# Approximate Bayesian Computation Based on Maxima Weighted Isolation Kernel Mapping

arXiv: https://arxiv.org/abs/2201.12745 · HTML: https://mlsanity.com/paper/2201.12745/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 47 references that are in the map.
- First posted on arXiv 30 Jan 2022.

## Builds on (most cited first, 5 of 5)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Sequential Kernel Herding: Frank-Wolfe Optimization for Particle Filtering](https://mlsanity.com/paper/1501.02056/) (2015)
- [Kernel Recursive ABC: Point Estimation with Intractable Likelihood](https://mlsanity.com/paper/1802.08404/) (2018)
- [Feature space approximation for kernel-based supervised learning](https://mlsanity.com/paper/2011.12651/) (2020)
- [Breaking the curse of dimensionality with Isolation Kernel](https://mlsanity.com/paper/2109.14198/) (2021)

## Abstract (arXiv)

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.