Getting pdfa #34

roiDaniela · 2022-07-06T15:34:08Z

roiDaniela
Jul 6, 2022

Hello,

I'm trying to get this prefix tree and learn it with alergia algorithm

I tried to build it using mdp but can not find how to set the states as accepting states
thanks

 `len_input = 4
states = []
for i in range(13):
    states.append(MdpState(f'q{i}'))

# 0
states[0].transitions['a'].append((states[1], 0.25))
states[0].transitions['a'].append((states[0], 0.75))

states[0].transitions['b'].append((states[4], 0.25))
states[0].transitions['b'].append((states[0], 0.75))

states[0].transitions['c'].append((states[7], 0.25))
states[0].transitions['c'].append((states[0], 0.75))

states[0].transitions['d'].append((states[10], 0.25))
states[0].transitions['d'].append((states[0], 0.75))

# 1
states[1].transitions['a'].append((states[2], 0.25))
states[1].transitions['a'].append((states[1], 0.75))

states[1].transitions['b'].append((states[1], 0.2))
states[1].transitions['b'].append((states[1], 0.8))

states[1].transitions['c'].append((states[1], 0.2))
states[1].transitions['c'].append((states[1], 0.8))

states[1].transitions['d'].append((states[1], 0.2))
states[1].transitions['d'].append((states[1], 0.8))

# 2
states[2].transitions['a'].append((states[3], 0.25))
states[2].transitions['a'].append((states[2], 0.75))

states[2].transitions['b'].append((states[2], 0.2))
states[2].transitions['b'].append((states[2], 0.8))

states[2].transitions['c'].append((states[2], 0.2))
states[2].transitions['c'].append((states[2], 0.8))

states[2].transitions['d'].append((states[2], 0.2))
states[2].transitions['d'].append((states[2], 0.8))

# 3
states[3].transitions['a'].append((states[3], 0.25))
states[3].transitions['a'].append((states[3], 0.75))

states[3].transitions['b'].append((states[3], 0.2))
states[3].transitions['b'].append((states[3], 0.8))

states[3].transitions['c'].append((states[3], 0.2))
states[3].transitions['c'].append((states[3], 0.8))

states[3].transitions['d'].append((states[3], 0.2))
states[3].transitions['d'].append((states[3], 0.8))

# 4
states[4].transitions['a'].append((states[4], 0.2))
states[4].transitions['a'].append((states[4], 0.8))

states[4].transitions['b'].append((states[5], 0.25))
states[4].transitions['b'].append((states[4], 0.75))

states[4].transitions['c'].append((states[4], 0.2))
states[4].transitions['c'].append((states[4], 0.8))

states[4].transitions['d'].append((states[4], 0.2))
states[4].transitions['d'].append((states[4], 0.8))

# 5
states[5].transitions['a'].append((states[5], 0.2))
states[5].transitions['a'].append((states[5], 0.8))

states[5].transitions['b'].append((states[6], 0.25))
states[5].transitions['b'].append((states[5], 0.75))

states[5].transitions['c'].append((states[5], 0.2))
states[5].transitions['c'].append((states[5], 0.8))

states[5].transitions['d'].append((states[5], 0.2))
states[5].transitions['d'].append((states[5], 0.8))

# 6
states[6].transitions['a'].append((states[6], 0.2))
states[6].transitions['a'].append((states[6], 0.8))

states[6].transitions['b'].append((states[6], 0.25))
states[6].transitions['b'].append((states[6], 0.75))

states[6].transitions['c'].append((states[6], 0.2))
states[6].transitions['c'].append((states[6], 0.8))

states[6].transitions['d'].append((states[6], 0.2))
states[6].transitions['d'].append((states[6], 0.8))

# 7
states[7].transitions['a'].append((states[7], 0.2))
states[7].transitions['a'].append((states[7], 0.8))

states[7].transitions['b'].append((states[8], 0.25))
states[7].transitions['b'].append((states[7], 0.75))

states[7].transitions['c'].append((states[7], 0.2))
states[7].transitions['c'].append((states[7], 0.8))

states[7].transitions['d'].append((states[7], 0.2))
states[7].transitions['d'].append((states[7], 0.8))

# 8
states[8].transitions['a'].append((states[8], 0.2))
states[8].transitions['a'].append((states[8], 0.8))

states[8].transitions['b'].append((states[9], 0.25))
states[8].transitions['b'].append((states[8], 0.75))

states[8].transitions['c'].append((states[8], 0.2))
states[8].transitions['c'].append((states[8], 0.8))

states[8].transitions['d'].append((states[8], 0.2))
states[8].transitions['d'].append((states[8], 0.8))

# 9
states[9].transitions['a'].append((states[9], 0.2))
states[9].transitions['a'].append((states[9], 0.8))

states[9].transitions['b'].append((states[9], 0.25))
states[9].transitions['b'].append((states[9], 0.75))

states[9].transitions['c'].append((states[9], 0.2))
states[9].transitions['c'].append((states[9], 0.8))

states[9].transitions['d'].append((states[9], 0.2))
states[9].transitions['d'].append((states[9], 0.8))

# 10
states[10].transitions['a'].append((states[10], 0.2))
states[10].transitions['a'].append((states[10], 0.8))

states[10].transitions['b'].append((states[11], 0.25))
states[10].transitions['b'].append((states[10], 0.75))

states[10].transitions['c'].append((states[10], 0.2))
states[10].transitions['c'].append((states[10], 0.8))

states[10].transitions['d'].append((states[10], 0.2))
states[10].transitions['d'].append((states[10], 0.8))

# 11
states[11].transitions['a'].append((states[11], 0.2))
states[11].transitions['a'].append((states[11], 0.8))

states[11].transitions['b'].append((states[11], 0.2))
states[11].transitions['b'].append((states[11], 0.8))

states[11].transitions['c'].append((states[12], 0.25))
states[11].transitions['c'].append((states[11], 0.75))

states[11].transitions['d'].append((states[11], 0.2))
states[11].transitions['d'].append((states[11], 0.8))

# 12
states[12].transitions['a'].append((states[12], 0.2))
states[12].transitions['a'].append((states[12], 0.8))

states[12].transitions['b'].append((states[12], 0.2))
states[12].transitions['b'].append((states[12], 0.8))

states[12].transitions['c'].append((states[12], 0.25))
states[12].transitions['c'].append((states[12], 0.75))

states[12].transitions['d'].append((states[12], 0.2))
states[12].transitions['d'].append((states[12], 0.8))

return Mdp(states[0], states), list(range(len_input))`

Answered by emuskardin

Jul 6, 2022

I would guess that the learned automaton is what is whitin ALERGIA's capabilites when it comes to learning of non-deterministic MDPs. So you get a deterministic approximation of non-det MDP.

What I mean by non-deterministic:

    states[0].transitions['a'].append((states[1], 0.25))
    states[0].transitions['a'].append((states[0], 0.75))

From the same state, same input a leads to a same output False. Even tho it is a different state, ALERGIA cannot differentiate it based on the output

View full answer

emuskardin · 2022-07-06T15:41:55Z

emuskardin
Jul 6, 2022
Maintainer

Hi,

What I would do, is set the output to True for accepting and False for rejecting states.

MdpState(f'q{i}', output=True)
or
states[12].output = True

Let me know if that serves the purpose :)

3 replies

roiDaniela Jul 6, 2022
Author

Thanks @emuskardin

I got this for the original

and for the learned automaton

is this ok?
the learned automaton is actually different

thanks
code is going like this:

    states = []
    for i in range(13):
        # curr_output = state_outputs.pop(0) if state_outputs else random.choice(outputs)
        if i == 3 or i == 6 or i == 9 or i == 12:
            states.append(MdpState(f'q{i}', output=True))
        else:
            states.append(MdpState(f'q{i}', output=False))

    # 0
    states[0].transitions['a'].append((states[1], 0.25))
    states[0].transitions['a'].append((states[0], 0.75))

    states[0].transitions['b'].append((states[4], 0.25))
    states[0].transitions['b'].append((states[0], 0.75))

    states[0].transitions['c'].append((states[7], 0.25))
    states[0].transitions['c'].append((states[0], 0.75))

    states[0].transitions['d'].append((states[10], 0.25))
    states[0].transitions['d'].append((states[0], 0.75))

    # 1
    states[1].transitions['a'].append((states[2], 0.25))
    states[1].transitions['a'].append((states[1], 0.75))

    states[1].transitions['b'].append((states[1], 0.2))
    states[1].transitions['b'].append((states[1], 0.8))

    states[1].transitions['c'].append((states[1], 0.2))
    states[1].transitions['c'].append((states[1], 0.8))

    states[1].transitions['d'].append((states[1], 0.2))
    states[1].transitions['d'].append((states[1], 0.8))

    # 2
    states[2].transitions['a'].append((states[3], 0.25))
    states[2].transitions['a'].append((states[2], 0.75))

    states[2].transitions['b'].append((states[2], 0.2))
    states[2].transitions['b'].append((states[2], 0.8))

    states[2].transitions['c'].append((states[2], 0.2))
    states[2].transitions['c'].append((states[2], 0.8))

    states[2].transitions['d'].append((states[2], 0.2))
    states[2].transitions['d'].append((states[2], 0.8))

    # 3
    states[3].transitions['a'].append((states[3], 0.25))
    states[3].transitions['a'].append((states[3], 0.75))

    states[3].transitions['b'].append((states[3], 0.2))
    states[3].transitions['b'].append((states[3], 0.8))

    states[3].transitions['c'].append((states[3], 0.2))
    states[3].transitions['c'].append((states[3], 0.8))

    states[3].transitions['d'].append((states[3], 0.2))
    states[3].transitions['d'].append((states[3], 0.8))

    # 4
    states[4].transitions['a'].append((states[4], 0.2))
    states[4].transitions['a'].append((states[4], 0.8))

    states[4].transitions['b'].append((states[5], 0.25))
    states[4].transitions['b'].append((states[4], 0.75))

    states[4].transitions['c'].append((states[4], 0.2))
    states[4].transitions['c'].append((states[4], 0.8))

    states[4].transitions['d'].append((states[4], 0.2))
    states[4].transitions['d'].append((states[4], 0.8))

    # 5
    states[5].transitions['a'].append((states[5], 0.2))
    states[5].transitions['a'].append((states[5], 0.8))

    states[5].transitions['b'].append((states[6], 0.25))
    states[5].transitions['b'].append((states[5], 0.75))

    states[5].transitions['c'].append((states[5], 0.2))
    states[5].transitions['c'].append((states[5], 0.8))

    states[5].transitions['d'].append((states[5], 0.2))
    states[5].transitions['d'].append((states[5], 0.8))

    # 6
    states[6].transitions['a'].append((states[6], 0.2))
    states[6].transitions['a'].append((states[6], 0.8))

    states[6].transitions['b'].append((states[6], 0.25))
    states[6].transitions['b'].append((states[6], 0.75))

    states[6].transitions['c'].append((states[6], 0.2))
    states[6].transitions['c'].append((states[6], 0.8))

    states[6].transitions['d'].append((states[6], 0.2))
    states[6].transitions['d'].append((states[6], 0.8))

    # 7
    states[7].transitions['a'].append((states[7], 0.2))
    states[7].transitions['a'].append((states[7], 0.8))

    states[7].transitions['b'].append((states[8], 0.25))
    states[7].transitions['b'].append((states[7], 0.75))

    states[7].transitions['c'].append((states[7], 0.2))
    states[7].transitions['c'].append((states[7], 0.8))

    states[7].transitions['d'].append((states[7], 0.2))
    states[7].transitions['d'].append((states[7], 0.8))

    # 8
    states[8].transitions['a'].append((states[8], 0.2))
    states[8].transitions['a'].append((states[8], 0.8))

    states[8].transitions['b'].append((states[9], 0.25))
    states[8].transitions['b'].append((states[8], 0.75))

    states[8].transitions['c'].append((states[8], 0.2))
    states[8].transitions['c'].append((states[8], 0.8))

    states[8].transitions['d'].append((states[8], 0.2))
    states[8].transitions['d'].append((states[8], 0.8))

    # 9
    states[9].transitions['a'].append((states[9], 0.2))
    states[9].transitions['a'].append((states[9], 0.8))

    states[9].transitions['b'].append((states[9], 0.25))
    states[9].transitions['b'].append((states[9], 0.75))

    states[9].transitions['c'].append((states[9], 0.2))
    states[9].transitions['c'].append((states[9], 0.8))

    states[9].transitions['d'].append((states[9], 0.2))
    states[9].transitions['d'].append((states[9], 0.8))

    # 10
    states[10].transitions['a'].append((states[10], 0.2))
    states[10].transitions['a'].append((states[10], 0.8))

    states[10].transitions['b'].append((states[11], 0.25))
    states[10].transitions['b'].append((states[10], 0.75))

    states[10].transitions['c'].append((states[10], 0.2))
    states[10].transitions['c'].append((states[10], 0.8))

    states[10].transitions['d'].append((states[10], 0.2))
    states[10].transitions['d'].append((states[10], 0.8))

    # 11
    states[11].transitions['a'].append((states[11], 0.2))
    states[11].transitions['a'].append((states[11], 0.8))

    states[11].transitions['b'].append((states[11], 0.2))
    states[11].transitions['b'].append((states[11], 0.8))

    states[11].transitions['c'].append((states[12], 0.25))
    states[11].transitions['c'].append((states[11], 0.75))

    states[11].transitions['d'].append((states[11], 0.2))
    states[11].transitions['d'].append((states[11], 0.8))

    # 12
    states[12].transitions['a'].append((states[12], 0.2))
    states[12].transitions['a'].append((states[12], 0.8))

    states[12].transitions['b'].append((states[12], 0.2))
    states[12].transitions['b'].append((states[12], 0.8))

    states[12].transitions['c'].append((states[12], 0.25))
    states[12].transitions['c'].append((states[12], 0.75))

    states[12].transitions['d'].append((states[12], 0.2))
    states[12].transitions['d'].append((states[12], 0.8))

    return Mdp(states[0], states)#, list(range(len_input))

emuskardin Jul 6, 2022
Maintainer

Learned automaton will for sure be different, as the automaton you create can be minimized.

Can you post the data generation and call to Alergia as well, then I can also run it

roiDaniela Jul 6, 2022
Author

In file Examples.py I replaced
in the function

def alergia_mdp_example():

mdp = generate_random_mdp(5, 2, 5)
with
mdp = my_generate_random_mdp()

which is

def my_generate_random_mdp():
    states = []
    for i in range(13):
        # curr_output = state_outputs.pop(0) if state_outputs else random.choice(outputs)
        if i == 3 or i == 6 or i == 9 or i == 12:
            states.append(MdpState(f'q{i}', output=True))
        else:
            states.append(MdpState(f'q{i}', output=False))

    # 0
    states[0].transitions['a'].append((states[1], 0.25))
    states[0].transitions['a'].append((states[0], 0.75))

    states[0].transitions['b'].append((states[4], 0.25))
    states[0].transitions['b'].append((states[0], 0.75))

    states[0].transitions['c'].append((states[7], 0.25))
    states[0].transitions['c'].append((states[0], 0.75))

    states[0].transitions['d'].append((states[10], 0.25))
    states[0].transitions['d'].append((states[0], 0.75))

    # 1
    states[1].transitions['a'].append((states[2], 0.25))
    states[1].transitions['a'].append((states[1], 0.75))

    states[1].transitions['b'].append((states[1], 0.2))
    states[1].transitions['b'].append((states[1], 0.8))

    states[1].transitions['c'].append((states[1], 0.2))
    states[1].transitions['c'].append((states[1], 0.8))

    states[1].transitions['d'].append((states[1], 0.2))
    states[1].transitions['d'].append((states[1], 0.8))

    # 2
    states[2].transitions['a'].append((states[3], 0.25))
    states[2].transitions['a'].append((states[2], 0.75))

    states[2].transitions['b'].append((states[2], 0.2))
    states[2].transitions['b'].append((states[2], 0.8))

    states[2].transitions['c'].append((states[2], 0.2))
    states[2].transitions['c'].append((states[2], 0.8))

    states[2].transitions['d'].append((states[2], 0.2))
    states[2].transitions['d'].append((states[2], 0.8))

    # 3
    states[3].transitions['a'].append((states[3], 0.25))
    states[3].transitions['a'].append((states[3], 0.75))

    states[3].transitions['b'].append((states[3], 0.2))
    states[3].transitions['b'].append((states[3], 0.8))

    states[3].transitions['c'].append((states[3], 0.2))
    states[3].transitions['c'].append((states[3], 0.8))

    states[3].transitions['d'].append((states[3], 0.2))
    states[3].transitions['d'].append((states[3], 0.8))

    # 4
    states[4].transitions['a'].append((states[4], 0.2))
    states[4].transitions['a'].append((states[4], 0.8))

    states[4].transitions['b'].append((states[5], 0.25))
    states[4].transitions['b'].append((states[4], 0.75))

    states[4].transitions['c'].append((states[4], 0.2))
    states[4].transitions['c'].append((states[4], 0.8))

    states[4].transitions['d'].append((states[4], 0.2))
    states[4].transitions['d'].append((states[4], 0.8))

    # 5
    states[5].transitions['a'].append((states[5], 0.2))
    states[5].transitions['a'].append((states[5], 0.8))

    states[5].transitions['b'].append((states[6], 0.25))
    states[5].transitions['b'].append((states[5], 0.75))

    states[5].transitions['c'].append((states[5], 0.2))
    states[5].transitions['c'].append((states[5], 0.8))

    states[5].transitions['d'].append((states[5], 0.2))
    states[5].transitions['d'].append((states[5], 0.8))

    # 6
    states[6].transitions['a'].append((states[6], 0.2))
    states[6].transitions['a'].append((states[6], 0.8))

    states[6].transitions['b'].append((states[6], 0.25))
    states[6].transitions['b'].append((states[6], 0.75))

    states[6].transitions['c'].append((states[6], 0.2))
    states[6].transitions['c'].append((states[6], 0.8))

    states[6].transitions['d'].append((states[6], 0.2))
    states[6].transitions['d'].append((states[6], 0.8))

    # 7
    states[7].transitions['a'].append((states[7], 0.2))
    states[7].transitions['a'].append((states[7], 0.8))

    states[7].transitions['b'].append((states[8], 0.25))
    states[7].transitions['b'].append((states[7], 0.75))

    states[7].transitions['c'].append((states[7], 0.2))
    states[7].transitions['c'].append((states[7], 0.8))

    states[7].transitions['d'].append((states[7], 0.2))
    states[7].transitions['d'].append((states[7], 0.8))

    # 8
    states[8].transitions['a'].append((states[8], 0.2))
    states[8].transitions['a'].append((states[8], 0.8))

    states[8].transitions['b'].append((states[9], 0.25))
    states[8].transitions['b'].append((states[8], 0.75))

    states[8].transitions['c'].append((states[8], 0.2))
    states[8].transitions['c'].append((states[8], 0.8))

    states[8].transitions['d'].append((states[8], 0.2))
    states[8].transitions['d'].append((states[8], 0.8))

    # 9
    states[9].transitions['a'].append((states[9], 0.2))
    states[9].transitions['a'].append((states[9], 0.8))

    states[9].transitions['b'].append((states[9], 0.25))
    states[9].transitions['b'].append((states[9], 0.75))

    states[9].transitions['c'].append((states[9], 0.2))
    states[9].transitions['c'].append((states[9], 0.8))

    states[9].transitions['d'].append((states[9], 0.2))
    states[9].transitions['d'].append((states[9], 0.8))

    # 10
    states[10].transitions['a'].append((states[10], 0.2))
    states[10].transitions['a'].append((states[10], 0.8))

    states[10].transitions['b'].append((states[11], 0.25))
    states[10].transitions['b'].append((states[10], 0.75))

    states[10].transitions['c'].append((states[10], 0.2))
    states[10].transitions['c'].append((states[10], 0.8))

    states[10].transitions['d'].append((states[10], 0.2))
    states[10].transitions['d'].append((states[10], 0.8))

    # 11
    states[11].transitions['a'].append((states[11], 0.2))
    states[11].transitions['a'].append((states[11], 0.8))

    states[11].transitions['b'].append((states[11], 0.2))
    states[11].transitions['b'].append((states[11], 0.8))

    states[11].transitions['c'].append((states[12], 0.25))
    states[11].transitions['c'].append((states[11], 0.75))

    states[11].transitions['d'].append((states[11], 0.2))
    states[11].transitions['d'].append((states[11], 0.8))

    # 12
    states[12].transitions['a'].append((states[12], 0.2))
    states[12].transitions['a'].append((states[12], 0.8))

    states[12].transitions['b'].append((states[12], 0.2))
    states[12].transitions['b'].append((states[12], 0.8))

    states[12].transitions['c'].append((states[12], 0.25))
    states[12].transitions['c'].append((states[12], 0.75))

    states[12].transitions['d'].append((states[12], 0.2))
    states[12].transitions['d'].append((states[12], 0.8))

    return Mdp(states[0], states)#, list(range(len_input))

emuskardin · 2022-07-06T17:02:37Z

emuskardin
Jul 6, 2022
Maintainer

I would guess that the learned automaton is what is whitin ALERGIA's capabilites when it comes to learning of non-deterministic MDPs. So you get a deterministic approximation of non-det MDP.

What I mean by non-deterministic:

    states[0].transitions['a'].append((states[1], 0.25))
    states[0].transitions['a'].append((states[0], 0.75))

From the same state, same input a leads to a same output False. Even tho it is a different state, ALERGIA cannot differentiate it based on the output

0 replies

emuskardin · 2022-07-06T17:04:21Z

emuskardin
Jul 6, 2022
Maintainer

We wrote about that in the preliminaries of the https://arxiv.org/pdf/2206.11708.pdf

4 replies

roiDaniela Jul 6, 2022
Author

Thanks, I thought it is the only way I can create probability prefix tree in the structure

Is there is a way to create determenistic mdp using AALPY?

emuskardin Jul 6, 2022
Maintainer

You have successfully created the structure on the image, but that one is by default non-deterministic.

To best of my knowledge, there is no algorithm that can learn non-deterministic MDPs. ALERGIA can approximate it, and that is the 2 state model that you get when you run the alg.

roiDaniela Jul 6, 2022
Author

Thanks @emuskardin

roiDaniela Jul 6, 2022
Author

@emuskardin just tp make things clear, Alergia can not learn a detemenistic automaton with probability? (meaning that action 'a' has 0.5 prob and action 'b' has 0.5 prob ...)

emuskardin · 2022-07-06T18:21:35Z

emuskardin
Jul 6, 2022
Maintainer

Alergia learns a deterministic MDPs correctly in a limit, but what you have here is a non-deterministic MDP where action a has 25% probability of going to a state with a label False and 75% chance to go to another state with the same label, creating the non-determinism.

If you have a deterministic MDP, meaning that each all transitions from a state-input pair lead to states with a different output, ALERGIA will learn the correct MDP in a limit. If multiple state-input transitions lead to different states with the same output, like what you have, it will create a deterministic approximation.

5 replies

roiDaniela Jul 7, 2022
Author

Thanks @emuskardin, The motivation for what I'm looking for is to reconstruct the automaton that was claimed fails to learn with alergia in the article - https://www.aaai.org/Papers/Symposia/Spring/1996/SS-96-05/SS96-05-006.pdf.
Do you know this article? I'm not sure the example I'm trying is good counterexample.

emuskardin Jul 7, 2022
Maintainer

I am doing last preparations before holiday, so I cannot dedicate the time to read the full paper now.
Some things to note:

In the paper they say that this is a DFA, not a probabilistic DFA. If you want to learn a DFA, then use a RPNI algorithm. It is not just "deterministic ALERGIA", the way it works is slightly different.
ALERGIA is not the best in itself with sequential data where you have to "count", like what you have here... If you need 2 a inputs to get to True with a third a input , there is a high chance that ALERGIA will simply have 2 states, where the probability of going to True output is 33%

roiDaniela Jul 7, 2022
Author

thanks, according to (1), the paper is scecificly regarding Alergia and not rpni (they assume probability)

emuskardin Jul 7, 2022
Maintainer

Ok, I was just being specific for that example as they say DFA.
Recent algorithm that performs seems to be mroe precise than ALERGIA can be found here, though I cannot say any more about it since I have never implemented/used it.

roiDaniela Jul 20, 2022
Author

ALERGIA is not the best in itself with sequential data where you have to "count", like what you have here... If you need 2 a inputs to get to True with a third a input , there is a high chance that ALERGIA will simply have 2 states, where the probability of going to True output is 33%

Why "a" is not a distinguish sequence between "a" and "a-a"? Althogh they have same probability but compatible test also check the output and the output of "aa" and "aaa" is different?
Thanks

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