# A new approach to learning in Dynamic Bayesian Networks (DBNs)

## TL;DR

This paper introduces a novel parameter estimation method for Dynamic Bayesian Networks that emphasizes model efficiency over distributional fit, using CMA-ES optimization, demonstrated on financial trend detection.

## Contribution

It proposes a new efficiency-focused parameter learning approach for DBNs, utilizing CMA-ES, which improves robustness against overfitting in financial applications.

## Key findings

- Parameters are less prone to overfitting than traditional methods.
- The approach outperforms moving average crossover in trend detection.
- Method is applicable to various real-world problems without physical laws.

## Abstract

In this paper, we revisit the parameter learning problem, namely the estimation of model parameters for Dynamic Bayesian Networks (DBNs). DBNs are directed graphical models of stochastic processes that encompasses and generalize Hidden Markov models (HMMs) and Linear Dynamical Systems (LDSs). Whenever we apply these models to economics and finance, we are forced to make some modeling assumptions about the state dynamics and the graph topology (the DBN structure). These assumptions may be incorrectly specified and contain some additional noise compared to reality. Trying to use a best fit approach through maximum likelihood estimation may miss this point and try to fit at any price these models on data. We present here a new methodology that takes a radical point of view and instead focus on the final efficiency of our model. Parameters are hence estimated in terms of their efficiency rather than their distributional fit to the data. The resulting optimization problem that consists in finding the optimal parameters is a hard problem. We rely on Covariance Matrix Adaptation Evolution Strategy (CMA-ES) method to tackle this issue. We apply this method to the seminal problem of trend detection in financial markets. We see on numerical results that the resulting parameters seem less error prone to over fitting than traditional moving average cross over trend detection and perform better. The method developed here for algorithmic trading is general. It can be applied to other real case applications whenever there is no physical law underlying our DBNs.