Linear Dynamical Systems (LDS) is used to model statistical properties of sequential or time series data by correlating sequences to a fixed size latent variable vector or a finite-dimensional latent state, whose evolution over the sequential course makes up dynamics of data. In LDS, the state is assumed to be in real domain and the noise terms are assumed to follow the Gaussian distribution. The statistical properties of the model are defined by real-valued vectors which denote the latent variable and observation at time step t, respectively; a transition matrix is a coefficient matrix that controls the evolution of latent states between two successive time steps; an observability matrix which specifies how observations are generated from the present latent state. The initial density is also given as Gaussian distribution. In LDS, the noise terms are assumed to follow zero-mean Gaussian distributions.
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