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MathGroup Archive 2006

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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[2]:=
RandomSequence[nsamples_,min_,max_]:=Table[
     Random[Integer,{min,max}], {nsamples}
     ]

(* Alphabet of a sequence *)
In[3]:=
SignalAlphabet[signal_]:=Union[signal]

(* Gives the probability of a symbol *)
In[13]:=
SymbolProbability[symbol_,signal_]:=Count[signal,symbol]/Length[signal]

(* Gives the list of all symbols and their probabilities *)
In[20]:=
SignalProbabilityList[signal_]:=Map[
     {#,SymbolProbability[#,signal]}&,
     SignalAlphabet[signal]]

(* Calculates the entropy *)
In[24]:=
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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