Efficient representation of uncertainty in multiple sequence - PowerPoint PPT Presentation

Efficient representation of uncertainty in multiple sequence alignments using directed acyclic graphs JOSEPH L HERMAN, ÁDÁM NOVÁK, RUNE LYNGSO, ADRIENN SZABÓ, ISTVÁN MIKLÓS AND JOTUN HEIN

Describing the Problem ��������� #1 ��������� ��������� Black Box ��������� #2 What do we do we do with a … million alignments?! ��������� #1000000

Sampling Procedure

Point Estimate

Solutions You can:  Take one sample alignment with  Maximum likelihood  In this case, MAP  Maximize positional homologies  Minimize the gaps  …  Or… Try to process the samples you have, and obtain a good estimate! ���������� ���� ����� ���� ��������� � ���� ����� ��������

Columns 0 2 0 4 1 6 0 2 2 4 + 7 2 Column Vectors Even Points

Objective An Alignment is a path from: 2� � 0 2� � 0 2� � 0 2� � 0

Example

Crossovers

Why do we care about ESS? � ��� ������� ⇒ � � , � � , ⋯ , � � ��� � ��� � � � � ◦ ��� �̅ � � ⇒ ���� ���������! � ������� ���������� ������� � � , � � , ⋯ , � � ��� � ��� � 1 ◦ ��� �̅ � � � ⇒ ��� ����������! ��� � ��� � � . Bayesian Alignment methods use MCMC  So each point is highly correlated to the last point  ESS is smaller than the sample size a lot ��� �� �� ��������� �� ��� ���� ��� �������� ������� ��� �����

Crossovers and ESS Suppose all alignments shared the even points A and B in their paths: A B Number of Original Alignments = 4 Number of possible alignments = 4*3*3

ESS

Equivalence classes

Approximate Inference o The independence assumption o The accuracy  The nearest point w.r.t KL divergence metric o Consequences

Pair marginals Each site is independent of the very last ones(except the immediately preceding one)

Pair HMMs

Mean Field Approximation Approximation

Mean Field vs Pair Marginals Pair Marginal  � ������ � ������ � � 1� Mean Field  � ������ � ��� ������ �� �������� �� ������ ��

Mean Field vs Pair Marginals Estimating Pair Marginals: ◦ For each column  2 � possible preceding columns. Estimating Mean field: ◦ Only approximate one parameter

Mean Field vs Pair Marginals Just the distribution estimation error

Mean Field vs Pair Marginals

More realistic case!

Point estimation The quality of an alignment can be defined in terms of: They argue that we only care about the positives, since the sample size is small!

Point Estimate

Loss function

Simplifying the space of loss functions

Simplifying a specific class

The dynamic programming problem Suppose the edges were weighted somehow

A Sample running

Some results