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-rw-r--r--slides/1.pdfbin45040 -> 47502 bytes
-rw-r--r--slides/2.pdfbin45694 -> 45152 bytes
-rw-r--r--slides/3.pdfbin46210 -> 45700 bytes
-rw-r--r--slides/4.pdfbin46191 -> 47792 bytes
-rw-r--r--slides/5.pdfbin0 -> 45141 bytes
-rw-r--r--slides/6.pdfbin0 -> 45735 bytes
-rw-r--r--slides/7.pdfbin0 -> 46283 bytes
-rw-r--r--slides/8.pdfbin0 -> 46263 bytes
-rw-r--r--slides/diagram.svg375
-rw-r--r--slides/file.svg34
-rw-r--r--slides/slides.tex110
11 files changed, 380 insertions, 139 deletions
diff --git a/slides/1.pdf b/slides/1.pdf
index 31bcf6b..cfdab56 100644
--- a/slides/1.pdf
+++ b/slides/1.pdf
Binary files differ
diff --git a/slides/2.pdf b/slides/2.pdf
index 1794dce..db2ced6 100644
--- a/slides/2.pdf
+++ b/slides/2.pdf
Binary files differ
diff --git a/slides/3.pdf b/slides/3.pdf
index 884f542..2ef00a1 100644
--- a/slides/3.pdf
+++ b/slides/3.pdf
Binary files differ
diff --git a/slides/4.pdf b/slides/4.pdf
index eaebe6e..388ed9b 100644
--- a/slides/4.pdf
+++ b/slides/4.pdf
Binary files differ
diff --git a/slides/5.pdf b/slides/5.pdf
new file mode 100644
index 0000000..567fb49
--- /dev/null
+++ b/slides/5.pdf
Binary files differ
diff --git a/slides/6.pdf b/slides/6.pdf
new file mode 100644
index 0000000..5080b60
--- /dev/null
+++ b/slides/6.pdf
Binary files differ
diff --git a/slides/7.pdf b/slides/7.pdf
new file mode 100644
index 0000000..2861a5b
--- /dev/null
+++ b/slides/7.pdf
Binary files differ
diff --git a/slides/8.pdf b/slides/8.pdf
new file mode 100644
index 0000000..b502d99
--- /dev/null
+++ b/slides/8.pdf
Binary files differ
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+ sodipodi:nodetypes="cccccc"
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+ <g
+ inkscape:label="Layer 1"
+ id="g3522"
+ transform="matrix(0.3545053,0,0,0.3545053,392.15676,-121.70881)">
+ <path
+ inkscape:connector-curvature="0"
+ style="fill:url(#linearGradient3528);fill-opacity:1;fill-rule:evenodd;stroke:#808080;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:round;stroke-opacity:1"
+ d="m 82,930.36218 -60,0 0,115.00002 85,0 0,-90.00002 -25,-25 z"
+ id="path3524"
+ sodipodi:nodetypes="cccccc" />
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+ inkscape:connector-curvature="0"
+ style="fill:url(#linearGradient3530);fill-opacity:1;fill-rule:evenodd;stroke:#808080;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:round;stroke-opacity:1"
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+ id="path3526"
+ sodipodi:nodetypes="cccc" />
+ </g>
</g>
<g
inkscape:groupmode="layer"
id="layer3"
inkscape:label="sellers"
- style="display:none">
+ style="display:inline"
+ transform="translate(-76.447662,-99.280643)">
<text
transform="translate(0,-0.00216797)"
xml:space="preserve"
@@ -1228,7 +1415,8 @@
inkscape:groupmode="layer"
id="layer5"
inkscape:label="seller2"
- style="display:none">
+ style="display:inline"
+ transform="translate(-76.447662,-99.280643)">
<text
sodipodi:linespacing="125%"
id="text9316"
@@ -1248,7 +1436,8 @@
inkscape:groupmode="layer"
id="layer4"
inkscape:label="buyer"
- style="display:none">
+ style="display:inline"
+ transform="translate(-76.447662,-99.280643)">
<path
transform="translate(0,-0.00216797)"
mask="none"
diff --git a/slides/file.svg b/slides/file.svg
new file mode 100644
index 0000000..2736728
--- /dev/null
+++ b/slides/file.svg
@@ -0,0 +1,34 @@
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diff --git a/slides/slides.tex b/slides/slides.tex
index 1bccd02..2c4b3fa 100644
--- a/slides/slides.tex
+++ b/slides/slides.tex
@@ -30,36 +30,14 @@
\begin{frame}{Motivation}
\begin{center}
- \includegraphics<1-4>[scale=0.5]{1.pdf}
- \includegraphics<5>[scale=0.5]{2.pdf}
- \includegraphics<6>[scale=0.5]{3.pdf}
- \includegraphics<7>[scale=0.5]{4.pdf}
- \end{center}
-
- \begin{center}
- \begin{overprint}
- \onslide<1>\begin{center}$N$ users\end{center}
- \onslide<2>
- \begin{center}
- $x_i\in\mathbb{R}^d$: public features (e.g. age, sex, height, etc.)
- \end{center}
- \onslide<3>
- \begin{center}
- $y_i\in\mathbb{R}$: private date (e.g. disease, etc.)
- \end{center}
- \onslide<4>
- \begin{center}
- Linear model: $y_i = \beta^Tx_i + \varepsilon_i$
- \end{center}
- \begin{displaymath}
- \beta^* = \arg\min_\beta \sum_i |y_i-\beta^Tx_i|^2
- \end{displaymath}
- \end{overprint}
+ \includegraphics<1>[scale=0.5]{1.pdf}
+ \includegraphics<2>[scale=0.5]{2.pdf}
+ \includegraphics<3>[scale=0.5]{3.pdf}
+ \includegraphics<4>[scale=0.5]{4.pdf}
\end{center}
\end{frame}
-
-
\begin{frame}{Challenges}
+ \pause
\begin{itemize}
\item Value of data?
\vspace{1cm}
@@ -72,6 +50,7 @@
\end{frame}
\begin{frame}{Contributions}
+ \pause
\begin{itemize}
\item case of the linear regression
\vspace{1cm}
@@ -95,7 +74,7 @@
\begin{frame}{Reverse auction}
\begin{itemize}
- \item set of $N$ sellers $\mathcal{A} = \{1,\ldots,N\}$ and a buyer
+ \item set of $N$ sellers: $\mathcal{A} = \{1,\ldots,N\}$; a buyer
\vspace{0.3cm}
\pause
\item $V$ value function of the buyer, $V:2^\mathcal{A}\rightarrow \mathbb{R}^+$
@@ -114,7 +93,7 @@
\begin{itemize}
\item Find $S\subset \mathcal{A}$ \alert{maximizing} $V(S)$
\vspace{0.3cm}
- \item Find \alert{payment} $p_i$ to seller $i$
+ \item Find \alert{payment} $p_i$ to seller $i\in S$
\end{itemize}
\end{block}
\end{frame}
@@ -179,14 +158,42 @@
\tableofcontents[currentsection]
\end{frame}
-\begin{frame}{Linear regression}
- Each user $i\in\mathcal{A}$ has:
+\begin{frame}{Linear Regression}
+ \begin{center}
+ \includegraphics<1-4>[scale=0.5]{5.pdf}
+ \includegraphics<5>[scale=0.5]{6.pdf}
+ \includegraphics<6>[scale=0.5]{7.pdf}
+ \includegraphics<7>[scale=0.5]{8.pdf}
+ \end{center}
+
+ \begin{center}
+ \begin{overprint}
+ \onslide<1>\begin{center}$N$ users\end{center}
+ \onslide<2>
+ \begin{center}
+ $x_i$: public features (e.g. age, gender, height, etc.)
+ \end{center}
+ \onslide<3>
+ \begin{center}
+ $y_i$: private data (e.g. disease, etc.)
+ \end{center}
+ \onslide<4>
+ \begin{center}
+ Gaussian Linear model: $y_i = \beta^Tx_i + \varepsilon_i$
+ \end{center}
+ \begin{displaymath}
+ \beta^* = \arg\min_\beta \sum_i |y_i-\beta^Tx_i|^2
+ \end{displaymath}
+ \end{overprint}
+ \end{center}
+\end{frame}
+
+\begin{frame}{Experimental design}
\begin{itemize}
- \item Public feature vector $x_i\in\mathbb{R}^d$
+ \item Public vector of features $x_i\in\mathbb{R}^d$
\item Private data $y_i\in\mathbb{R}$
\end{itemize}
- \pause
\vspace{0.5cm}
Gaussian linear model:
@@ -204,14 +211,14 @@
\begin{block}{Experimental Design}
\begin{displaymath}
- \textsf{\alert{maximize}}\quad V(S) = \log\det\left(I_d + \sum_{i\in S} x_i x_i^T\right),\quad S\subset\mathcal{A}
+ \textsf{\alert{maximize}}\quad V(S) = \log\det\left(I_d + \sum_{i\in S} x_i x_i^T\right)\quad \textsf{\alert{subject to}}\quad |S|\leq k
\end{displaymath}
\end{block}
\end{frame}
-\begin{frame}{Experimental design}
+\begin{frame}{Budgeted Experimental design}
\begin{displaymath}
- \textsf{\alert{maximize}}\quad V(S) = \log\det\left(I_d + \sum_{i\in S} x_i x_i^T\right),\quad S\subset\mathcal{A}
+ \textsf{\alert{maximize}}\quad V(S) = \log\det\left(I_d + \sum_{i\in S} x_i x_i^T\right)\quad \textsf{\alert{subject to}}\quad \sum_{i\in S}c_i\leq B
\end{displaymath}
\vspace{1cm}
@@ -233,7 +240,7 @@
\begin{frame}{Main result}
\begin{theorem}
There exists a budget feasible, individually rational and truthful mechanism for
- experimental design which runs in polynomial time. Its
+ budgeted experimental design which runs in polynomial time. Its
approximation ratio is:
\begin{displaymath}
\frac{10e-3 + \sqrt{64e^2-24e + 9}}{2(e-1)}
@@ -243,7 +250,7 @@
\end{frame}
\begin{frame}{Sketch of proof}
- \begin{block}{Mechanism (Chen et. al, 2011)}
+ \begin{block}{Mechanism (Chen et. al, 2011) for submodular $V$}
\begin{itemize}
\item Find $i^* = \arg\max_i V(\{i\})$
\item Compute $S_G$ greedily
@@ -268,13 +275,24 @@
\vspace{0.5cm}
\pause
- \alert{Solution:} Replace $V(OPT_{-i^*})$ with $L^*$:
- \pause
- \begin{itemize}
- \item computable in polynomial time
+ \begin{columns}[c]
+ \begin{column}{0.53\textwidth}
+ \alert{Solution:} Replace $V(OPT_{-i^*})$ with \alert<7>{$L^*$}:
\pause
- \item close to $V(OPT_{-i^*})$
- \end{itemize}
+ \begin{itemize}
+ \item computable in polynomial time
+ \pause
+ \item close to $V(OPT_{-i^*})$
+ \end{itemize}
+ \end{column}
+ \pause
+ \begin{column}{0.45\textwidth}
+ \begin{itemize}
+ \item Knapsack (Chen et al., 2011)
+ \item Coverage (Singer, 2012)
+ \end{itemize}
+ \end{column}
+ \end{columns}
\end{frame}
\begin{frame}{Sketch of proof (2)}
@@ -316,9 +334,9 @@
\pause
\vspace{0.5cm}
- \begin{block}{Value function: entropy reduction}
+ \begin{block}{Value function: Information gain}
\begin{displaymath}
- V(S) = H(f) - H(f\mid Y_S),\quad S\subset\mathcal{A}
+ V(S) = H(f) - H(f\mid S),\quad S\subset\mathcal{A}
\end{displaymath}
\end{block}
generated by cgit v1.2.3-70-g09d2 (git 2.52.0) at 2025-12-21 17:26:10 +0000