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+

Statistical Connectomics

+

Thesis Committee Meeting

+
+

Jaewon Chung

+

(he/him) - NeuroData lab
+Johns Hopkins University
+Department of Biomedical Engineering

+

icon j1c@jhu.edu
+icon @j1c (Github)
+icon @j1c (Twitter)

+
+
+

Outline

+
    +
  • +

    What we've done

    +
      +
    • Deriving Connectomes of Human Brains
      • +
    • Statistical Modeling for Connectomes
      • +
    • Heritability of Human Connectomes
      • +
    • graspologic + hyppo + m2g
      • +
    +
    • +
  • +

    Graduation plan

    +
    • +
+
+
+

Representing brains as networks

+
+
+Networks (or graphs) are mathematical abstractions to represent relational data +
    +
  • Vertices - the set of objects (brain regions)
    • +
  • Edges - the set of connections between those objects (brain regions) +
      +
    • E.g. region 1 connects to region 2 with 100 neural bundles
      • +
    +
    • +
+
+
+

center

+
+
+
+
+

Connectomes from diffusion MRI (dMRI)

+
    +
  • in vivo imaging technique
    • +
  • Exploits direction of water diffusion +
      +
    • Anisotropic in white matter tracts
      • +
    • Isotropic in other tissues
      • +
    +
    • +
  • Estimates of number of white matter tracts
    • +
+

center

+
+
+

MRI to graphs (m2g)

+
+
+
    +
  • Easy to use end-to-end pipeline +
      +
    • Input: MRI data
      • +
    • Output: Connectomes, QA measures, derivatives
      • +
    +
    • +
  • Biological properties +
      +
    • Stronger ipsilateral connections
      • +
    +
    • +
  • High discriminability +
      +
    • Same subjects' connectomes are more similar than different subjects'
      • +
    +
    • +
+
+
+

center

+
+
+ +
+
+

Outline

+
    +
  • +

    What we've done

    +
      +
    • Connectomes of Human Brains
      • +
    • Statistical Modeling for Connectomes
      • +
    • Heritability of Human Connectomes
      • +
    • graspologic + hyppo + m2g
      • +
    +
    • +
  • +

    Graduation plan

    +
    • +
+
+
+

Different networks, same statistics

+
    +
  • These four networks have same (graph) statistics!
    • +
+
+
+

center

+ +
+
+

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.
      • +
    • =
      • +
    +
    • +
+

center

+
+
+

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
+

center

+
+
+ +
+
+

Outline

+
    +
  • +

    What we've done

    +
      +
    • Connectomes of Human Brains
      • +
    • Statistical Modeling for Connectomes
      • +
    • Heritability of Human Connectomes
      • +
    • graspologic + hyppo + m2g
      • +
    +
    • +
  • +

    Graduation plan

    +
    • +
+
+
+

Heritability as causal problem

+

center

+ +
+
+

Do genomes affect connectomes?

+
+
+
    +
  • +

    Our hypothesis:
    +C, GCG
    +C, GCG

    +
    • +
  • +

    Known as independence testing

    +
    • +
  • +

    Test statistic: distance correlation (Dcorr)

    +
    • +
  • +

    Implication if false: there exists an associational heritability.

    +
    • +
+
+
+
+
+

center

+
+
+
+
+

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)
    • +
  • Implication if false: there exists causal dependence of connectomes on genomes.
    • +
+
+
+

center

+
+
+
+
+

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
      • +
    +
    • +
+
+
+

We see stochastic ordering along familial relationships

+
+
+

Connectome Models
+center

+
+
+

Neuroanatomy

+

center

+
+
+

center

+
+
+

We detect heritability (associational)

+

center

+
+
+

Some signals disappear after conditioning

+

center

+
+
+

To sum up...

+

center

+ +
    +
  • Statistical models = nuanced investigations
    • +
  • Connectomes are dependent on genome, up to some common structures.
    • +
+
+
+

Outline

+
    +
  • +

    What we've done

    +
      +
    • Connectomes of Human Brains
      • +
    • Statistical Modeling for Connectomes
      • +
    • Heritability of Human Connectomes
      • +
    • graspologic + hyppo + m2g
      • +
    +
    • +
  • +

    Graduation plan

    +
    • +
+
+
+

How to use these tools?

+
+
+

graspologic

+


+
+

+



+

+
+
+

hyppo

+


+
+

+

+
+
+

m2g

+


+
+

+
+
+
+
+

Outline

+
    +
  • +

    What we've done

    +
      +
    • Connectomes of Human Brains
      • +
    • Statistical Modeling for Connectomes
      • +
    • Heritability of Human Connectomes
      • +
    • graspologic + hyppo
      • +
    +
    • +
  • +

    Graduation plan

    +
    • +
+
+
+

Summary of work so far

+
+
+

Manuscripts

+
    +
  • (Co)-First author +
      +
    • Heritability, in review at Imaging Neuro (2024)
      • +
    • m2g, in review at Nature Methods (2024)
      • +
    • Two-sample graph testing, Stat (2022)
      • +
    • Statistical Connectomics, ARISA (2021)
      • +
    • graspologic, JMLR (2019)
      • +
    +
    • +
  • Second author +
      +
    • Indep. Testing in Time Series, TMLR (2024)
      • +
    • Causal Conditional DCorr, in review (2023)
      • +
    • Multiscale Connectomics, in review (2023)
      • +
    +
    • +
  • Others +
      +
    • 5 others published
      • +
    +
    • +
+
+
+

Conference Presentations

+
    +
  • OHBM (x3)
    • +
  • SfN (x3)
    • +
  • Neuromatch (x2)
    • +
+ +

Invited Lectures & Talks

+
    +
  • JSM, 2023
    • +
  • Advanced Graph Analytics Workshop (JHU), 2023
    • +
  • OHBM, 2019
    • +
+

Awards

+
    +
  • BRAIN Initiative Trainee Highlight Award
    • +
  • AWS Research Credit Grants (x2)
    • +
+
+
+
+
+

Summary of work to be done

+
+
+

Manuscripts

+
    +
  • Respond to reviews
    • +
  • Collaboration with Child Mind Institute
    • +
+ +

Conferences/Talks

+
    +
  • Collaborative Research in Computational Neuroscience (CRCNS)
    • +
  • Advanced Graph Analytics Workshop (JHU), 2024
    • +
+
+
+

Code

+
    +
  • Continue to develop graspologic and hyppo
    • +
+
+
+
+

Graduation May 2024

+
+
+

Acknowledgements

+

Team

+
+
+

person
+Eric Bridgeford

+
+
+

person
+Ben Pedigo

+
+
+

person
+Derek Pisner

+
+
+

person
+Cencheng Shen

+
+
+

person
+Ronak Mehta

+
+
+

person
+Vivek Gopalakrishnan

+
+
+

person
+Mike Powell

+
+
+

person
+Carey Priebe

+
+
+

person
+Joshua Vogelstein

+
+
+

NeuroData lab, Microsoft Research

+
+
+

Feedback?

+


+
+
+

+ +

Jaewon Chung

+

icon j1c@jhu.edu
+icon @j1c (Github)
+icon j1c.org

+
+
+

Appendix

+
+
+

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
+
+
+
+

Neuroanatomy (mediator), Age (confounder)

+
    +
  • 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?

+
    +
  • +

    Random dot product graph (RDPG)

    +
      +
    • Each vertex (region of interest) has a low dimensional latent vector (position).
      • +
    • Estimate latent position matrix via adjacency spectral embedding.
      • +
    +
    • +
  • +

    d(Connectome, Connectome) =

    +
    • +
+
+
+

Distance correlation

+
    +
  • Measures dependence between two multivariate quantities. +
      +
    • For example: connectomes, genomes.
      • +
    +
    • +
  • Can detect nonlinear associations.
    • +
  • Measures correlation between pairwise distances.
    • +
+

center

+
+
+

Conditional distance correlation

+
    +
  • Augment distance correlation procedure with third distance matrix.
    • +
+
+

center

+
+
+

Human Connectome Project

+
    +
  • Brain scans from identical (monozygotic), fraternal (dizygotic), non-twin siblings.
    • +
  • Regions defined using Glasser parcellation (180 regions).
    • +
+
+

center

+
+Van Essen, David C., et al., The WU-Minn human connectome project: an overview (2013) +

Glasser, Matthew F., et al. "A multi-modal parcellation of human cerebral cortex." Nature (2016).

+
+
+
+

Associational Test for Connectomic Heritability

+
    +
  • Connectome, GenomeConnectomeGenome
    +Connectome, GenomeConnectomeGenome
    • +
+

center

+
+
+ + + + + + + + + + + + + + + + + +
SexAllFemalesMales
p-value
+
+
+
+

Associational Test for Neuroanatomy

+
    +
  • Neuroanatomy, GenomeNeuroanatomyGenome
    +Neuroanatomy, GenomeNeuroanatomyGenome
    • +
+

center

+
+
+ + + + + + + + + + + + + + + + + +
SexAllFemalesMales
p-value
+
+
+
+

Causal Test for Connectomic Heritability

+
    +
  • Conn., Genome|CovariatesConn.|CovariatesGenome|Covariates
    +Conn., Genome|CovariatesConn.|CovariatesGenome|Covariates
    • +
+
+
+ + + + + + + + + + + + + + + + + +
SexAllFemalesMales
p-value
+
+
+

https://neurodata.io/talks/tathey1/23_06_12_thesis/pres.html#2

![center h:525](../images/fiber-tract-vert.jpeg)

<footer> + +Athreya et al. "RDPG..." _JMLR_ (2021) + +</footer>

- Causal models = rigorous, interpretab

![w:450](../images/logos/brain-logo.jpeg)

- NeurIPS Workshop (x1)

- Collaboration with Alex Badea

- $P[i\rightarrow j]$ = $\langle x_i, x_j\rangle$

\ No newline at end of file diff --git a/docs/committee/committee.md b/docs/committee/committee.md index de5262c..bef0358 100644 --- a/docs/committee/committee.md +++ b/docs/committee/committee.md @@ -107,7 +107,7 @@ Networks (or graphs) are mathematical abstractions to represent relational data @@ -146,207 +146,183 @@ Networks (or graphs) are mathematical abstractions to represent relational data # Statistical Models for Networks - Random dot product graphs (RDPGs) - - Each vertex has a low $d$ dimensional latent vector. + - Each vertex has a low $d$ dimensional latent position. - Estimate latent position matrix $X$ via adjacency spectral embedding. - $P[i\rightarrow j]$ = $\langle x_i, x_j\rangle$ -
- ![center h:300](./images/ase.png) ---- + --- -# Outline +# Two sample graph testing -- What we've done +
- - Connectomes of Human Brains - - Statistical Modeling for Connectomes - - **Heritability of Human Connectomes** - - `graspologic` + `hyppo` + `m2g` +
-- Graduation plan +- Suppose we have two networks +- Want to test if they are "same" or not ---- +Hypothesis: -# Heritability as causal problem +- $H_0: F($Network 1$) = F($Network 2$)$ +- $H_A: F($Network 1$) \neq F($Network 2$)$ -![center h:500](../images/heritability/dag.png) +More precisely: -
+- $H_0: F_X = F_Y \circ W$ +- $H_A: F_X \neq F_Y \circ W$ -[Chung et al. "Are human connectomes heritable?" In prep, Imaging Neuroscience (2024)](https://www.biorxiv.org/content/10.1101/2023.04.02.532875v3) +
+
- +###### Drosophila Left vs Right Brain ---- +![center w:450](./images/nonpar.png) -# Do genomes affect connectomes? +
-- Our hypothesis: - $H_0: F($Connectome|Genome$) = F($Connectome$)$ - $H_A: F($Connectome|Genome$) \neq F($Connectome$)$ +
-- Alternatively: - $H_0: F($Connectome, Genome$) = F($Connectome$)F($Genome$)$ - $H_A: F($Connectome, Genome$) \neq F($Connectome$)F($Genome$)$ + --- -# How do we compare connectomes? +# Outline -- Random dot product graph (RDPG) +- What we've done - - Each vertex (region of interest) has a low $d$ dimensional latent vector (position). - - Estimate latent position matrix $X$ via adjacency spectral embedding. - + - Connectomes of Human Brains + - Statistical Modeling for Connectomes + - **Heritability of Human Connectomes** + - `graspologic` + `hyppo` + `m2g` -- d(Connectome$_k$, Connectome$_l$) = $||X^{(k)} - X^{(l)}R||_F$ +- Graduation plan --- -# Distance correlation - -- Measures dependence between two _multivariate_ quantities. - - For example: connectomes, genomes. -- Can detect nonlinear associations. -- Measures correlation between pairwise distances. +# Heritability as causal problem -![center w:800](./images/unconditional_test.png) +![center h:500](../images/heritability/dag.png) ---- + --- -# Conditional distance correlation +# Do genomes affect connectomes? -- Augment distance correlation procedure with third distance matrix. +
-
+
-![center h:350](./images/conditional_test.png) +- Our hypothesis: + $H_0: F($C, G$) = F($C$)F($G$)$ + $H_A: F($C, G$) \neq F($C$)F($G$)$ ---- +- Known as independence testing +- Test statistic: _distance correlation (Dcorr)_ +- Implication if false: there exists an **associational** heritability. -# How do we compare genomes? +
-- Neuroimaging twin studies do not sequence genomes. -- Coefficient of kinship ($\phi_{ij}$) - - Probabilities of finding a particular gene at a particular location. -- d(Genome$_i$, Genome$_j$) = 1 - 2$\phi_{ij}$. +

-
- -| Relationship | $\phi_{ij}$ | $1-2\phi_{ij}$ | -| :---------------: | :-----------: | :------------: | -| Monozygotic | $\frac{1}{2}$ | $0$ | -| Dizygotic | $\frac{1}{4}$ | $\frac{1}{2}$ | -| Non-twin siblings | $\frac{1}{4}$ | $\frac{1}{2}$ | -| Unrelated | $0$ | $1$ | - -
+
---- +![center](./images/associational.png) -# Neuroanatomy (mediator), Age (confounder) +
-- Literature show: - - neuroanatomy (e.g. brain volume) is highly heritable. - - age affects genomes and potentially connectomes -- d(Covariates$_i$, Covariates$_j$) = ||Covariates$_i$ - Covariates$_j$||$_F$ +
--- -# Human Connectome Project +# Do genomes affect connectomes given covariates? -- Brain scans from identical (monozygotic), fraternal (dizygotic), non-twin siblings. -- Regions defined using Glasser parcellation (180 regions). +
+
-
+- Want to test: + $H_0: F($C, G|Co$) = + F($C|Co$) F($G|Co$)$ + $H_A: F($C, G|Co$) \neq F($C|Co$)F($G|Co$)$ +- Known as conditional independence test +- Test statistic: Conditional distance correlation (CDcorr) +- Implication if false: there exists causal dependence of connectomes on genomes. +
-![center w:700](./images/hcp_demographics.svg) +
-
- +
--- -# Associational Test for Connectomic Heritability +# Methods of comparing connectomes -- $H_0: F($Connectome, Genome$) = F($Connectome$)F($Genome$)$ - $H_A: F($Connectome, Genome$) \neq F($Connectome$)F($Genome$)$ +- 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 -![center h:205](./images/hist-plot-connectomes.png) +--- -
+# We see stochastic ordering along familial relationships -
- -| Sex | **All** | **Females** | **Males** | -| :-----: | :---------------: | :---------------: | :---------------: | -| p-value | $<1\times10^{-5}$ | $<1\times10^{-3}$ | $<1\times10^{-2}$ | +
-
+
---- +Connectome Models +![center h:450](./images/hist-plot-vert.png) -# Associational Test for Neuroanatomy +
-- $H_0: F($Neuroanatomy, Genome$) = F($Neuroanatomy$)F($Genome$)$ - $H_A: F($Neuroanatomy, Genome$) \neq F($Neuroanatomy$)F($Genome$)$ +
-![center h:205](./images/hist-plot-neuroanatomy.png) +Neuroanatomy -
+![center h:150](./images/hist-plot-neuro-vert.png) -
+
-| Sex | **All** | **Females** | **Males** | -| :-----: | :---------------: | :---------------: | :---------------: | -| p-value | $<1\times10^{-3}$ | $<1\times10^{-2}$ | $<1\times10^{-2}$ | + - +![center h:75](./images/legend.png) --- -# Causal Test for Connectomic Heritability +# We detect heritability (associational) -- $H_0: F($Conn., Genome|Covariates$) = F($Conn.|Covariates$)F($Genome|Covariates$)$ - $H_A: F($Conn., Genome|Covariates$) \neq F($Conn.|Covariates$)F($Genome|Covariates$)$ - -
+![center w:700](./images/associationa-tests.png) -
+--- -| Sex | **All** | **Females** | **Males** | -| :-----: | :---------------: | :---------------: | :---------------: | -| p-value | $<1\times10^{-2}$ | $<1\times10^{-2}$ | $<1\times10^{-2}$ | +# Some signals disappear after conditioning -
+![center w:700](./images/all-tests.png) --- @@ -354,11 +330,10 @@ Glasser, Matthew F., et al. "A multi-modal parcellation of human cerebral cortex ![center h:250](./images/genome_to_connectome.png) -- Present a causal model for heritability of connectomes. -- Leveraged recent advances: - 1. Statistical models for networks, allowing meaningful comparison of connectomes. - 2. Distance and conditional distance correlation as test statistic for causal analysis$^1$. -- Connectomes are dependent on genome, suggesting heritability. + + +- Statistical models = nuanced investigations +- Connectomes are dependent on genome, up to some common structures. --- @@ -412,7 +387,7 @@ Glasser, Matthew F., et al. "A multi-modal parcellation of human cerebral cortex [![h:30](https://img.shields.io/github/stars/neurodata/m2g?style=social)](https://github.com/neurodata/m2g) [![h:30](https://img.shields.io/github/contributors/neurodata/m2g)](https://github.com/neurodata/m2g/graphs/contributors) -![w:450](../images/logos/brain-logo.jpeg) + @@ -614,8 +589,6 @@ NeuroData lab, Microsoft Research --- -![bg center blur:3px opacity:20%](../../images/background.svg) - # Feedback? @@ -635,3 +608,145 @@ section { ![icon](../images/icons/mail.png) [j1c@jhu.edu](mailto:j1c@jhu.edu) ![icon](../images/icons/github.png) [@j1c (Github)](https://github.com/j1c) ![icon](../images/icons/web.png) [j1c.org](https://j1c.org/) + +--- + + + +# Appendix + +--- + +# How do we compare genomes? + +- Neuroimaging twin studies do not sequence genomes. +- Coefficient of kinship ($\phi_{ij}$) + - Probabilities of finding a particular gene at a particular location. +- d(Genome$_i$, Genome$_j$) = 1 - 2$\phi_{ij}$. + +
+
+ +| Relationship | $\phi_{ij}$ | $1-2\phi_{ij}$ | +| :---------------: | :-----------: | :------------: | +| Monozygotic | $\frac{1}{2}$ | $0$ | +| Dizygotic | $\frac{1}{4}$ | $\frac{1}{2}$ | +| Non-twin siblings | $\frac{1}{4}$ | $\frac{1}{2}$ | +| Unrelated | $0$ | $1$ | + +
+ +--- + +# Neuroanatomy (mediator), Age (confounder) + +- Literature show: + - neuroanatomy (e.g. brain volume) is highly heritable. + - age affects genomes and potentially connectomes +- d(Covariates$_i$, Covariates$_j$) = ||Covariates$_i$ - Covariates$_j$||$_F$ + +--- + +# How do we compare connectomes? + +- Random dot product graph (RDPG) + + - Each vertex (region of interest) has a low $d$ dimensional latent vector (position). + - Estimate latent position matrix $X$ via adjacency spectral embedding. + + +- d(Connectome$_k$, Connectome$_l$) = $||X^{(k)} - X^{(l)}R||_F$ + +--- + +# Distance correlation + +- Measures dependence between two _multivariate_ quantities. + - For example: connectomes, genomes. +- Can detect nonlinear associations. +- Measures correlation between pairwise distances. + +![center w:800](./images/unconditional_test.png) + +--- + +# Conditional distance correlation + +- Augment distance correlation procedure with third distance matrix. + +
+ +![center h:350](./images/conditional_test.png) + +--- + +# Human Connectome Project + +- Brain scans from identical (monozygotic), fraternal (dizygotic), non-twin siblings. +- Regions defined using Glasser parcellation (180 regions). + +
+ +![center w:700](./images/hcp_demographics.svg) + + + +--- + +# Associational Test for Connectomic Heritability + +- $H_0: F($Connectome, Genome$) = F($Connectome$)F($Genome$)$ + $H_A: F($Connectome, Genome$) \neq F($Connectome$)F($Genome$)$ + +![center h:205](./images/hist-plot-connectomes.png) + +
+ +
+ +| Sex | **All** | **Females** | **Males** | +| :-----: | :---------------: | :---------------: | :---------------: | +| p-value | $<1\times10^{-5}$ | $<1\times10^{-3}$ | $<1\times10^{-2}$ | + +
+ +--- + +# Associational Test for Neuroanatomy + +- $H_0: F($Neuroanatomy, Genome$) = F($Neuroanatomy$)F($Genome$)$ + $H_A: F($Neuroanatomy, Genome$) \neq F($Neuroanatomy$)F($Genome$)$ + +![center h:205](./images/hist-plot-neuroanatomy.png) + +
+ +
+ +| Sex | **All** | **Females** | **Males** | +| :-----: | :---------------: | :---------------: | :---------------: | +| p-value | $<1\times10^{-3}$ | $<1\times10^{-2}$ | $<1\times10^{-2}$ | + +
+ +--- + +# Causal Test for Connectomic Heritability + +- $H_0: F($Conn., Genome|Covariates$) = F($Conn.|Covariates$)F($Genome|Covariates$)$ + $H_A: F($Conn., Genome|Covariates$) \neq F($Conn.|Covariates$)F($Genome|Covariates$)$ + +
+ +
+ +| Sex | **All** | **Females** | **Males** | +| :-----: | :---------------: | :---------------: | :---------------: | +| p-value | $<1\times10^{-2}$ | $<1\times10^{-2}$ | $<1\times10^{-2}$ | + +
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