Examples Of Higher Dimensional Graphs
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%20influence%20graph%20or%20causal%20graph%20of%20a%20high-dimensional%20multivariate%20discrete-time%20Markov%20process%20with%20memory.%20At%20any%20discrete%20time%20instant%2C%20each%20observed%20variable%20of%20the%20multivariate%20process%20is%20a%20binary%20string%20of%20random%20length%2C%20which%20is%20parameterized%20by%20an%20unobservable%20or%20hidden%20[0%2C1]-valued%20scalar.%20The%20hidden%20scalars%20corresponding%20to%20the%20variables%20evolve%20according%20to%20discrete-time%20linear%20stochastic%20dynamics%20dictated%20by%20the%20underlying%20influence%20graph%20whose%20nodes%20are%20the%20variables.%20We%20extend%20an%20existing%20algorithm%20for%20learning%20i.i.d.%20graphical%20models%20to%20this%20Markovian%20setting%20with%20memory%20and%20prove%20that%20it%20can%20learn%20the%20influence%20graph%20based%20on%20the%20binary%20observations%20using%20logarithmic%20(in%20number%20of%20variables%20or%20nodes)%20samples%20when%20the%20degree%20of%20the%20influence%20graph%20is%20bounded.%20The%20crucial%20analytical%20contribution%20of%20this%20work%20is%20the%20derivation%20of%20the%20sample%20complexity%20result%20by%20upper%20and%20lower%20bounding%20the%20rate%20of%20convergence%20of%20the%20observed%20Markov%20process%20with%20memory%20to%20its%20stationary%20distribution%20in%20terms%20of%20the%20parameters%20of%20the%20influence%20graph.)
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