Approximate Bayesian Computation Based on Maxima Weighted Isolation Kernel Mapping

TL;DR

This paper introduces a novel Approximate Bayesian Computation method utilizing Maxima Weighted Isolation Kernel Mapping to efficiently estimate parameters in complex, high-dimensional stochastic models like cancer evolution, demonstrating its effectiveness on real and simulated data.

Contribution

It presents a new ABC approach based on Isolation Kernel mapping and a heuristic, dimension-independent parameter estimation algorithm for complex stochastic models.

Findings

Effective parameter estimation on multidimensional data

Dimension-independent heuristic algorithm

Successful application to cancer cell evolution data

Abstract

Motivation: A branching processes model yields an unevenly stochastically distributed dataset that consists of sparse and dense regions. This work addresses the problem of precisely evaluating parameters for such a model. Applying a branching processes model to an area such as cancer cell evolution faces a number of obstacles, including high dimensionality and the rare appearance of a result of interest. We take on the ambitious task of obtaining the coefficients of a model that reflects the relationship of driver gene mutations and cancer hallmarks on the basis of personal data regarding variant allele frequencies. Results: An approximate Bayesian computation method based on Isolation Kernel is developed. The method involves the transformation of row data to a Hilbert space (mapping) and the measurement of the similarity between simulated points and maxima weighted Isolation Kernel mapping related to the observation point. We also design a heuristic algorithm for parameter estimation that requires no calculation and is dimension independent. The advantages of the proposed machine learning method are illustrated using multidimensional test data as well as a specific example focused on cancer cell evolution.