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Diffstat (limited to 'paper/sections')
| -rw-r--r-- | paper/sections/discussion.tex | 2 | ||||
| -rw-r--r-- | paper/sections/lowerbound.tex | 2 | ||||
| -rw-r--r-- | paper/sections/model.tex | 2 | ||||
| -rw-r--r-- | paper/sections/results.tex | 2 |
4 files changed, 4 insertions, 4 deletions
diff --git a/paper/sections/discussion.tex b/paper/sections/discussion.tex index 03e7ff2..2f0fd36 100644 --- a/paper/sections/discussion.tex +++ b/paper/sections/discussion.tex @@ -17,7 +17,7 @@ This model therefore falls into the 1-bit compressed sensing framework \cite{Boufounos:2008}. Several recent papers study the theoretical guarantees obtained for 1-bit compressed sensing with specific measurements \cite{Gupta:2010, Plan:2014}. Whilst they obtained bounds of the order -${\cal O}(n \log \frac{m}{s}$), no current theory exists for recovering +${\cal O}(s \log \frac{m}{s}$), no current theory exists for recovering positive bounded signals from binary measurememts. This research direction may provide the first clues to solve the ``adaptive learning'' problem: if we are allowed to adaptively \emph{choose} the source nodes at the beginning of diff --git a/paper/sections/lowerbound.tex b/paper/sections/lowerbound.tex index 36fbbbe..215d3e6 100644 --- a/paper/sections/lowerbound.tex +++ b/paper/sections/lowerbound.tex @@ -1,5 +1,5 @@ In \cite{Netrapalli:2012}, the authors explicitate a lower bound of -$\Omega(s\log\frac{n}{s})$ on the number of cascades necessary to achieve good +$\Omega(s\log\frac{m}{s})$ on the number of cascades necessary to achieve good support recovery with constant probability under a \emph{correlation decay} assumption. In this section, we will consider the stable sparse recovery setting of Section~\ref{sec:relaxing_sparsity}. Our goal is to obtain an diff --git a/paper/sections/model.tex b/paper/sections/model.tex index b704b9e..41c00da 100644 --- a/paper/sections/model.tex +++ b/paper/sections/model.tex @@ -164,7 +164,7 @@ the set of blue nodes at time step $t$, then we have: Thus, the linear voter model is a Generalized Linear Cascade model with inverse link function $f: z \mapsto z$. -\subsubsection{Discretization of Continous Model} +\subsubsection{Discretization of Continuous Model} Another motivation for the Generalized Linear Cascade model is that it captures the time-discretized formulation of the well-studied continuous-time diff --git a/paper/sections/results.tex b/paper/sections/results.tex index f68ecee..7eb3973 100644 --- a/paper/sections/results.tex +++ b/paper/sections/results.tex @@ -273,7 +273,7 @@ condition on the \emph{gram matrix} of the observations $X^T X = \paragraph{(RE) with high probability} The Generalized Linear Cascade model yields a probability distribution over the -observed sets of infeceted nodes $(x^t)_{t\in\mathcal{T}}$. It is then natural +observed sets of infected nodes $(x^t)_{t\in\mathcal{T}}$. It is then natural to ask whether the restricted eigenvalue condition is likely to occur under this probabilistic model. Several recent papers show that large classes of correlated designs obey the restricted eigenvalue property with high |