Efficient representation of uncertainty in multiple sequence - - PowerPoint PPT Presentation

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Efficient representation of uncertainty in multiple sequence - - PowerPoint PPT Presentation

Oct 22, 2023 40 likes •344 views

Efficient representation of uncertainty in multiple sequence alignments using directed acyclic graphs JOSEPH L HERMAN, DM NOVK, RUNE LYNGSO, ADRIENN SZAB, ISTVN MIKLS AND JOTUN HEIN Describing the Problem #1

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SLIDE 1

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

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Describing the Problem

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

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Sampling Procedure

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Point Estimate

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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!
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Columns

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

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Objective

An Alignment is a path from:

2 2 2 2

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Example

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Crossovers

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Why do we care about ESS?

⇒ , , ⋯ ,

  • ̅
  • ⇒ !

, , ⋯ ,

  • ̅ ⇒ !

.

Bayesian Alignment methods use MCMC  So each point is highly correlated to the last point  ESS is smaller than the sample size a lot

1

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Crossovers and ESS

Suppose all alignments shared the even points A and B in their paths:

Number of Original Alignments = 4 Number of possible alignments = 4*3*3 A B

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ESS

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Equivalence classes

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Approximate Inference

  • The independence assumption
  • The accuracy  The nearest point w.r.t KL divergence metric
  • Consequences
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Pair marginals

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

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Pair HMMs

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Mean Field Approximation

Approximation

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Mean Field vs Pair Marginals

Pair Marginal  1 Mean Field

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Estimating Pair Marginals:

  • For each column  2 possible preceding columns.

Estimating Mean field:

  • Only approximate one parameter

Mean Field vs Pair Marginals

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Mean Field vs Pair Marginals

Just the distribution estimation error

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Mean Field vs Pair Marginals

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More realistic case!

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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!

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Point Estimate

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Loss function

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Simplifying the space of loss functions

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Simplifying a specific class

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The dynamic programming problem

Suppose the edges were weighted somehow

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A Sample running

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Some results