       Joint Entropy

• To: mathgroup at smc.vnet.net
• Subject: [mg65575] Joint Entropy
• From: Sensei <senseiwa at mac.com>
• Date: Sun, 9 Apr 2006 04:32:02 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi! I'm writing some functions to analyze the informative content of
sequences, and I've stopped trying to produce the joint entropy.

These are my auxiliary functions:

(* Generates a sequence of random numbers *)
In:=
RandomSequence[nsamples_,min_,max_]:=Table[
Random[Integer,{min,max}], {nsamples}
]

(* Alphabet of a sequence *)
In:=
SignalAlphabet[signal_]:=Union[signal]

(* Gives the probability of a symbol *)
In:=
SymbolProbability[symbol_,signal_]:=Count[signal,symbol]/Length[signal]

(* Gives the list of all symbols and their probabilities *)
In:=
SignalProbabilityList[signal_]:=Map[
{#,SymbolProbability[#,signal]}&,
SignalAlphabet[signal]]

(* Calculates the entropy *)
In:=
SignalEntropy[signal_]:=-1*Fold[Plus, 0,
Map[Log[2,Last[#]]&,SignalProbability[signal]]]

Now, my question is, how to produce the joint probability of two
sequences ``mathematica style''? So, given X and Y, I can produce the
alphabet of XY, that is the cartesian product of the two alphabets
(using CartesianProduct), but... well, I don't know how to make a
good code! As I said previously, I'm new to mathematica... How should
I proceed?

Thanks for any hints!

PS. If the code above is not so good, please let me know! :)

--
Sensei <senseiwa at mac.com>

The optimist thinks this is the best of all possible worlds.
The pessimist fears it is true.      [J. Robert Oppenheimer]

```

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