Estimating information in time-varying signals
Fig 6
Information estimation for multilevel inputs.
(A) Extension of Example 2 from Fig 2B to q = 2, …, 5 discrete inputs. We chose the inputs such that the response for the system at T < 1000 converges towards q equally spaced levels with the same dynamic range as the original example; dynamics at T ≥ 1000 remain unchanged from the original Example 2. (B) Model-based information bounds as a function of the number of input levels for trajectories represented as d = 100 dimensional vectors: exact Monte Carlo calculation (dark gray), MAP decoding bound (black), upper bound (light gray). (C) Performance of model-free estimators, as indicated in the panel, compared to the MAP bound (black). Dashed lines show estimations using N = 103 sample trajectories per condition, solid lines using N = 104 samples per condition; in both cases, we show an average over 20 independent replicates, error bars are suppressed for readability.