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Diffstat (limited to 'paper/sections/linear_threshold.tex')
| -rw-r--r-- | paper/sections/linear_threshold.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/paper/sections/linear_threshold.tex b/paper/sections/linear_threshold.tex index 8ff64b3..2c0fb62 100644 --- a/paper/sections/linear_threshold.tex +++ b/paper/sections/linear_threshold.tex @@ -13,9 +13,9 @@ where we defined again $\theta_j\defeq (\Theta_{1,j},\ldots,\Theta_{m,j})$ and $ \begin{equation} \label{eq:lt} \tag{LT} - y_{t} = \text{sign} \left(\inprod{\theta_j}{X^t} - t_j \right) + y^t_j = \text{sign} \left(\inprod{\theta_j}{X^t} - t_j \right) \end{equation} The linear threshold model can therefore be cast as a variant of the recently introduced 1-bit compressed sensing model \cite{Boufounos:2008}. Several recent papers study the theoretical guarantees obtained for 1-bit compressed sensing with specific measurements \cite{Gupta:2010}, \cite{Plan:2014}. Others study adaptive mechanisms \cite{Jacques:2013}. -Support recovery results in the 1-bit compressed sensing model rely on the fact that well-chosen random hyperplanes segment a compact set into small cells. Knowing which side of the hyperplanes you are on situates you in one of these cells of bounded size. Whilst the obtained bounds are also of the order ${\cal O}(n \log \frac{n}{s}$), no current theory exists for recovering positive bounded signal from bernoulli hyperplanes. We leave this research direction to future work.
\ No newline at end of file +Support recovery results in the 1-bit compressed sensing model rely on the fact that well-chosen random hyperplanes segment a compact set into small cells. Knowing which side of the hyperplanes you are on situates you in one of these cells of bounded size. Whilst they obtained bounds are also of the order ${\cal O}(n \log \frac{n}{s}$), no current theory exists for recovering positive bounded signals from bernoulli hyperplanes. We leave this research direction to future work.
\ No newline at end of file |