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Package for training Generalized Mixture Transition Distribution (MTDg) models

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mtd-learn: Package for training Generalized Mixture Transition Distribution (MTDg) models

Installation

pip install mtdlearn

MTDg model

The Generalized Mixture Transition Distribution (MTDg) model was proposed in 1985 by Raftery[1]. It aimed to approximate higher order Markov Chains, but can be used as a standalone model.

Definition

mtd_def

Where lambdas are lag parameters and Qg = [qigi0(g)] is a m x m transition matrix representing relationship between g lag and the present state.

To parameters have to meet following constraints to produce probabilities:

mtd_constr

The model can be easier understood as weighted probabilities (by lambdas) of Qg matrices. The example below shows how to calculate a probability of transition B->C->A->B from an order 3 MTDg model:

mtd_img

Number of independent parameters

The number independent parameters of the MTDg model equals (ml - m + 1)(l - 1) and for Markov Chain ml(m-1). You can find a comparison of the number of parameters below.

States Order Markov Chain MTDg[1]
2 1 2 2
2 2 4 3
2 3 8 4
2 4 16 5
3 1 6 6
3 2 18 10
3 3 54 14
3 4 162 18
5 1 20 20
5 2 100 36
5 3 500 52
5 4 2500 68
10 1 90 90
10 2 900 171
10 3 9000 252
10 4 90000 333

Usage examples

from mtdlearn.mtd import MTD
from mtdlearn.preprocessing import PathEncoder
from mtdlearn.datasets import ChainGenerator

## Generate data

cg = ChainGenerator(('A', 'B', 'C'), 3, min_len=4, max_len=5)
x, y = cg.generate_data(1000)

## Encode paths

pe = PathEncoder(3)
pe.fit(x, y)
x_tr3, y_tr3 = pe.transform(x, y)

## Fitting model

model = MTD(order=3)
model.fit(x_tr3, y_tr3)

For more usage examples please refer to examples section.

Communication

GitHub Issues for bug reports, feature requests and questions.

Contribution

Any contribution is welcome! Please follow this branching model.

License

MIT License (see LICENSE).

References

  1. Introduction to MTDg model The Mixture Transition Distribution Model for High-Order Markov Chains and Non-Gaussian Time Series by André Berchtold and Adrian Raftery
  2. Paper with estimation algorithm implemented in the package An EM algorithm for estimation in the Mixture Transition Distribution model by Sophie Lèbre and Pierre-Yves Bourguinon.

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Package for training Generalized Mixture Transition Distribution (MTDg) models

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