Variable Markov Oracle

A variable Markov oracle is a type of computational model that is used in the field of computational biology and bioinformatics to predict and analyze sequences of nucleotides or amino acids.

The basic idea behind a variable Markov oracle is to build a probabilistic model that can predict the next symbol in a given sequence based on the previous symbols. The model is based on a statistical technique called a Markov chain, which assumes that the probability of the next symbol in a sequence depends only on the current symbol and a fixed number of previous symbols.

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However, in a variable Markov oracle, the number of previous symbols used to predict the next symbol is not fixed, but rather varies depending on the current state of the model. The model uses an algorithm to dynamically adjust the number of previous symbols used based on the accuracy of the predictions.

This ability to adjust the model in real-time allows the variable Markov oracle to make more accurate predictions than a fixed Markov chain model, which always uses the same number of previous symbols. The variable Markov oracle has been used in a variety of applications, including DNA sequence analysis, protein structure prediction, and natural language processing.

import numpy as np
from collections import defaultdict

class VariableMarkovOracle:
    def __init__(self, max_order=4):
        self.max_order = max_order
        self.model = defaultdict(lambda: defaultdict(float))
        self.order = 1
        
    def train(self, sequence):
        for i in range(len(sequence)):
            for j in range(1, self.max_order+1):
                if i >= j:
                    context = tuple(sequence[i-j:i])
                    symbol = sequence[i]
                    self.model[context][symbol] += 1.0
        self.order += 1
        
    def predict(self, sequence):
        predictions = []
        for i in range(len(sequence)):
            prediction = None
            for j in range(1, self.max_order+1):
                if i >= j:
                    context = tuple(sequence[i-j:i])
                    if context in self.model:
                        prediction = max(self.model[context], key=self.model[context].get)
                        break
            predictions.append(prediction)
        return predictions

model = VariableMarkovOracle(max_order=3)
sequence = "ACGTACGTA"
model.train(sequence)