text: OCD

text/problem/thething/main.tex

@@ -22,7 +22,7 @@ Take for example the scenario in Figure~\ref{fig:st-cont}, where {\thethings} ar
 If we want to protect the {\thething} points, we have to allocate at most a budget of $\varepsilon$ to the {\thethings}, while saving some for the release of regular events.
 Essentially, the more budget we allocate to an event the less we protect it, but at the same time we maintain its utility.
 With {\thething} privacy we propose to distribute the budget taking into account only the existence of the {\thethings} when we release an event of the time series, i.e.,~allocating $\frac{\varepsilon}{5}$ ($4\ \text{\thethings} + 1\ \text{regular point}$) to each event (see  Figure~\ref{fig:st-cont}).
-This way, we still guarantee\footnote{$\epsilon$-differential privacy guarantees that the allocated budget should be less or equal to $\epsilon$, and not precisely how much.\kat{Mano check.}} that the {\thethings} are  adequately protected, as they receive a total budget of $\frac{4\varepsilon}{5}<\varepsilon$. 
+This way, we still guarantee\footnote{$\varepsilon$-differential privacy guarantees that the allocated budget should be less or equal to $\varepsilon$, and not precisely how much.\kat{Mano check.}} that the {\thethings} are  adequately protected, as they receive a total budget of $\frac{4\varepsilon}{5}<\varepsilon$. 
 At the same time, we avoid over-perturbing the regular events, as we allocate to them  a higher total budget ($\frac{4\varepsilon}{5}$) compared to the user-level scenario ($\frac{\varepsilon}{2}$), and thus less noise.
   
 

text/problem/thething/solution.tex

@@ -77,7 +77,7 @@ Intuitively, knowing the data set at timestamp $t$ stops the propagation of the
 %\kat{do we see this in the formula 1 ?}
 %when calculating the forward or backward privacy loss respectively.
 
-Cao et al.~\cite{cao2017quantifying} propose a method for computing the total temporal privacy loss $\alpha_t$ at a timestamp $t$ as the sum of the backward and forward privacy loss, $\alpha^B_t$ and $\alpha^F_t$, minus the privacy budget $\varepsilon_t$ 
+Cao et al.~\cite{cao2017quantifying} propose a method for computing the temporal privacy loss $\alpha_t$ at a timestamp $t$ as the sum of the backward and forward privacy loss, $\alpha^B_t$ and $\alpha^F_t$, minus the privacy budget $\varepsilon_t$ 
 to account for the extra privacy loss due to previous and next releases $\pmb{o}$ of $\mathcal{M}$ under temporal correlation.
 By Theorem~\ref{theor:thething-prv}, at every timestamp $t$ we consider the data at $t$ and at the {\thething} timestamps $L$.
 %According to the Definitions~{\ref{def:bpl} and \ref{def:fpl}}, we calculate the backward and forward privacy loss by taking into account the privacy budget at previous and next data releases respectively.