This work draws on previous works regarding spectral learning algorithm for structured data (see \cite{Hsu:COLT09-long}, \cite{DBLP:conf/icml/SongSGS10}, \cite{DBLP:conf/pkdd/BalleQC11}, \cite{DBLP:conf/nips/AnandkumarCHKSZ11}, \cite{DBLP:conf/icml/ParikhSX11}). We present an extension of the \emph{Hidden Markov Models}, called \emph{Graphical Weighted Models (GWM)}, whose purpose is to model distributions over labeled graphs. We describe the spectral algorithm for GWM, which generalizes the previous spectral algorithms for sequences and trees. We show that this algorithm is \emph{consistant}, and we provide statistical convergence bounds for the parameters estimate and for the learned distribution.
