Bayesian Optimization for

Demographic History

 Inference

Ekaterina Noskova

Supervisor: Vladimir Ulyantsev

04 April 2022

Demographic History

Demographic History

Demographic history is the history of evolution and development of populations. It includes such parameters as size of population, time of splits and migration rates.

Demographic Inference

Demographic Inference

Demographic Inference

 Pipeline

GADMA — Genetic Algorithm for Demographic Model Analysis

  • Several simulation engines ($\partial a \partial i$, moments)
  • Has common interface
  • Effective optimization based on the genetic algorithm
  • Handles up to 3 populations

Bayesian Optimization

Bayesian Optimization

Goal: minimize unknown function $f$ in as few evaluations as possible.

  • Black-box optimization
  • Expensive evaluations

On each iteration:

  • Approximate objective function $f$ with a surrogate model $M$
  • Choose next point as $argmax$ of the acquisition function $\alpha_M$ $$ \htmlClass{fragment}{ x_{n+1} = \argmax_{x\in\c{X}} \alpha_M(x) } $$

Bayesian Optimization

Bayesian Optimization

Bayesian Optimization

Bayesian Optimization

Acquisition Functions

  • Expected Improvement:

    $EI = \mathbb{E}[max\{0, f_{min} - f(x)\}] $

  • Probability of Improvement:

    $PI = P(f(x) \leq f_{min})$

  • Lower Confidence Bound:

    $LCB = \mu(x) - \kappa \cdot \sigma(x)$

  • Log Expected Improvement:

    $logEI = \mathbb{E}[max\{0, e^{f_{min}} - e^{f(x)}\}]$

Bayesian Optimization

for Demographic Inference

Datasets

Datasets

Bayesian Optimization Performance

Bayesian Optimization Performance

Automatic Kernel Selection and Ensembling

Automatic Kernel Selection and Ensembling

Automatic Kernel Selection and Ensembling

Comparison with Genetic Algorithm

Comparison with Genetic Algorithm

Wall Clock Time

Wall Clock Time: 3 Populations

Wall Clock Time: 4 Populations

Wall Clock Time: 5 Populations

Conclusions

 and Future Work

Conclusions

  • Performance depends on kernel and acquisition function.
  • Leave-one-out cross-validation good for automatic kernel selection at the beginning.
  • Bayesian optimization with automatic kernel choice showed faster convergence than the genetic algorithm for 4 and 5 populations.

Future Work

  • Combine Bayesian optimization and genetic algorithm.
  • Stop criteria for Bayesian optimization.
  • More experiments on real data.

Thank you!