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Diffstat (limited to 'notes')
| -rw-r--r-- | notes/formalisation.pdf | bin | 194405 -> 197923 bytes | |||
| -rw-r--r-- | notes/formalisation.tex | 18 |
2 files changed, 9 insertions, 9 deletions
diff --git a/notes/formalisation.pdf b/notes/formalisation.pdf Binary files differindex 2bdcb11..2d64bb0 100644 --- a/notes/formalisation.pdf +++ b/notes/formalisation.pdf diff --git a/notes/formalisation.tex b/notes/formalisation.tex index 871fe50..bdd6aab 100644 --- a/notes/formalisation.tex +++ b/notes/formalisation.tex @@ -56,8 +56,8 @@ Two main goals: chosen uniformly at random) and on the cascade diffusion process. Such a model is probably not very realistic, but is necessary to obtain theoretical guarantees. The unrealism of the model is not a problem - \emph{per se}; the eventual validity of this approach will be - experimental anyway. + \emph{per se}; the eventual validity of this approach will be confirmed + experimentally anyway. \item It seems likely that we will want the rows of the sensing matrix to be independent realizations of the same distribution. However, \textbf{this will never be the case} if we have one row for each time @@ -67,17 +67,17 @@ Two main goals: cascade. \item Something which makes this problem very different from the usual compressed sensing problems is that the measurements depend on the - signal we wish to recover: cascades propagates along the edges - contained in the signal. More precisely, not only the rows of the - sensing matrix are correlated (if we do not aggregate them by cascade) - but they are correlated through the signal. Is this a problem? I don't - know, this looks scary though. + signal we wish to recover: cascades propagate along the edges contained + in the signal. More precisely, not only the rows of the sensing matrix + are correlated (if we do not aggregate them by cascade) but also they + are correlated through the signal. Is this a problem? I don't know, + this looks scary though. \item A slightly more general model which we will need in the independent cascade case considers a signal $s\in[0,1]^{V\times V}$. We can always go from this model to the binary case by first recovering the non-binary $s$ and then applying a thresholding procedure. But if we - only care about recovering the support of $s$, can we do better? (TO - DO: read stuff about support recovery). + only care about recovering the support of $s$, can we do better than + this two-step process? (TO DO: read stuff about support recovery). \end{itemize} \end{remark} |