Figure 2.

Calculation of causal similarity using data smashing. (a) We quantize raw signals to symbolic sequences over the chosen alphabet and compute a causal similarity between such sequences. The underlying theory is established assuming the existence of generative probabilistic automata for these sequences, but our algorithms do not require explicit model construction, or a priori knowledge of their structures. (b) Concept of stream inversion; while we can find the group inverse of a given PFSA algebraically, we can also transform a generated sequence directly to one that represents the inverse model, without constructing the model itself. (c) Summing PFSAs G and its inverse −G yields the zero PFSA W. We can carry out this smashing purely at the sequence level to get FWN. (d) Circuit that allows us to measure similarity distance between streams s₁, s₂ via computation of , and (see table 1). Given a threshold , if , then we have sufficient data for stream s_k (k = 1,2). Additionally, if , then we conclude that s₁, s₂ have the same stochastic source with high probability (which converges exponentially fast to 1 with length of input). (Online version in colour.)