\section{Laplace\+Distribution Class Reference} \label{classmlpack_1_1distribution_1_1LaplaceDistribution}\index{Laplace\+Distribution@{Laplace\+Distribution}} The multivariate Laplace distribution centered at 0 has pdf. \subsection*{Public Member Functions} \begin{DoxyCompactItemize} \item \textbf{ Laplace\+Distribution} () \begin{DoxyCompactList}\small\item\em Default constructor, which creates a Laplace distribution with zero dimension and zero scale parameter. \end{DoxyCompactList}\item \textbf{ Laplace\+Distribution} (const size\+\_\+t dimensionality, const double scale) \begin{DoxyCompactList}\small\item\em Construct the Laplace distribution with the given scale and dimensionality. \end{DoxyCompactList}\item \textbf{ Laplace\+Distribution} (const arma\+::vec \&mean, const double scale) \begin{DoxyCompactList}\small\item\em Construct the Laplace distribution with the given mean and scale parameter. \end{DoxyCompactList}\item size\+\_\+t \textbf{ Dimensionality} () const \begin{DoxyCompactList}\small\item\em Return the dimensionality of this distribution. \end{DoxyCompactList}\item void \textbf{ Estimate} (const arma\+::mat \&observations) \begin{DoxyCompactList}\small\item\em Estimate the Laplace distribution directly from the given observations. \end{DoxyCompactList}\item void \textbf{ Estimate} (const arma\+::mat \&observations, const arma\+::vec \&probabilities) \begin{DoxyCompactList}\small\item\em Estimate the Laplace distribution from the given observations, taking into account the probability of each observation actually being from this distribution. \end{DoxyCompactList}\item double \textbf{ Log\+Probability} (const arma\+::vec \&observation) const \begin{DoxyCompactList}\small\item\em Return the log probability of the given observation. \end{DoxyCompactList}\item void \textbf{ Log\+Probability} (const arma\+::mat \&x, arma\+::vec \&log\+Probabilities) const \begin{DoxyCompactList}\small\item\em Evaluate log probability density function of given observation. \end{DoxyCompactList}\item const arma\+::vec \& \textbf{ Mean} () const \begin{DoxyCompactList}\small\item\em Return the mean. \end{DoxyCompactList}\item arma\+::vec \& \textbf{ Mean} () \begin{DoxyCompactList}\small\item\em Modify the mean. \end{DoxyCompactList}\item double \textbf{ Probability} (const arma\+::vec \&observation) const \begin{DoxyCompactList}\small\item\em Return the probability of the given observation. \end{DoxyCompactList}\item void \textbf{ Probability} (const arma\+::mat \&x, arma\+::vec \&probabilities) const \begin{DoxyCompactList}\small\item\em Evaluate probability density function of given observation. \end{DoxyCompactList}\item arma\+::vec \textbf{ Random} () const \begin{DoxyCompactList}\small\item\em Return a randomly generated observation according to the probability distribution defined by this object. \end{DoxyCompactList}\item double \textbf{ Scale} () const \begin{DoxyCompactList}\small\item\em Return the scale parameter. \end{DoxyCompactList}\item double \& \textbf{ Scale} () \begin{DoxyCompactList}\small\item\em Modify the scale parameter. \end{DoxyCompactList}\item {\footnotesize template$<$typename Archive $>$ }\\void \textbf{ serialize} (Archive \&ar, const unsigned int) \begin{DoxyCompactList}\small\item\em Serialize the distribution. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Detailed Description} The multivariate Laplace distribution centered at 0 has pdf. \[ f(x|\theta) = \frac{1}{2 \theta}\exp\left(-\frac{\|x - \mu\|}{\theta}\right) \] given scale parameter $\theta$ and mean $\mu$. This implementation assumes a diagonal covariance, but a rewrite to support arbitrary covariances is possible. See the following paper for more information on the non-\/diagonal-\/covariance Laplace distribution and estimation techniques\+: \begin{DoxyCode} @article\{eltoft2006multivariate, title=\{\{On the Multivariate Laplace Distribution\}\}, author=\{Eltoft, Torbj\(\backslash\)orn and Kim, Taesu and Lee, Te-Won\}, journal=\{IEEE Signal Processing Letters\}, volume=\{13\}, number=\{5\}, pages=\{300--304\}, year=\{2006\} \} \end{DoxyCode} Note that because of the diagonal covariance restriction, much of the algebra in the paper above becomes simplified, and the P\+DF takes roughly the same form as the univariate case. Definition at line 50 of file laplace\+\_\+distribution.\+hpp. \subsection{Constructor \& Destructor Documentation} \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_a83291cefd1754252b508778f63010e9a}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Laplace\+Distribution@{Laplace\+Distribution}} \index{Laplace\+Distribution@{Laplace\+Distribution}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Laplace\+Distribution()\hspace{0.1cm}{\footnotesize\ttfamily [1/3]}} {\footnotesize\ttfamily \textbf{ Laplace\+Distribution} (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Default constructor, which creates a Laplace distribution with zero dimension and zero scale parameter. Definition at line 57 of file laplace\+\_\+distribution.\+hpp. \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_a598b5dc7055687d35a2ae19304de0c16}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Laplace\+Distribution@{Laplace\+Distribution}} \index{Laplace\+Distribution@{Laplace\+Distribution}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Laplace\+Distribution()\hspace{0.1cm}{\footnotesize\ttfamily [2/3]}} {\footnotesize\ttfamily \textbf{ Laplace\+Distribution} (\begin{DoxyParamCaption}\item[{const size\+\_\+t}]{dimensionality, }\item[{const double}]{scale }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Construct the Laplace distribution with the given scale and dimensionality. The mean is initialized to zero. \begin{DoxyParams}{Parameters} {\em dimensionality} & Dimensionality of distribution. \\ \hline {\em scale} & Scale of distribution. \\ \hline \end{DoxyParams} Definition at line 66 of file laplace\+\_\+distribution.\+hpp. \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_a4d7d471d63f2b083d0f445eaaac1fc5c}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Laplace\+Distribution@{Laplace\+Distribution}} \index{Laplace\+Distribution@{Laplace\+Distribution}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Laplace\+Distribution()\hspace{0.1cm}{\footnotesize\ttfamily [3/3]}} {\footnotesize\ttfamily \textbf{ Laplace\+Distribution} (\begin{DoxyParamCaption}\item[{const arma\+::vec \&}]{mean, }\item[{const double}]{scale }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Construct the Laplace distribution with the given mean and scale parameter. \begin{DoxyParams}{Parameters} {\em mean} & Mean of distribution. \\ \hline {\em scale} & Scale of distribution. \\ \hline \end{DoxyParams} Definition at line 76 of file laplace\+\_\+distribution.\+hpp. \subsection{Member Function Documentation} \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_a78eda6bfb9e9462afa0fc85e32abe1af}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Dimensionality@{Dimensionality}} \index{Dimensionality@{Dimensionality}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Dimensionality()} {\footnotesize\ttfamily size\+\_\+t Dimensionality (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Return the dimensionality of this distribution. Definition at line 80 of file laplace\+\_\+distribution.\+hpp. \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_a8e4f3f3159adc7073194a9c71d5c6fc4}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Estimate@{Estimate}} \index{Estimate@{Estimate}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Estimate()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily void Estimate (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{observations }\end{DoxyParamCaption})} Estimate the Laplace distribution directly from the given observations. \begin{DoxyParams}{Parameters} {\em observations} & List of observations. \\ \hline \end{DoxyParams} Referenced by Laplace\+Distribution\+::\+Random(). \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_a486d2a322d6bfd15f62127c5e25e20f0}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Estimate@{Estimate}} \index{Estimate@{Estimate}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Estimate()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily void Estimate (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{observations, }\item[{const arma\+::vec \&}]{probabilities }\end{DoxyParamCaption})} Estimate the Laplace distribution from the given observations, taking into account the probability of each observation actually being from this distribution. \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_a7063c1fb92f512f32bf44542c7528739}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Log\+Probability@{Log\+Probability}} \index{Log\+Probability@{Log\+Probability}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Log\+Probability()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily double Log\+Probability (\begin{DoxyParamCaption}\item[{const arma\+::vec \&}]{observation }\end{DoxyParamCaption}) const} Return the log probability of the given observation. \begin{DoxyParams}{Parameters} {\em observation} & Point to evaluate logarithm of probability. \\ \hline \end{DoxyParams} Referenced by Laplace\+Distribution\+::\+Log\+Probability(), and Laplace\+Distribution\+::\+Probability(). \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_aabd4dbf56bd3d719aede447516d68296}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Log\+Probability@{Log\+Probability}} \index{Log\+Probability@{Log\+Probability}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Log\+Probability()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily void Log\+Probability (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{x, }\item[{arma\+::vec \&}]{log\+Probabilities }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Evaluate log probability density function of given observation. \begin{DoxyParams}{Parameters} {\em x} & List of observations. \\ \hline {\em log\+Probabilities} & Output probabilities for each input observation. \\ \hline \end{DoxyParams} Definition at line 113 of file laplace\+\_\+distribution.\+hpp. References Laplace\+Distribution\+::\+Log\+Probability(). \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_a6db5f5d76cbd055347cecd9ca90eea86}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Mean@{Mean}} \index{Mean@{Mean}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Mean()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily const arma\+::vec\& Mean (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Return the mean. Definition at line 163 of file laplace\+\_\+distribution.\+hpp. \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_a94becb1cd872c0334328c37f130db253}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Mean@{Mean}} \index{Mean@{Mean}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Mean()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily arma\+::vec\& Mean (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the mean. Definition at line 165 of file laplace\+\_\+distribution.\+hpp. \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_ab72935d592516e77511d0b5e703c0d41}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Probability@{Probability}} \index{Probability@{Probability}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Probability()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily double Probability (\begin{DoxyParamCaption}\item[{const arma\+::vec \&}]{observation }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Return the probability of the given observation. \begin{DoxyParams}{Parameters} {\em observation} & Point to evaluate probability at. \\ \hline \end{DoxyParams} Definition at line 87 of file laplace\+\_\+distribution.\+hpp. References Laplace\+Distribution\+::\+Log\+Probability(). \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_a1e516aca34e9c99caf1431a822d87fc6}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Probability@{Probability}} \index{Probability@{Probability}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Probability()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily void Probability (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{x, }\item[{arma\+::vec \&}]{probabilities }\end{DoxyParamCaption}) const} Evaluate probability density function of given observation. \begin{DoxyParams}{Parameters} {\em x} & List of observations. \\ \hline {\em probabilities} & Output probabilities for each input observation. \\ \hline \end{DoxyParams} \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_a2c6f8d5bb4eacf7de767d2172b320756}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Random@{Random}} \index{Random@{Random}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Random()} {\footnotesize\ttfamily arma\+::vec Random (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Return a randomly generated observation according to the probability distribution defined by this object. This is inlined for speed. \begin{DoxyReturn}{Returns} Random observation from this Laplace distribution. \end{DoxyReturn} Definition at line 128 of file laplace\+\_\+distribution.\+hpp. References Laplace\+Distribution\+::\+Estimate(). \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_ab30d1e52df44eb451081926df999fc17}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Scale@{Scale}} \index{Scale@{Scale}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Scale()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily double Scale (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Return the scale parameter. Definition at line 168 of file laplace\+\_\+distribution.\+hpp. \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_a8190151e4134e9f69f1f51cd013ba43c}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!Scale@{Scale}} \index{Scale@{Scale}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{Scale()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily double\& Scale (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the scale parameter. Definition at line 170 of file laplace\+\_\+distribution.\+hpp. \mbox{\label{classmlpack_1_1distribution_1_1LaplaceDistribution_af0dd9205158ccf7bcfcd8ff81f79c927}} \index{mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}!serialize@{serialize}} \index{serialize@{serialize}!mlpack\+::distribution\+::\+Laplace\+Distribution@{mlpack\+::distribution\+::\+Laplace\+Distribution}} \subsubsection{serialize()} {\footnotesize\ttfamily void serialize (\begin{DoxyParamCaption}\item[{Archive \&}]{ar, }\item[{const unsigned}]{int }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Serialize the distribution. Definition at line 176 of file laplace\+\_\+distribution.\+hpp. The documentation for this class was generated from the following file\+:\begin{DoxyCompactItemize} \item /var/www/mlpack.\+ratml.\+org/mlpack.\+org/\+\_\+src/mlpack-\/git/src/mlpack/core/dists/\textbf{ laplace\+\_\+distribution.\+hpp}\end{DoxyCompactItemize}