Committee

Joshua Vogelstein

Carey Priebe

Mike Powell
Collaborators

Alex B.

Eric B.

Derek P.

Cencheng S.

Ronak M.
Different networks, same statistics
- These four networks have same (network) statistics!

- Consider all non-isomorphic graphs with 10 vertices

Statistical models for networks
- Random dot product graphs (RDPGs)
- Each vertex has a low dimensional latent position.
- Estimate latent position matrix via adjacency spectral embedding.
- =

Two sample graph testing
- Suppose we have two networks
- Want to test if they are "same" or not
Hypothesis:
- Network 1Network 2
- Network 1Network 2
More precisely:
Drosophila Left vs Right Brain

Outline
- Connectomes of Human Brains
- Statistical Modeling for Connectomes
- Heritability of Human Connectomes
- Open-source Software
Human Connectome Project
- Brain scans from identical (monozygotic), fraternal (dizygotic), non-twin siblings.
- Regions defined using Glasser parcellation (180 regions).

Heritability as causal problem

Methods of comparing connectomes
- Exact : measures all differences in latent positions
- Differences in the latent positions implying differences in the connectomes themselves
- Global : considers the latent positions of one connectome are a scaled version of the other
- E.g. males may have globally fewer connections than females
- Vertex : similar to the global differences, but it allows for each vertex to be scaled differently
- E.g regions have preferences in connections
- regions tend to connect strongly within hemisphere
Distribution of distances between connectomes
- Stochastic ordering along familial relationships
- Monozygotic twins have the smallest distances
- Medians (diamonds) shift towards the right as relatedness decreases
- Shifts in medians "decrease" in vertex model
Do genomes affect connectomes?
-
Our hypothesis:
C, GCG
C, GCG
-
Known as independence testing
-
Test statistic: distance correlation (Dcorr)
-
p-value: "If genomes don't affect connectomes, what is the probability there is associational correlation?"
Genomes affect connectomes
-
Our hypothesis:
C, GCG
C, GCG
-
p-value: "If genomes don't affect connectomes, what is the probability there is associational correlation?"
-
All p-values
Do genomes affect connectomes given covariates?
- Want to test:
C, G|CoC|CoG|Co
C, G|CoC|CoG|Co
- Known as conditional independence test
- Test statistic: Conditional distance correlation (CDcorr)
- p-value: "If genomes don't affect connectomes, what is the probability there is causal correlation?"
Genomes affect connectomes given covariates
- Want to test:
C, G|CoC|CoG|Co
C, G|CoC|CoG|Co
- p-value: "If genomes don't affect connectomes, what is the probability there is causal correlation?"
- p-values for only exact and global models
What if we remove "heritable" vertices?
-
Test per vertex :
, G|Co|CoG|Co
, G|Co|CoG|Co
-
Then test "non-heritable" subgraphs ():
, G|Co|CoG|Co
, G|Co|CoG|Co
-
p-value: "If genomes don't affect connectome subgraphs, what is the probability there is causal correlation?"
-
p-values for 3 hypotheses
To sum up...
Are human connectomes heritable?
Depends on the context.
- Connectomes are heritable, up to some common structures.
Outline
- Connectomes of Human Brains
- Statistical Modeling for Connectomes
- Heritability of Human Connectomes
- Open-source Software
How do we compare genomes?
- Neuroimaging twin studies do not sequence genomes.
- Coefficient of kinship ()
- Probabilities of finding a particular gene at a particular location.
- d(Genome, Genome) = 1 - 2.
Relationship |
|
|
Monozygotic |
|
|
Dizygotic |
|
|
Non-twin siblings |
|
|
Unrelated |
|
|
- Literature show:
- neuroanatomy (e.g. brain volume) is highly heritable.
- age affects genomes and potentially connectomes
- d(Covariates, Covariates) = ||Covariates - Covariates||
How do we compare connectomes?
Distance correlation
- Measures dependence between two multivariate quantities.
- For example: connectomes, genomes.
- Can detect nonlinear associations.
- Measures correlation between pairwise distances.

Conditional distance correlation
- Augment distance correlation procedure with third distance matrix.

Associational Test for Connectomic Heritability
- Connectome, GenomeConnectomeGenome
Connectome, GenomeConnectomeGenome

Sex |
All |
Females |
Males |
p-value |
|
|
|
Associational Test for Neuroanatomy
- Neuroanatomy, GenomeNeuroanatomyGenome
Neuroanatomy, GenomeNeuroanatomyGenome

Sex |
All |
Females |
Males |
p-value |
|
|
|
Causal Test for Connectomic Heritability
- Conn., Genome|CovariatesConn.|CovariatesGenome|Covariates
Conn., Genome|CovariatesConn.|CovariatesGenome|Covariates
Sex |
All |
Females |
Males |
p-value |
|
|
|
before i get into the bulk of the talk, i want to steal a page from previous lab members, and start my defense with the acknowledgements. That way if you glaze over or fall asleep later in the talk, I hope you'll remember the important part, which is my graditute to the people which I should probably express more often.
First, to my advisor, my committee, and close collaborators. I will be forever humbled that you all trusted me to work on data and problems that you all have spent so much time and energy on. I'm grateful for that opportunity and for all I've learned from you over the years, and I'm confident that we'll keep working together for a long while...
I want to thank many current and past members of the neurodata lab and hopkins. It has been a great honor to get to learn from you all on a daily basis, and not just about machine learning or neuroscience or statistics, but also frisbee
Loftus
Saad-Eldin
Wang
...
...
...
Falk
...
...
...
Crowley
Bridgeford
Helm
How
Dey
Arroyo
Shin
Ullah
Patsolic
Mehta
Perry
Lawrence
Panda
Panda
Bai
To my parents and my brother - I obviously owe them everything that got me to this point. Their unwavering support, encouragement, and love have been the foundation of my journey.
To my partner Lina. Im so grateful for the support and that we've made it through this chapter and with so many great memories from traveling many parts of the world. i cant wait to see what the future holds for us in the future.

Brain diseases disrupt communication between brain regions. This is why studying connectivity can help us develop targeted therapies for diseases like Alzheimer's and Parkinson's.
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Athreya et al. "RDPG..." _JMLR_ (2021)
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