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Model Selection in  Parameterizing Cell Images and Populations Model Selection in  Parameterizing Cell Images and Populations

Model Selection in Parameterizing Cell Images and Populations - PowerPoint Presentation

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Model Selection in Parameterizing Cell Images and Populations - PPT Presentation

MMBIOS April 2015 Gregory R Johnson Nuclear shape Cell shape Object pos probability Object number Object appearance Microtubule distribution Object positions Object distribution CellOrganizer ID: 784287

images cell model distribution cell images distribution model parameters parameterizations parameterization spatial models shape object network image morphology number

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Slide1

Model Selection in Parameterizing Cell Images and Populations

MMBIOS, April 2015

Gregory R. Johnson

Slide2

Nuclear shape

Cell shape

Object

pos. probability

Object number

Object appearance

Microtubule distribution

Object

positions

Object

distribution

CellOrganizer

Training

Synthesis

Cell

Images

Synthetic

Images

Model Parameters

Slide3

CellOrganizer

Models Cell Populations

Learn how spatial relationships of cell compartments vary across cell populations

Generate high-quality

in

silico

representations (i.e. images) cell shape and the relationships of compartments within them

X

1

X

2

X

3

X

4

Xn

…p1*

p

2*…

p

m*x1*

x2*

x

m

*

P(

pi|Ɵ)

Images

Parameterizations

Cell Morphology

Distribution

Sampled

Parameterizations

Synthesized

Images

f

(x) = p

d({p

1

,…,

p

n

}) =

Ɵ

b(

Ɵ

) = p*

g(p) = x

p

1

p

2

p

3

p

4

p

n

Slide4

CellOrganizer Models Cell Populations

Represent cell morphology and organization of components in an

invertable

, compact manner

Learn a distribution over these compact parameterizations

X

1

X

2

X

3

X

4

X

n

p1*

p2*

pm*

x1*

x2*

x

m*

P(

p

i|Ɵ)

Cell Morphology

Distribution

Sampled

Parameterizations

Synthesized

Images

f

(x) = p

d({p

1

,…,

p

n

}) =

Ɵ

b(

Ɵ

) = p*

g(p) = x

p

1

p

2

p

3

p

4

p

n

Slide5

Image To Parameterization

Represent cell morphology in a compact set of parameters

We also desire an invertible function such that we can recover the original image

X

1

p

1

Images

Parameterizations[ , , ]

cell

nucleus

protein pattern

f

(x

i

) = pi ⟺ g(pi) = xi, i

.,e. xi

pi,1pi,2

pi,3

p1

x1

Slide6

Image parameterization is

lossy

Image parameterizations vs number of parameters

Becomes Likelihood Maximization problem if K is known

GMM parameters

Represent the mixture from parameters

LAMP2 Protein Pattern

Full covariance matrix

Gaussian fit

Spherical covariance matrix

Gaussian fit

Slide7

MDS

0.85

0.63

0.74

0.90

a.

b.

c.

d.

Shape Space Modeling Pipeline

Slide8

Image parameterization is

lossy

(contd.)

Fig 2 from

T

.

Peng et al, “Instance-based generative biological shape modeling” 2009.

x

1

x2 x

3 x4

g(p1)

g(p2)g(p3)

g(p4)

Where

Slide9

Multidimensional Scaling

= measured distance between shapes

i

, j

= Euclidian

embeddings

for all shapes

= Euclidean distance between embedding coordinates for shapes

i

, j

= Indicator for if

D

i,j

is observed

Slide10

Shape space dimensionality vs Reconstruction

Reconstruction is dependent on the number of observed distances and the dimensionality of the embedding

blue = 1 dimensional embedding

red = “complete” embedding

Slide11

Prediction of cell and nuclear dependency

Slide12

The “goodness” of a cell parameterization

Many ways to do this

Pixel-pixel Mean Squared

Sørensen

-Dice Coefficient for binary images and shapesLikelihood function…

Slide13

Parameters to distribution

p

1

p

n

p

*

P(pi|Ɵ)

d({p

1

,…,

pn}) = Ɵb(p|Ɵ) = p*

Slide14

Parameters to distribution

“Straight forward” distribution learning and model selection

Some parameterization may

overfit

(i.e. point-mass)Many models can not be learned via closed-form solutionsPredictive Maximum Likelihood i.e.

p1

…p

n

p*

P(pi|Ɵ)

d({p

1

,…,pn

}) = Ɵb(p|

Ɵ) = p*where n is the number of hold outs x

n is some hold-out subset and Ɵn is corresponding trained model

Slide15

Distributions of object position

SEC23B

ACBD5

HIP1

Slide16

Possible Models

Puncta

are dependent on organelles, but independent of each other

Poisson process

Puncta are dependent on organelles and each otherFiskel point process

Slide17

Model with no puncta-puncta spatial interaction indicates greater likelihood!

Five-fold cross validation to choose the best model

Slide18

Toward Spatial Network Models

C

olocalization

is a complex network with interdependencies

Simplify it by use one-direction dependencies (network -> DAG)

A diagram of a simplified spatial interaction network

A spatial network exhibiting negative

colocalization

a)

b)

c)

d

prot

dcell

dnuc

p

prot

nprot

sprot

iprot

dprot

Protein N

Slide19

Pattern Modeling contd.

Generative Models

Add parameters to account for spatial dependency of arbitrary numbers of protein patterns

19

P(Chloroplast | Cell)

P(ER | Cell, Chloroplast)

3D rendering of a protoplast

P(Chloroplast | Cell)

P( ER | Cell)

Slide20

Big Picture…

Want most precise cell parameterization

f(x) = p, g(p) = x

Best-generalizing distribution

d({p1,…,p

n}) = Ɵ

X1X2

X3

X4

Xn

p1

p2

p3

p4

…pn

p

1

*

p

2

*

p

m*

x

1*

x2*

xm*

P(

p

i

|Ɵ)

Images

Parameterizations

Cell Morphology

Distribution

Sampled

Parameterizations

Synthesized

Images

f

(x) = p

d({p

1

,…,

p

n

}) =

Ɵ

b(

Ɵ

) = p*

g(p) = x

Slide21

Master Modeling function

How to build a master model-selection model

g(p

i

) with least error between x

i

and g(pi)d({p1,…,pn}) = Ɵ

with greatest likelihoodEven if errtot is some sort of proabilistic

model, it is not clear how to balance errtot and likelihood of the modelESPECIALLY BECAUSE G(X) DRASTICTLY CHANGES VALUES OF

Ɵ