vlmc · PyPI

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Variable-Length Markov Chains for Python

vlmc fits variable-length Markov chains to discrete sequences. It provides one Python model class with three context-tree selection methods:

Method	Purpose	Main control
`bct`	Exact Bayesian context-tree MAP estimator; the default	`beta`
`bic`	Penalized maximum-likelihood / MDL baseline	`penalty`
`peres_shield`	Peres–Shields maximal-fluctuation estimator	sample size

The implementation is written in Rust and exposed through Python bindings.

Installation

Published wheels can be installed with:

pip install vlmc

To build this checkout, install Rust and Maturin, activate a Python environment, and run:

pip install maturin
maturin develop --release

Quick start

import vlmc

rows = [
    [0, 1, 0, 1, 0, 1],
    [1, 0, 1, 0, 1, 0],
]

model = vlmc.VLMC(
    alphabet_size=2,
    max_depth=2,
    method="bct",       # default
)
model.fit(rows)

contexts = model.get_contexts()
context = model.get_suffix([1, 0, 1])

model.get_counts(context)            # observations following this context
model.get_transition_counts(context) # raw next-symbol counts
model.get_distribution(context)      # Jeffreys-smoothed probabilities
model.predict_proba([1, 0, 1])       # suffix lookup + probabilities

Symbols must be integers in 0 <= symbol < alphabet_size. Invalid symbols raise a ValueError instead of panicking.

Constructor

vlmc.VLMC(
    alphabet_size,
    max_depth=10,
    method="bct",
    beta=None,
    penalty=None,
    boundary="condition",
)

alphabet_size must be at least two.
max_depth is the largest candidate history length.
method is "bct", "bic", or "peres_shield".
beta is BCT-only and must satisfy 0.5 <= beta < 1, the range in which the algorithm identifies the exact MAP tree. When omitted it is 1 - 2 ** (-(alphabet_size - 1)), the value recommended by the BCT paper.
penalty is BIC-only and multiplies the standard BIC penalty. It defaults to 1.
boundary="condition" treats every row as an independent realization. For a depth D, its first D symbols form the conditioned initial history and only later symbols are fitted. Rows are never concatenated. A row of length at most D therefore contributes no fitted outcomes.

The fitted sample_size property reports the exact number of outcomes used by every node comparison. node_count and context_count report the retained model size. effective_max_depth equals max_depth for BCT/BIC and the data-dependent ln(ln(sample_size)) cap for Peres–Shields.

Selection methods

BCT (default)

BCT selects a maximum a posteriori context tree using a Dirichlet-1/2 (Jeffreys) prior for transition probabilities. It is the recommended general-purpose default.

BIC

BIC maximizes

log maximum likelihood - penalty * leaves * (alphabet_size - 1) / 2 * log(sample_size)

This is useful when a conventional penalized maximum-likelihood model is preferred.

Peres–Shields

For an extension v and suffix w, this method uses the paper's raw-count fluctuation

max_a |N(va) - N(wa) * N(v) / N(w)|

and the asymptotic threshold sample_size ** (3/4). Eligible extensions have absolute depth at most min(max_depth, floor(ln(ln(sample_size)))). Because this is an asymptotic criterion, it can be conservative for moderate samples.

Probability and context semantics

get_contexts() returns selected predictive contexts, ordered by length and then lexically. BCT and BIC return leaves of a proper context tree. Peres–Shields may also return an internal sparse fallback context together with deeper exceptional contexts, as allowed by its prediction suffix tree construction.

get_distribution(context) always returns probabilities, using Jeffreys smoothing:

P(a | context) = (N(context, a) + 1/2) /
                 (N(context) + alphabet_size / 2)

Use get_transition_counts(context) when raw next-symbol counts are required. get_counts(context) returns N(context), the number of usable outcomes following that context.

References

Kontoyiannis et al., Bayesian Context Trees: modelling and exact inference for discrete time series.
Csiszár and Talata, Context tree estimation for not necessarily finite memory processes, via BIC and MDL.
Dalevi and Dubhashi, The Peres–Shields Order Estimator for Fixed and Variable Length Markov Models.

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vlmc 0.3.0

Variable-Length Markov Chains for Python

Installation

Quick start

Constructor

Selection methods

BCT (default)

BIC

Peres–Shields

Probability and context semantics

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