markov query

[kpp9c]

markov query

I have noticed a couple markov implementations in python, but none
quite seem to do what i would like. Most seem to do an analysis of some
text and create a new text based on that... I think, (sorry i just
don't know terminology well) a markov table (or is it called a
transition table) to describe how to get from one event to another. So
if i have 3 events, say, A, B, and C which can come in any order, a
Markov chain describes the probability of what the next event will be
using a table. The following table demonstrates a first-order Markov
chain. There are three possible states. Either the current event is A,
B, or C. For each possible current state, there are three possible next
letters. Each row in the table indicates the relative probability of
going to the next letter. For example, if you are currently on letter
A, there is a 20% chance of repeating letter A, a 50% chance of going
to B, and a 30% chance of going to C. Note that the sum of changes for
each row is 100% (20 + 50 + 30 = 100).

Current -- next -- next -- next
A ----- B ----- C
A: 20% -- 50% -- 30%
B: 35% -- 25% -- 40%
C: 70% -- 14% -- 16%

Here the sequence C B and C C would be rare and the sequence C A
common.

This is a first-order Markov chain, which means that only the current
state affects the choice of the next event. A second-order Markov chain
would mean that the current state and the last state affect the choice
of the next event. A third-order Markov chain would indicate that the
current state and the last two states in the sequence will affect the
choice of the next state, and so on. Here is an example transition
table for a 2nd order Markov chain.

Current -- next -- next -- next
A ----- B ----- C
A A 15% 55% 30%
A B 20% 45% 35%
A C 60% 30% 10%
B A 35% 25% 40%
B B 49% 48% 3%
B C 60% 20% 20%
C A 5% 75% 20%
C B 0% 90% 10%
C C 70% 14% 16%

For example, if the current event is B and the last one was A, then the
probability of the next event being A is 20%, B is 45% and C is 35%.
The pattern C B A will never occur, and the pattern B B C will occur
rarely.

Does anyone know of any modules or packages that include markov tables
for creating patterns like shown above.


P.S. Does any one know first of all whether these are called markov
tables, transition tables or probability tables? I am not sure i am
referring to this correctly and what the differences would be if any

cheers,

kp

 

[Stefan Behnel]

Don't know of a Python module (although this doesn't look complex enough for a
package anyway...), but

P.S. Does any one know first of all whether these are called markov
tables, transition tables or probability tables? I am not sure i am
referring to this correctly and what the differences would be if any

as for terminology:

http://www.csse.monash.edu.au/~lloyd/tildeMML/Structured/HMM.html
http://en.wikipedia.org/wiki/Hidden_Markov_model


Hope it helps,
Stefan

 

[Erik Max Francis]

I have noticed a couple markov implementations in python, but none
quite seem to do what i would like. Most seem to do an analysis of some
text and create a new text based on that... I think, (sorry i just
don't know terminology well) a markov table (or is it called a
transition table) to describe how to get from one event to another.

Yes, a system which does this has to build a Markov chain from a data
set and then traverse it.

Does anyone know of any modules or packages that include markov tables
for creating patterns like shown above.

Any program that actually uses Markov chains to generate new text based
on existing input as you've described will necessarily create a Markov
chain. So if what you want is the Markov chain itself, then it's
already in there somewhere.

P.S. Does any one know first of all whether these are called markov
tables, transition tables or probability tables? I am not sure i am
referring to this correctly and what the differences would be if any

They're called Markov chains.

 

[kpp9c]

Yes, a system which does this has to build a Markov chain from a data

set and then traverse it.

Any program that actually uses Markov chains to generate new text based
on existing input as you've described will necessarily create a Markov
chain.

I think you misunderstood. If you see my original post my whole point
was that this was exactly what i don't want. There are several
algorithms out that that already do that. I want to use a table that i
define from scratch to shape a stochastic process. In this case there
is no original input to analyze and i don't want a chain built by
analysis and i am not using necessarily texts.

 

[kpp9c]

Yes, a system which does this has to build a Markov

chain from a data set and then traverse it.

Hi. That isn't really what i have described. If i did i could use
exsisting algorithms. What you describe is exactly what i don't want in
this particular case. I am actually not wanting it to build a chain
from some input that it analyzes. There is no input. If you see, i am
trying to define a table that tells it how to proceed forward from
scratch as a stochastic process.

cheers,

-kp--

 

[Robert Kern]

Hi. That isn't really what i have described. If i did i could use
exsisting algorithms. What you describe is exactly what i don't want in
this particular case. I am actually not wanting it to build a chain
from some input that it analyzes. There is no input. If you see, i am
trying to define a table that tells it how to proceed forward from
scratch as a stochastic process.

Any such program has two main parts, one that trains the transition matrix from
a data set, and one that generates output from that transition matrix. You
should be able to take such a program and only use the latter component with
your transition matrix, however you choose to create it. Googling for 'python
markov' generates several leads.

--
Robert Kern
(e-mail address removed)

"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
-- Umberto Eco