>
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<table style="font-size: 70%">
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<tr><th>YearsEmployed</th><th>COUNT</th></tr>
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<tr><td>1</td> <td>1</td> </tr>
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<tr><td>2</td> <td>4</td> </tr>
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<tr><td>3</td> <td>2</td> </tr>
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<tr><td>4</td> <td>1</td> </tr>
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</table>
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<table>
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<tr class="fragment"><td style="font-size: 70%"><code>COUNT(DISTINCT YearsEmployed)</code> </td><td class="fragment">$= 4$</td></tr>
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<tr class="fragment"><td style="font-size: 70%"><code>MIN(YearsEmployed)</code> </td><td class="fragment">$= 1$</td></tr>
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<tr class="fragment"><td style="font-size: 70%"><code>MAX(YearsEmplyed)</code> </td><td class="fragment">$= 4$</td></tr>
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<tr class="fragment"><td style="font-size: 70%"><code>COUNT(*) YearsEmployed = 2</code> </td><td class="fragment">$= 4$</td></tr>
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</table>
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</section>
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<section>
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<h3>Histograms</h3>
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<table style="font-size: 70%">
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<tr><th>YearsEmployed</th><th>COUNT</th></tr>
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<tr><td>1-2</td> <td>5</td> </tr>
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<tr><td>3-4</td> <td>3</td> </tr>
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</table>
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<table>
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<tr class="fragment"><td style="font-size: 70%"><code>COUNT(DISTINCT YearsEmployed)</code> </td><td class="fragment">$= 4$</td></tr>
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<tr class="fragment"><td style="font-size: 70%"><code>MIN(YearsEmployed)</code> </td><td class="fragment">$= 1$</td></tr>
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<tr class="fragment"><td style="font-size: 70%"><code>MAX(YearsEmplyed)</code> </td><td class="fragment">$= 4$</td></tr>
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<tr class="fragment"><td style="font-size: 70%"><code>COUNT(*) YearsEmployed = 2</code> </td><td class="fragment">$= \frac{5}{2}$</td></tr>
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</table>
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</section>
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<section>
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<h3>The Extreme Case</h3>
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<table style="font-size: 70%">
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<tr><th>YearsEmployed</th><th>COUNT</th></tr>
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<tr><td>1-4</td> <td>8</td> </tr>
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</table>
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<table>
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<tr class="fragment"><td style="font-size: 70%"><code>COUNT(DISTINCT YearsEmployed)</code> </td><td class="fragment">$= 4$</td></tr>
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<tr class="fragment"><td style="font-size: 70%"><code>MIN(YearsEmployed)</code> </td><td class="fragment">$= 1$</td></tr>
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<tr class="fragment"><td style="font-size: 70%"><code>MAX(YearsEmplyed)</code> </td><td class="fragment">$= 4$</td></tr>
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<tr class="fragment"><td style="font-size: 70%"><code>COUNT(*) YearsEmployed = 2</code> </td><td class="fragment">$= \frac{8}{4}$</td></tr>
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</table>
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</section>
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<section>
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<h3>More Example Data</h3>
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<table style="font-size: 80%; float: left;">
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<tr><th>Value</th> <th>COUNT</th> </tr>
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<tr><td> 1-10</td> <td>20</td> </tr>
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<tr><td>11-20</td> <td> 0</td> </tr>
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<tr><td>21-30</td> <td>15</td> </tr>
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<tr><td>31-40</td> <td>30</td> </tr>
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<tr><td>41-50</td> <td>22</td> </tr>
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<tr><td>51-60</td> <td>63</td> </tr>
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<tr><td>61-70</td> <td>10</td> </tr>
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<tr><td>71-80</td> <td>10</td> </tr>
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</table>
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<table style="margin-top: 100px;">
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<tr class="fragment">
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<td style="font-size: 70%; width: 350px;"><code>SELECT … WHERE A = 33</code> </td>
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<td class="fragment" style="font-size: 80%; text-align: left; width: 200px;">$= \frac{1}{40-30}\cdot 30 = 3$</td>
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</tr>
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<tr><td style="height: 70px;"></td><td></td></tr>
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<tr class="fragment">
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<td style="font-size: 70%; width: 350px;"><code>SELECT … WHERE A > 33</code> </td>
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<td class="fragment" style="font-size: 80%; text-align: left; width: 200px;">$= \frac{40-33}{40-30}\cdot 30+22$ $\;\;\;+63+10+10$ $= 126$ </td>
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</tr>
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</table>
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</section>
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</section>
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<section>
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<section>
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<h3>(Some) Estimation Techniques</h3>
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<dl style="font-size: 80%">
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<dt style="color: grey;">Guess Randomly</dt>
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<dd style="color: grey;">Rules of thumb if you have no other options...</dd>
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<dt style="color: grey;">Uniform Prior</dt>
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<dd style="color: grey;">Use basic statistics to make a very rough guess.</dd>
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<dt style="color: grey;">Sampling / History</dt>
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<dd style="color: grey;">Small, Quick Sampling Runs (or prior executions of the query).</dd>
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<dt style="color: grey;">Histograms</dt>
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<dd style="color: grey;">Using more detailed statistics for improved guesses.</dd>
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<dt style="color: blue;">Constraints</dt>
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<dd style="color: blue;">Using rules about the data for improved guesses.</dd>
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</dl>
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</section>
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</section>
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</div></div>
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After Width: | Height: | Size: 14 KiB |
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Reference in a new issue