Draft of Mimir Presentation
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slides/talks/2018-1-Tour-Mimir/data/UADBs/10pct.csv
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slides/talks/2018-1-Tour-Mimir/data/UADBs/10pct.csv
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Label, PDB-1, PDB-2, PDB-3
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Deterministic,4.714,4.073,5.238
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Mimir,4.962,4.257,6.989
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MayBMS,21.814,9.171,18.137
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<p class="fragment">Tons of Curation Heuristics Available!</p>
|
||||
<svg data-src="papers/heuristics.svg" height="600px" width="900px"/>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>We have tools that can solve these problem!</p>
|
||||
<img src="graphics/happy_alice.svg" width="200px" height="200px" />
|
||||
<imagecredits>(OpenClipArt.org)</imagecredits>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<img src="graphics/StateStreet.png"/>
|
||||
<p class="fragment">... that can be wrong</p>
|
||||
<p>... most of the time</p>
|
||||
<imagecredits>(google.com)</imagecredits>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<img src="graphics/Mickey12.png" height="400px"/>
|
||||
<p>... very wrong</p>
|
||||
<imagecredits>(nytimes.com)</imagecredits>
|
||||
<p>
|
||||
<b>Problem:</b> It's hard to trust tools that can be wrong!
|
||||
</p>
|
||||
</section>
|
||||
|
||||
</section>
|
||||
|
||||
<section>
|
||||
|
||||
<section>
|
||||
<h2>Options</h2>
|
||||
<ol style="margin-top: 50px">
|
||||
<li class="fragment">Ignore the Problem</li>
|
||||
<li style="color: white;"></li>
|
||||
<li style="color: white;"></li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>
|
||||
In the name of Codd,<br/><span class="fragment grow highlight-current-blue" data-fragment-index="2">thou shalt not give the user a wrong answer.</span>
|
||||
</h3>
|
||||
<svg data-src="graphics/dataquality-normal.svg"/>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>
|
||||
<b>In the name of Codd</b><br/><span class="fragment grow highlight-current-blue" data-fragment-index="2">Thou shalt not give the user a wrong answer.</span>
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<svg data-src="graphics/blackbox.svg" class="stretch" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>... but when combined with heuristics</p>
|
||||
<img src="graphics/obamacare_stats_fail.jpg" height="400" />
|
||||
<imagecredits>(Fox News)</imagecredits>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
|
||||
<section>
|
||||
<h2>Options</h2>
|
||||
<ol style="margin-top: 50px">
|
||||
<li style="text-decoration: line-through; color: grey;">Ignore the Problem</li>
|
||||
<li class="fragment">Heresy</li>
|
||||
<li style="color: white;"></li>
|
||||
</ol>
|
||||
</section>
|
||||
<section>
|
||||
<h3>On representing incomplete information in a relational data base</h3>
|
||||
<h4>T. Imielinski & W. Lipski Jr.<span style="margin-left: 40px">(<i>VLDB 1981</i>)</span></h4>
|
||||
<p class="fragment" style="margin-top: 60px">
|
||||
Incomplete and Probabilistic Databases<br/>have existed since the 1980s...
|
||||
</p>
|
||||
<p style="font-size: smaller">T. Imielinski & W. Lipski Jr.<span style="margin-left: 40px">(<i>VLDB 1981</i>)</span></p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
|
|
@ -253,8 +264,13 @@
|
|||
</section>
|
||||
|
||||
<section>
|
||||
<img src="graphics/blackbox.svg" height="400">
|
||||
<p>(Typical Heuristics)</p>
|
||||
<svg data-src="graphics/probdb-query.svg" class="stretch"/>
|
||||
<p><b>1.</b> ProbDBs Produce Probability Distributions as Outputs</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<svg data-src="graphics/probdb-init.svg" class="stretch"/>
|
||||
<p><b>2.</b> ProbDBs Require Probability Distributions as Inputs</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
|
|
@ -273,7 +289,7 @@
|
|||
"labelString": "Query Runtime (s)"
|
||||
}
|
||||
}]
|
||||
}
|
||||
}
|
||||
}}
|
||||
-->
|
||||
Label , PDB-1, PDB-2, PDB-3, TPCH-1, TPCH-3, TPCH-5, TPCH-9
|
||||
|
|
@ -284,17 +300,21 @@ Sampling (x10), 300, 242.5666234549135, 300, 119.61607021316885, 162.00108394436
|
|||
</canvas>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<img src="graphics/Normal_Distribution_PDF.svg" height="500" />
|
||||
<p>(Probabilistic Query Outputs)</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Probabilistic Databases...</h2>
|
||||
<ol style="margin-top: 50px;">
|
||||
<li class="fragment">... require probabilities as inputs</li>
|
||||
<li class="fragment">... are slow</li>
|
||||
<li class="fragment">... produce probabilities as outputs</li>
|
||||
<li>... require probabilities as inputs</li>
|
||||
<li>... produce probabilities as outputs</li>
|
||||
<li>... are slow</li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Options</h2>
|
||||
<ol style="margin-top: 50px">
|
||||
<li style="text-decoration: line-through; color: grey;">Ignore the Problem</li>
|
||||
<li style="text-decoration: line-through; color: grey;">Heresy</li>
|
||||
<li>?</li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
|
|
@ -317,38 +337,598 @@ Sampling (x10), 300, 242.5666234549135, 300, 119.61607021316885, 162.00108394436
|
|||
</section>
|
||||
|
||||
<section>
|
||||
<ul style="font-size: larger">
|
||||
<li style="color: lightgrey;">Why should you care about uncertain data?</li>
|
||||
<li style="font-weight: bold">Background: K-Relations and Possible Worlds</li>
|
||||
<li>Uncertainty-Annotated Databases<div style="font-size: smaller; font-weight: normal; font-style: italic;">(Joint work with Boris Glavic, Su Feng, Aaron Huber)</div></li>
|
||||
<li>Other Mimir Projects</li>
|
||||
</ul>
|
||||
<h3>Uncertainty-Annotated Databases</h3>
|
||||
<p style="font-size: smaller">(Joint work with Boris Glavic, Su Feng, Aaron Huber)</p>
|
||||
<div style="margin-top: 50px" class="fragment">
|
||||
<h3>Other Projects</h3>
|
||||
<ul>
|
||||
<li>Adaptive Schemas</li>
|
||||
<li>Probabilistic Query Compilers</li>
|
||||
</ul>
|
||||
</div>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<ul>
|
||||
<li>Semirings</li>
|
||||
<li>K-Relations</li>
|
||||
<h2>Background</h2>
|
||||
|
||||
<ol>
|
||||
<li>Possible Worlds</li>
|
||||
<li>Certain, Possible Tuples</li>
|
||||
</ul>
|
||||
<li>$K$-Semirings</li>
|
||||
<li>$K^W$-Semrings</li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<svg data-src="graphics/possibleworlds.svg" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>$K$-Semirings</h2>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table><tr>
|
||||
<td><table>
|
||||
<tr><th style="border-right: solid 1px">R</th><th>A</th><th>B</th></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>2</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>3</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>4</td><td>3</td></tr>
|
||||
</table></td>
|
||||
<td style="width: 50px"></td>
|
||||
<td><table>
|
||||
<tr><th style="border-right: solid 1px">S</th><th>B</th><th>C</th></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>2</td><td>5</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>3</td><td>6</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>3</td><td>6</td></tr>
|
||||
</table></td>
|
||||
</tr></table>
|
||||
<p class="fragment">The relational view</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>The functional view</p>
|
||||
<p>
|
||||
$$R(1, 2) \mapsto 1$$
|
||||
$$R(1, 3) \mapsto 1$$
|
||||
$$R(4, 3) \mapsto 1$$
|
||||
</p>
|
||||
<p class="fragment">
|
||||
$$R(4, 5) \mapsto 0$$
|
||||
</p>
|
||||
<p class="fragment">
|
||||
$$S(3, 6) \mapsto 2$$
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
$$[R_1 \cup R_2](\vec X) \equiv R_1(\vec X) + R_2(\vec X)$$
|
||||
|
||||
<div style="margin-top: 100px; width: 500px; margin-left: auto; margin-right: auto; text-align: left;" class="fragment">
|
||||
$[S \cup S](3, 6)$
|
||||
<p class="fragment" style="margin-left: 100px;">$= S(3, 6) + S(3, 6)$</p>
|
||||
<p class="fragment" style="margin-left: 100px;">$= 2 + 2 = 4$</p>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
$$[R_1 \bowtie R_2](\vec X) \equiv R_1(\vec X) \times R_2(\vec X)$$
|
||||
|
||||
<div style="margin-top: 100px; width: 500px; margin-left: auto; margin-right: auto; text-align: left;" class="fragment">
|
||||
$[R \bowtie S](4, 3, 6)$
|
||||
<p class="fragment" style="margin-left: 100px;">$= R(4, 3) \times S(3, 6)$</p>
|
||||
<p class="fragment" style="margin-left: 100px;">$= 1 \times 2 = 2$</p>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
$$[\pi_{\vec A} R](\vec X) \equiv \sum_{\vec Y} R(\vec X \vec Y)$$
|
||||
<!-- \in adom(sch(R)-A) -->
|
||||
|
||||
<div style="margin-top: 100px; width: 500px; margin-left: auto; margin-right: auto; text-align: left;" class="fragment">
|
||||
$[\pi_{B} R](3)$
|
||||
<p class="fragment" style="margin-left: 100px;">$= \sum_{Y} R(Y, 3)$</p>
|
||||
<p class="fragment" style="margin-left: 100px;">$ = R(1, 3) + R(4, 3) + \ldots$</p>
|
||||
<p class="fragment" style="margin-left: 100px;">$= 1 + 1 + 0 = 2$</p>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table>
|
||||
<tr><td>$\cup$ </td><td style="width: 100px; font-size: smaller;">$\approx$</td><td>$+$</td></tr>
|
||||
<tr><td>$\bowtie$</td><td style="width: 100px; font-size: smaller;">$\approx$</td><td>$\times$</td></tr>
|
||||
<tr><td>$\pi$ </td><td style="width: 100px; font-size: smaller;">$\approx$</td><td>$+$</td></tr>
|
||||
</table>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Provenance Semirings</h3>
|
||||
<p style="font-size: smaller">T.J. Green & G. Karvounarakis & V. Tannen<span style="margin-left: 40px">(<i>PODS 2007</i>)</span></p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
$$\left<\;\mathcal K,\;\oplus,\;\otimes,\;\mathbb 0,\;\mathbb 1\;\right>$$
|
||||
|
||||
<table style="margin-top: 50px;" class="fragment">
|
||||
<tr>
|
||||
<th>Semiring</th><th>Equivalent Query Semantics</th>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>$\left<\mathbb N, +, \times, 0, 1\right>$</td>
|
||||
<td>Bag Semantics</td>
|
||||
</tr>
|
||||
<tr class="fragment">
|
||||
<td>$\left<\mathbb B, \vee, \wedge, \bot, \top\right>$</td>
|
||||
<td>Set Semantics</td>
|
||||
</tr>
|
||||
<tr class="fragment">
|
||||
<td>$\left<\mathcal K^W, \vec \oplus, \vec \otimes, \mathbb{\vec 0}, \mathbb{\vec 1}\right>$</td>
|
||||
<td>Possible Worlds Semantics</td>
|
||||
</tr>
|
||||
</table>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<ul>
|
||||
<li>$K^W$-Relations</li>
|
||||
<li>$PW_i$, Certain, Possible</li>
|
||||
<li>Performance</li>
|
||||
</ul>
|
||||
<h2>$K^W$-Semirings</h2>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table>
|
||||
<tr><th style="border-right: solid 1px">R</th><th>A</th><th>B</th></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>2</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>3</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td><img src="graphics/nine_or_four.svg" style="height: 30px; margin: 0px;"></td><td>3</td></tr>
|
||||
</table>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table><tr>
|
||||
<td><table>
|
||||
<tr><th style="border-right: solid 1px">$R_1$</th><th>A</th><th>B</th></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>2</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>3</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td style="color: red">4</td><td>3</td></tr>
|
||||
</table></td>
|
||||
<td style="width: 50px"></td>
|
||||
<td><table>
|
||||
<tr><th style="border-right: solid 1px">$R_2$</th><th>A</th><th>B</th></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>2</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>3</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td style="color: red">9</td><td>3</td></tr>
|
||||
</table></td>
|
||||
</tr></table>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table>
|
||||
<tr><th style="border-right: solid 1px">R</th><th>A</th><th>B</th><td></td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>2</td><td>$\mapsto [1,1]$</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>3</td><td>$\mapsto [1,1]$</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>4</td><td>3</td><td>$\mapsto [1,0]$</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>9</td><td>3</td><td>$\mapsto [0,1]$</td></tr>
|
||||
</table>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Extractors</h3>
|
||||
|
||||
$$\mathcal K^W \rightarrow \mathcal K$$
|
||||
(plug in any $K$-Semiring-compatible $\mathcal K$)
|
||||
|
||||
<dl>
|
||||
<dt class="fragment" data-fragment-index="1" style="margin-top: 50px;">Possible World Value</dt>
|
||||
<dd class="fragment" data-fragment-index="1">$\texttt{PW_i}(\vec k) \equiv \vec k_i$</dd>
|
||||
<dt class="fragment" data-fragment-index="2" style="margin-top: 20px;">Certain Value</dt>
|
||||
<dd class="fragment" data-fragment-index="2">$\mathcal C(\vec k) \equiv min(\vec k)$</dd>
|
||||
<dt class="fragment" data-fragment-index="3" style="margin-top: 20px;">Possible Value</dt>
|
||||
<dd class="fragment" data-fragment-index="3">$\mathcal P(\vec k) \equiv max(\vec k)$</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table>
|
||||
<tr>
|
||||
<td>
|
||||
<table>
|
||||
<tr><th style="border-right: solid 1px">R</th><th>A</th><th>B</th><td></td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>2</td><td>$\mapsto [1,1]$</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>3</td><td>$\mapsto [1,1]$</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>4</td><td>3</td><td>$\mapsto [1,0]$</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>9</td><td>3</td><td>$\mapsto [0,1]$</td></tr>
|
||||
</table>
|
||||
</td>
|
||||
<td style="padding-left: 50px;">
|
||||
<p class="fragment" data-fragment-index="1">$$\texttt{PW}_0(R(1, 2)) = 1$$</p>
|
||||
<p class="fragment" data-fragment-index="2">$$\texttt{PW}_0(R(4, 3)) = 1$$</p>
|
||||
<p class="fragment" data-fragment-index="3">$$\texttt{PW}_1(R(4, 3)) = 0$$</p>
|
||||
<p class="fragment" data-fragment-index="4">$$\mathcal C(R(4, 3)) = 0$$</p>
|
||||
<p class="fragment" data-fragment-index="5">$$\mathcal P(R(4, 3)) = 1$$</p>
|
||||
</td>
|
||||
</tr>
|
||||
</table>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h5>Thanks...</h5>
|
||||
|
||||
<section>
|
||||
<p>A quick step back into reality...</p>
|
||||
<img src="graphics/dagobert83-female-user-icon-800px.png" height="100px" class="fragment">
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<img src="graphics/probdb-query.svg" height="200px"/>
|
||||
<img src="graphics/sad_alice.svg" width="200px" height="200px" style="margin-left: 50px" class="fragment" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table style="display: inline-block;">
|
||||
<tr><th style="border-right: solid 1px">R</th><th>A</th><th>B</th></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>2</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>3</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>4 or 9</td><td>3</td></tr>
|
||||
</table>
|
||||
<p> </p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table style="display: inline-block;">
|
||||
<tr><th style="border-right: solid 1px">R</th><th>A</th><th>B</th></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>2</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>3</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>4 <span style="color: lightgrey; text-decoration: line-through red;">or 9</span></td><td>3</td></tr>
|
||||
</table>
|
||||
<p><b>Standard practice:</b> "Just use the best option."</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<img src="graphics/Mickey12.png">
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>What's in between these extremes?</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table style="display: inline-block;">
|
||||
<tr><th style="border-right: solid 1px">R</th><th>A</th><th>B</th><td></td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>2</td><td></td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>3</td><td></td></tr>
|
||||
<tr class="fragment highlight-current-red" data-fragment-index="2"><td style="border-right: solid 1px"> </td><td>4</td><td>3</td><td style="font-weight: bold;" class="fragment" data-fragment-index="1">*</td></tr>
|
||||
</table>
|
||||
<img src="graphics/happy_alice.svg" width="200px" height="200px" style="margin-left: 150px" class="fragment" data-fragment-index="4" />
|
||||
<p class="fragment" data-fragment-index="3">Use the best option, but mark potential errors.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
To answer $Q(\mathcal D)$ we want...
|
||||
|
||||
<table style="margin-top: 70px;">
|
||||
<tr class="fragment">
|
||||
<td>$PW_{i}(Q(\mathcal D))$</td>
|
||||
<td>The results Alice would have "just used".</td>
|
||||
</tr>
|
||||
<tr style="height: 50px;"><td></td><td></td></tr>
|
||||
<tr class="fragment">
|
||||
<td>$\mathcal C(Q(\mathcal D))$</td>
|
||||
<td>Which of those results are trustworthy.</td>
|
||||
</tr>
|
||||
</table>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
$$\texttt{PW}_i(Q(\mathcal D)) \equiv Q(\texttt{PW}_i(\mathcal D))$$
|
||||
<p class="fragment">(Computing $PW_{i}(Q(\mathcal D))$ is cheap!)</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>Can we do the same thing for $\mathcal C(Q(\mathcal D))$?</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h1>No.</h1>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table>
|
||||
<tr><th style="border-right: solid 1px">R</th><th>A</th><th>B</th><td></td><th>$K^W$</th><th>$\mathcal C$</th></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>2</td><td>$\mapsto$</td><td>$[1,1]$</td><td>1</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>1</td><td>3</td><td>$\mapsto$</td><td>$[1,1]$</td><td>1</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>4</td><td>3</td><td>$\mapsto$</td><td>$[1,0]$</td><td>0</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>9</td><td>3</td><td>$\mapsto$</td><td>$[0,1]$</td><td>0</td></tr>
|
||||
</table>
|
||||
<p class="fragment">Compute $\pi_B(R)$</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table>
|
||||
<tr><th style="border-right: solid 1px">$\pi_B$R</th><th>B</th><td></td><th>$K^W$</th><th>$\mathcal C$</th></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>2</td><td>$\mapsto$</td><td>$[1,1]$</td><td class="fragment">$1$</td></tr>
|
||||
<tr><td style="border-right: solid 1px"> </td><td>3</td><td>$\mapsto$</td><td>$[2,2]$</td><td class="fragment">$1+0+0=1$</td></tr>
|
||||
</table>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>So what <u>can</u> we do with $\mathcal C$?</h2>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>We can Approximate</h3>
|
||||
<dl>
|
||||
<dt>Soundness</dt>
|
||||
<dd class="fragment" data-fragment-index="1">$Q(\mathcal C(\mathcal D)) \leq \mathcal C(Q(\mathcal D))$</dd>
|
||||
<dd class="fragment" data-fragment-index="2">We can efficiently compute a conservative approximation of $\mathcal C$.
|
||||
|
||||
<dt>Completeness</dt>
|
||||
<dd class="fragment" data-fragment-index="3">$Q(\mathcal C(\mathcal D)) = \mathcal C(Q(\mathcal D))$ ...if $Q$ is <i>safe</i></dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>... also attribute level uncertainty</p>
|
||||
</section>
|
||||
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<!-- <img src="graphics/system.png"> -->
|
||||
<svg data-src="graphics/system.svg" class="stretch"/>
|
||||
<imagecredits>Su Feng</imagecredits>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Defining Possible Worlds</h3>
|
||||
<p>Mimir allows users to define special UDFs called <i>Models</i>.</p>
|
||||
<pre><code class="sql">
|
||||
CREATE MODEL TYPE Geocoder AS mimir.models.GeocodingModel;
|
||||
|
||||
CREATE MODEL INSTANCE Text_To_Loc USING Geocoder('Google');
|
||||
|
||||
SELECT C.name, C.id, Text_To_Loc(C.address) AS address
|
||||
FROM Customer C;
|
||||
</code></pre>
|
||||
<p style="font-size: small;" class="fragment">(Not actual Mimir-SQL. Language adapted for your viewing pleasure.)</p>
|
||||
<p style="text-align: left; width: 600px; margin-left: auto; margin-right: auto;" class="fragment">Models...<br/>... return one <b>best guess</b><br/>... define the space of alternatives</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Example Models</h3>
|
||||
|
||||
<ul>
|
||||
<li>Geocoding Addresses</li>
|
||||
<li>Imputation using a SparkML classifier</li>
|
||||
<li>Heuristic detection of order-by columns for interpolation</li>
|
||||
<li>Schema matching based on edit-distance</li>
|
||||
<li>MayBMS-style probabilistic repair-key</li>
|
||||
<li>And more...</li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Convenience Operators: Lenses</h3>
|
||||
|
||||
<p>Lenses instantiate/train a model and wrap a query</p>
|
||||
<ul style="font-size: 16pt">
|
||||
<li>Domain Constraint Repair / Missing Value Imputation</li>
|
||||
<li>Schema Matching</li>
|
||||
<li>Sequence Repair</li>
|
||||
<li>Key Repair</li>
|
||||
<li>Arbitrary Choice</li>
|
||||
<li>Type Detection *</li>
|
||||
<li>Header Detection *</li>
|
||||
<li>JSON Shredder *</li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>Evaluation handled by a DBMS or Spark via query rewriting.</p>
|
||||
<pre><code class="sql">
|
||||
SELECT C.name, C.id, Text_To_Loc(C.address) AS address
|
||||
FROM Customer C;
|
||||
</code></pre>
|
||||
<p>becomes...</p>
|
||||
<pre><code class="sql">
|
||||
SELECT C.name, C.id, Text_To_Loc(C.address) AS address,
|
||||
1 AS name_certain, 1 AS id_certain,
|
||||
0 AS address_certain, 1 AS row_certain
|
||||
FROM Customer C;
|
||||
</code></pre>
|
||||
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<canvas data-chart="bar">
|
||||
<!--
|
||||
{"options": {
|
||||
"title" : {
|
||||
"display" : true,
|
||||
"text" : ["Query Performance on PDBench"," (1 GB; 10% Uncertainty)"]
|
||||
},
|
||||
"scales": {
|
||||
"yAxes": [{
|
||||
"ticks" : {
|
||||
"beginAtZero" : true
|
||||
},
|
||||
"scaleLabel": {
|
||||
"display": true,
|
||||
"labelString": "Query Runtime (s)"
|
||||
}
|
||||
}]
|
||||
}
|
||||
}}
|
||||
-->
|
||||
Label, PDB-1, PDB-2, PDB-3
|
||||
Deterministic, 4.714, 4.073, 5.238
|
||||
Mimir+SQLite, 4.962, 4.257, 6.989
|
||||
MayBMS, 21.814, 9.171, 18.137
|
||||
</canvas>
|
||||
</section>
|
||||
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>A few more things we're doing with Mimir...</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<h3>Adaptive Schemas</h3>
|
||||
|
||||
<ul style="font-size: 16pt" class="fragment">
|
||||
<li>Domain Constraint Repair / Missing Value Imputation</li>
|
||||
<li>Schema Matching</li>
|
||||
<li>Sequence Repair</li>
|
||||
<li>Key Repair</li>
|
||||
<li>Arbitrary Choice</li>
|
||||
<li>Type Detection *</li>
|
||||
<li>Header Detection *</li>
|
||||
<li>JSON Shredder *</li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Adaptive Schemas</h3>
|
||||
|
||||
<ul style="font-size: 16pt">
|
||||
<li style="color: lightgrey;">Domain Constraint Repair / Missing Value Imputation</li>
|
||||
<li style="color: lightgrey;">Schema Matching</li>
|
||||
<li style="color: lightgrey;">Sequence Repair</li>
|
||||
<li style="color: lightgrey;">Key Repair</li>
|
||||
<li style="color: lightgrey;">Arbitrary Choice</li>
|
||||
<li>Type Detection *</li>
|
||||
<li>Header Detection *</li>
|
||||
<li>JSON Shredder *</li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<pre><code class="sql">
|
||||
LOAD 'customers.csv';
|
||||
|
||||
SELECT name FROM customers WHERE last_purchase < LAST_WEEK();
|
||||
</code></pre>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>How does the system know...</h3>
|
||||
<dl>
|
||||
<dt style="margin-top: 50px">... which column is 'name'?</dt>
|
||||
<dd class="fragment">Guess that row 1 is headers.</dd>
|
||||
|
||||
<dt style="margin-top: 50px">... that 'last_purchase' is a <span style="font-family: Courier">date</span>?</dt>
|
||||
<dd class="fragment">All rows look like <span style="font-family: Courier">YYYY-MM-DD</span></dd>
|
||||
</dl>
|
||||
<p class="fragment">This is all guesswork!</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p><b>Idea:</b> Make the System Catalog a Probabilistic Table</p>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<h3>Probabilistic Query Compilers</h3>
|
||||
<p style="margin-top: 100px">Sampling from ProbDBs is Sloooow</p>
|
||||
</section>
|
||||
<section>
|
||||
<h3>Trivial Sampling</h3>
|
||||
<p>Evaluate the query $N$ times.<br/>Plug in samples instead of best guesses.</p>
|
||||
<div class="fragment" style="margin-top: 60px;">
|
||||
<h3>Better Solutions</h3>
|
||||
<p>Merge evaluation to mitigate redundancy.</p>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Sparse Encoding</h3>
|
||||
<table>
|
||||
<tr><td>
|
||||
<table>
|
||||
<tr><th style="border-right: 1px solid;">$R_1$</th><th>A</th><th>B</th></tr>
|
||||
<tr><td style="border-right: 1px solid;"></td><td>1</td><td>2</td></tr>
|
||||
<tr><td style="border-right: 1px solid;"></td><td>3</td><td>4</td></tr>
|
||||
<tr><td></td><td></td><td></td></tr>
|
||||
<tr><th style="border-right: 1px solid;">$R_2$</th><th>A</th><th>B</th></tr>
|
||||
<tr><td style="border-right: 1px solid;"></td><td>1</td><td>5</td></tr>
|
||||
</table>
|
||||
</td><td style="vertical-align: middle;">
|
||||
➔
|
||||
</td><td style="vertical-align: middle;">
|
||||
<table>
|
||||
<tr><th style="border-right: 1px solid;">$R_{sparse}$</th><th>A</th><th>B</th><th>S#</th></tr>
|
||||
<tr><td style="border-right: 1px solid;"></td><td>1</td><td>2</td><td>1</td></tr>
|
||||
<tr><td style="border-right: 1px solid;"></td><td>3</td><td>4</td><td>1</td></tr>
|
||||
<tr><td style="border-right: 1px solid;"></td><td>1</td><td>5</td><td>2</td></tr>
|
||||
</table>
|
||||
</td></tr>
|
||||
</table>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Tuple Bundles</h3>
|
||||
<table>
|
||||
<tr><td>
|
||||
<table>
|
||||
<tr><th style="border-right: 1px solid;">$R_1$</th><th>A</th><th>B</th></tr>
|
||||
<tr><td style="border-right: 1px solid;"></td><td>1</td><td>2</td></tr>
|
||||
<tr><td style="border-right: 1px solid;"></td><td>3</td><td>4</td></tr>
|
||||
<tr><td></td><td></td><td></td></tr>
|
||||
<tr><th style="border-right: 1px solid;">$R_2$</th><th>A</th><th>B</th></tr>
|
||||
<tr><td style="border-right: 1px solid;"></td><td>1</td><td>5</td></tr>
|
||||
</table>
|
||||
</td><td style="vertical-align: middle;">
|
||||
➔
|
||||
</td><td style="vertical-align: middle;">
|
||||
<table>
|
||||
<tr><th style="border-right: 1px solid;">$R_{bundle}$</th><th>A</th><th>B</th><th>$\phi$</th></tr>
|
||||
<tr><td style="border-right: 1px solid;"></td><td>1</td><td>[2,5]</td><td>[T,T]</td></tr>
|
||||
<tr><td style="border-right: 1px solid;"></td><td>3</td><td>4</td><td>[T,F]</td></tr>
|
||||
</table>
|
||||
</td></tr>
|
||||
</table>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<canvas data-chart="bar">
|
||||
<!--
|
||||
{"options": {
|
||||
"title" : {
|
||||
"display" : true,
|
||||
"text" : ["Query Performance on TPC-H"," (1 GB; 5 min timeout)"]
|
||||
},
|
||||
"scales": {
|
||||
"yAxes": [{
|
||||
"ticks" : {
|
||||
"beginAtZero" : true
|
||||
},
|
||||
"scaleLabel": {
|
||||
"display": true,
|
||||
"labelString": "Query Runtime (s)"
|
||||
}
|
||||
}]
|
||||
}
|
||||
}}
|
||||
-->
|
||||
Label, TPCH-1, TPCH-3, TPCH-5
|
||||
Sparse Tables, 119.6160702, 162.0010839, 258.7416881
|
||||
Tuple Bundles, 14.65919489, 300, 300
|
||||
</canvas>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p><b>Idea:</b> Let the compiler pick the right representation<br/>(or combination)</p>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<table>
|
||||
<tr>
|
||||
<th colspan="5" style="font-size: 12pt">Students</th>
|
||||
|
|
@ -364,21 +944,21 @@ Sampling (x10), 300, 242.5666234549135, 300, 119.61607021316885, 162.00108394436
|
|||
</td>
|
||||
<td width="100px">
|
||||
<img src="people/aaron.jpg" width="64px" height="80px" style="margin-bottom: 0px"/>
|
||||
<p style="margin-top: 0px; font-size: 10pt;">Aaron<br/>(PhD-3Y)</p>
|
||||
<p style="margin-top: 0px; font-size: 10pt; font-weight: bold;">Aaron<br/>(PhD-3Y)</p>
|
||||
</td>
|
||||
<td width="100px">
|
||||
<img src="people/lisa.jpg" width="71px" height="80px" style="margin-bottom: 0px"/>
|
||||
<p style="margin-top: 0px; font-size: 10pt;">Lisa<br/>(PhD-0Y)</p>
|
||||
</td>
|
||||
<td width="100px">
|
||||
<img src="people/olivia.png" width="50px" height="80px" style="margin-bottom: 0px"/>
|
||||
<p style="margin-top: 0px; font-size: 10pt;">Olivia<br/>(BS-Sr)</p>
|
||||
<img src="people/gourab.jpg" width="80px" height="80px" style="margin-bottom: 0px"/>
|
||||
<p style="margin-top: 0px; font-size: 10pt;">Gourab<br/>(MS-2Y)</p>
|
||||
</td>
|
||||
</tr>
|
||||
</table>
|
||||
<table style="display: inline-block;">
|
||||
<tr>
|
||||
<th colspan="4" style="font-size: 12pt">Alumni</th>
|
||||
<th colspan="5" style="font-size: 12pt">Alumni</th>
|
||||
</tr>
|
||||
<tr height="80px">
|
||||
<td width="100px">
|
||||
|
|
@ -395,7 +975,11 @@ Sampling (x10), 300, 242.5666234549135, 300, 119.61607021316885, 162.00108394436
|
|||
</td>
|
||||
<td width="100px">
|
||||
<img src="people/shivang.jpg" width="55px" height="80px" style="margin-bottom: 0px"/>
|
||||
<p style="margin-top: 0px; font-size: 10pt;">Shivang<br/>(MS-2Y)</p>
|
||||
<p style="margin-top: 0px; font-size: 10pt;">Shivang<br/>(MS 2018)</p>
|
||||
</td>
|
||||
<td width="100px">
|
||||
<img src="people/olivia.png" width="50px" height="80px" style="margin-bottom: 0px"/>
|
||||
<p style="margin-top: 0px; font-size: 10pt;">Olivia<br/>(BS 2017)</p>
|
||||
</td>
|
||||
</tr>
|
||||
</table>
|
||||
|
|
@ -431,10 +1015,10 @@ Sampling (x10), 300, 242.5666234549135, 300, 119.61607021316885, 162.00108394436
|
|||
</table>
|
||||
<table style="margin-top: 5px">
|
||||
<tr>
|
||||
<td width="140px" style="font-size: 10pt;">
|
||||
<td width="140px" style="font-size: 10pt; font-weight: bold;">
|
||||
Boris Glavic<br/>(IIT)
|
||||
</td>
|
||||
<td width="140px" style="font-size: 10pt;">
|
||||
<td width="140px" style="font-size: 10pt; font-weight: bold;">
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||||
Su Feng<br/>(IIT)
|
||||
</td>
|
||||
<td width="140px" style="font-size: 10pt;">
|
||||
|
|
@ -451,27 +1035,10 @@ Sampling (x10), 300, 242.5666234549135, 300, 119.61607021316885, 162.00108394436
|
|||
</td>
|
||||
</tr>
|
||||
</table>
|
||||
<p style="font-size: 10pt; font-weight: bold;">Mimir is supported by NSF Award ACI-1640864, NPS Award N00244-16-1-0022, and gifts from Oracle</p>
|
||||
<p style="font-size: 10pt; text-decoration: underline;">Mimir is supported by NSF Award ACI-1640864, NPS Award N00244-16-1-0022, and gifts from Oracle</p>
|
||||
</section>
|
||||
|
||||
|
||||
|
||||
|
||||
<section>
|
||||
|
||||
<p style="font-size: x-large;"><img src="graphics/mimir_logo_final.png" height="150px"><br/><a href="http://mimirdb.info">http://mimirdb.info</a></p>
|
||||
|
||||
<ul style="font-size: smaller;">
|
||||
<li>It's not the data that's uncertain, it's the interpretation.</li>
|
||||
<li>Tagged best-guess evaluation is faster and easier to understand.</li>
|
||||
<li>Not committing to one representation allows faster query processing.</li>
|
||||
</ul>
|
||||
|
||||
<p><b>Thanks!</b></p>
|
||||
|
||||
</section>
|
||||
|
||||
|
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