bayesian_online.py

import numpy as np
import pandas as pd
import json
import os
from config import logger, OUTPUT_DIR, Color

class NormalInverseWishartUpdater:
    """
    Maintains a Normal-Inverse-Wishart (NIW) prior over the expected returns and covariance.
    Allows for online, incremental updates of beliefs without full ML model retraining.
    """
    def __init__(self, tickers, initial_mu=None, initial_cov=None, kappa_0=10.0, nu_0=None):
        self.tickers = tickers
        self.d = len(tickers)
        self.kappa = float(kappa_0)
        self.nu = float(nu_0 if nu_0 is not None else self.d + 2)
        
        if initial_mu is not None:
            self.mu = initial_mu.copy()
        else:
            self.mu = np.zeros(self.d)
            
        if initial_cov is not None:
            # Scale matrix Lambda = nu * Sigma
            self.Lambda = initial_cov * self.nu
        else:
            self.Lambda = np.eye(self.d) * self.nu
            
        self.state_path = os.path.join(OUTPUT_DIR, "niw_prior_state.json")
        
    def save_state(self):
        state = {
            'tickers': self.tickers,
            'kappa': self.kappa,
            'nu': self.nu,
            'mu': self.mu.tolist(),
            'Lambda': self.Lambda.tolist()
        }
        with open(self.state_path, 'w') as f:
            json.dump(state, f)
            
    def load_state(self):
        if os.path.exists(self.state_path):
            try:
                with open(self.state_path, 'r') as f:
                    state = json.load(f)
                if state['tickers'] == self.tickers:
                    self.kappa = state['kappa']
                    self.nu = state['nu']
                    self.mu = np.array(state['mu'])
                    self.Lambda = np.array(state['Lambda'])
                    return True
            except Exception as e:
                logger.warning(f"Failed to load NIW state: {e}")
        return False
        
    def update(self, x_new):
        """
        Updates the NIW parameters given a new observation x_new (1D array of returns).
        """
        x = np.asarray(x_new)
        if x.shape[0] != self.d:
            raise ValueError("Observation dimension mismatch.")
            
        # Update formulas for single observation (n=1)
        kappa_n = self.kappa + 1.0
        nu_n = self.nu + 1.0
        
        diff = x - self.mu
        mu_n = (self.kappa * self.mu + x) / kappa_n
        
        # Rank-1 update to the scale matrix
        Lambda_n = self.Lambda + (self.kappa / kappa_n) * np.outer(diff, diff)
        
        # To prevent kappa and nu from growing infinitely (which would freeze the prior),
        # we can apply a slight exponential decay to the weights (rolling window effect).
        # We cap kappa and nu at a rolling window equivalent of 252 days.
        max_memory = 252.0
        if kappa_n > max_memory:
            decay = max_memory / kappa_n
            kappa_n *= decay
            nu_n *= decay
            Lambda_n *= decay
            
        self.kappa = kappa_n
        self.nu = nu_n
        self.mu = mu_n
        self.Lambda = Lambda_n
        
    def get_posterior(self):
        """Returns posterior expected returns and covariance matrix."""
        # The expected value of the covariance matrix under Inverse-Wishart is Lambda / (nu - d - 1)
        # Using a safer denominator max(1, nu - d - 1)
        denom = max(1.0, self.nu - self.d - 1)
        cov_posterior = self.Lambda / denom
        return self.mu, cov_posterior
        
    def compute_divergence(self, new_mu, new_cov):
        """
        Computes the Mahalanobis distance between the new ML predictions and the NIW prior.
        """
        try:
            cov_inv = np.linalg.inv(new_cov)
        except np.linalg.LinAlgError:
            cov_inv = np.linalg.pinv(new_cov)
            
        diff = new_mu - self.mu
        # Simple Mahalanobis distance
        dist = np.sqrt(np.dot(diff.T, np.dot(cov_inv, diff)))
        return float(dist)