SLSSLM

SLSSLM stands for Sparse Latent State-Space Linear Model, a probabilistic framework used to analyze time-series data generated by a small number of latent processes. The model assumes a linear state-space structure in which the latent state x_t ∈ R^d evolves as x_{t+1} = A x_t + w_t, with w_t ~ N(0,Q), and observations y_t ∈ R^m are produced by y_t = C x_t + v_t, with v_t ~ N(0,R). Sparsity is imposed on latent loadings or on the activity of latent components to promote compact, interpretable dynamics, often via L1 penalties or structured sparsity priors.

Inference and learning in SLSSLM typically aim to estimate the system matrices A and C, along with noise covariances Q and R, and to determine which latent components are active at each time. Common approaches include Expectation-Maximization and variational inference, possibly with sparsity-aware regularization. Online variants exist to update parameters as new data arrive, using recursive filtering or online EM. Identifiability is addressed through constraints on the state-space parameters or by fixing scale and sign conventions of the latent states.

Applications of SLSSLM span domains requiring compact dynamic representations with interpretable factors. It has been applied to sensor fusion and robotics for robust state estimation, to finance for modeling interdependent latent drivers, and to neuroscience for uncovering latent temporal processes. Strengths include the balance between predictive performance and interpretability due to sparsity, while limitations include the assumption of linear dynamics and Gaussian noise, which may be extended in nonlinear or non-Gaussian variants.

See also Kalman filter, state-space model, sparse coding, latent variable models, EM algorithm.