Cover Slide 1

Problem

Phasing

Humans are diploid. We have two copies of each chromosome. The genotype is the sum of these two copies. Given the genotype for a number of individuals, we can find the haplotypes by haplotype phasing techniques.

Imputation

Due to the experimentation, there can be a lot of missing data. But many methods are only working for a full dataset.

State of the Art

Fastphase

Bayesian model and EM algorithm

An optimization formulation

$$ \begin{aligned} & \underset{A,S}{\text{minimize}} & & \sum_{i = 0}^{n-1} \sum_{j = 0}^{m-1} \| h_{i,j}^{1} - a_{s_{i,j}^{1},j}\|^2 + \| h_{i,j}^{2} - a_{s_{i,j}^{2},j}\|^2\\ &&& + \lambda \mathbb{1}_{s_{i,j}^{1} \neq s_{i,j-1}^{1}} + \lambda \mathbb{1}_{s_{i,j}^{2} \neq s_{i,j-1}^{2}} \\ & \text{subject to} & & a_{i,j} \in \left[0,1\right], h_{i,j} \in \lbrace 0, 1\rbrace, s_{i,j} \in \lbrace 0, 1, \ldots, k-1\rbrace\\ & & & g_{i,j} = h_{i,j}^{1} + h_{i,j}^{2} \end{aligned} $$

About the algorithm

• An optimization problem
• with constraints
• graph algorithm : forward backward

Results : Speed

Results : Imputation

Links

• https://guides.github.com/features/mastering-markdown/

• https://github.com/adam-p/markdown-here/wiki/Markdown-Cheatsheet

Q&A Slide