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<!DOCTYPE html>
<html>
<head>
<title>Connectal Coding</title>
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<textarea id="source">
name:opening
**Connectal Coding: Discovering the Mechanism Linking Cognitive Phenotypes to Individual Histories**<br>
Joshua T. Vogelstein |
{[BME](https://www.bme.jhu.edu/),[ICM](https://icm.jhu.edu/),[CIS](http://cis.jhu.edu/),[KNDI](http://kavlijhu.org/)}@[JHU](https://www.jhu.edu/)
<a href="https://neurodata.io"><img src="images/neurodata_purple.png" style="height:430px;"/></a>
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.foot[[jovo@jhu.edu](mailto:[email protected]) | <http://neurodata.io/talks> | [@neuro_data](https://twitter.com/neuro_data)]
---
class: center, middle
## .center[https://neurodata.io/graspy/]
---
## Outline
- Background
- Example Connectomes
- Connectal Coding
- Applications
- Discussion
---
## .k[Background]
---
### Two definitions
.r[Neural (activity) coding]: inferring the relationships between neural activity and stimuli or responses
--
.r[Connectal coding]: inferring the relationships between *neural circuit structure* and *individual histories*
--
- .r[Individual histories]: genetic, developmental, experiential
- .r[Neural circuit structure (aka, a connectome)]: a network of a brain
---
### Genotype, Phenotype, Connectotype
- .r[Phenotype]: a description of an individual's properties with regard to a phenomenon of interest
- .r[Genotype]: a set of genes and associated variants associated with that phenotype
- .r[Connectotype]: a set of nodes, edges, and their properties that are associated with that phenotype
--
<br><br>
.center[Genotype --> Connectotype --> Phenotype]
**Connectotypes are the implementation-level mechanisms linking genotypes to phenotypes**
---
### Connectome in Literature
- Sporns et al. *PLoS CB* (2005)
- Hagmann (2005)
- PubMed (circa 2018): .r[3000+] hits.
---
### Connectome according to jovo
- .r[Network] of a brain, at a spatiotemporal precision & extent
- .r[Nodes] are distinct biophysical entities
- .r[Edges] are *structural* objects connecting a pair of nodes
- .r[Attributes] of the network, nodes, or edges are possible
--
<br>
- Example nodes: neurons, neural compartment, neural ensembles
- Example edges: synapses, gap junction, fiber bundles
---
### Implications
- A brain could have many .r[different] connectomes, at different times and/or resolutions
- We measure properties of the brain to .r[estimate] connectomes
- Those measurements can be .r[structural] or .r[functional]
- Estimates are always .r[noisy]
--
### Some caveats
- connectomes are not comprehensive, unlike genomes
- nodes can be abstractions, eg, all neurons type A
- attributes can be arbitrary, eg, distribution of synaptic vesicles
- connectomics is the study of neural circuitry
---
### Connectomes for Connectal Coding
<br>
Hhypothesis generation not hypothesis testing
---
## .k[Example Connectomes]
---
### C Elegans
<img src="images/elegans_connectome.png" style="height: 450px;"/>
- directed, multi
---
### Drosophila Mushroom Body
<img src="images/drosophila_left_mb.png" style="height: 450px;"/>
- directed
---
### Mouse Ex Vivo Diffusion MRI
<img src="images/mousedMRI_connectome.png" style="height: 450px;"/>
- undirected
---
### Human MRI
<img src="images/human_connectome.png" style="height: 450px;"/>
- undirected, multi (semi-dense)
---
## .k[Connectal Coding]
---
### Connectome Analysis Styles
- bag of edges
- bag of features
- bag of parameters
---
### Bag of Edges
- treat each edge as independent
- does this completely ignores graph structure of data (hint: yes)?
- requires multiple hypothesis correction for valid tests
- does anybody know a good way to correct (hint: no)?
- BH: way under-conservative (false positives)
- Bonferroni: way over-conservative (false negatives)
- Network based statistics: no theoretical guarantees
---
### Bag of Features
- choose m features and compute them per node or graph
- how do i choose m? how do i choose which features (hint: arbitrary)?
- how many features are possible given a graph with n nodes (hint: many)?
- does these features characterize the brain (hint: no)?
- can we make causal claims using these features (hint: no)?
- least well known of the approaches
---
### Bag of Parameters
- build a statistical parametric model of brain network
- does it treat edges independently (hint: no)?
- do we have ways of choosing model and model complexity (hint: kind of)?
- do these models characterize the brain (hint: yup!)?
- can we make causal claims (hint: kind of)?
---
## What is a Code?
A code is a system of (potentially stochastic) rules that translate from one representation of information into another.
.pull-left[
Examples:
- Morse: one-to-one
- genetic: deterministic
- neural: stochastic
]
.pull-right[
<img src="https://upload.wikimedia.org/wikipedia/commons/b/b5/International_Morse_Code.svg" style="height: 400px;"/>
]
---
## Statistical Coding
- Random variables: X, Y
- Distributions: X ~ P, Y ~ P
- Conditionals: P[X | Y], P[Y | X]
Formally, codes are conditional distributions.
---
## Connectal Coding Model
Random variables of interest include:
- P: phenotypes
- C: connectomes
- G: genome
- E: environment
---
## Abstract Connectome Codes
- Pr[C | G]: prob of connectome, given a genome
- Pr[P | C]: prob of phenotype, given a connectome
- Pr[P | C, G, E]: probability of phenotype given connectome, genome, and environment
---
## .k[Statistical Models of Connectomes]
---
### Independent & Identical Edges
Erdos-Renyi (ER): akin to assuming a neuron's spike rate is Poisson with a fixed rate.
- edges are binary
- all edges independent
- all edges sampled from identical distribution
- $\Rightarrow$ only 1 parameter: prob of an edge
Notes
- directed vs. undirected
- loopy vs. no loops
- Simplest random graph model
- lacks sufficient complexity/descriptive power for most questions
---
### Independent & Identical Edges
.r[Weighted] Erdos-Renyi: akin to Poisson model using a bigger bin width.
- edges can take .r[any value]
- edges are independent
- edges are sampled from identical distribution
- $\Rightarrow$ can still only be 1 parameter: expected weight of an edge
Notes
- directed vs. undirected
- loopy vs. no loops
- simplest .r[weighted] random graph model
- lacks sufficient complexity/descriptive power for most questions
---
### Independent & Identical Edge
.r[Zero-Inflated] Weighted Erdos-Renyi: akin to assuming a bursty neuron, modeling both probability of burst and expected number of spikes in each burst
- edges can take any value
- edges are independent
- edges are sampled from identical distribution
- .r[2 parameters]: prob of edge, and expected weight of edge.
Notes
- directed vs. undirected
- loopy vs. no loops
- simplest sparse weighted random graph model
- can provide useful/interesting description of a connectome
---
### IIE Models of Connectomes
<br>
<img src="images/independent_edge_connectome_estimates.png" style="width: 800px;"/>
---
### Independent Edge Model
- edges are binary
- edges are independent
- edges are sampled from .r[differnt] distribuions
- .r[n*n parameters]: prob of edge between each pair.
- P[ A(i,j) ] = p(i,j)
Notes
- same generalizations as above apply here as well
- n*n paramers is much larger than 1,
- still ignores structure
- can't fit without lots of samples or further assumptions/restrictions
---
## Categorical Conditionally Independent Edge Models
Stochastic Block Model (SBM): akin to assuming a neuron's are in different states, which determine Poisson rate.
- edges are binary
- edges are .r[conditionally] independent
- each node has a class assignment
- P[ A(i,j) ] = B(class i, class j)
Notes
- directed vs. undirected
- loopy vs. no loops
- simplest >2 parameter model
---
## Connectome SBMs
<img src="images/fig_sbm.png" style="width: 800px;"/>
---
## Generalized SBMs
Weighted Stochastic Block Model (SBM)
- edges are .r[weighted]
- edges are conditionally independent
- each node has a class assignment
- P[ A(i,j) ] = B(class i, class j) is expected weight of connection
Notes
- directed vs. undirected
- loopy vs. no loops
---
## Generalized SBMs
Zero-Inflated Weighted Stochastic Block Model (SBM)
- edges are weighted
- edges are conditionally independent
- each node has a class assignment
- P[ A(i,j) ] = is defined by a matrix of probabilities of connection, and a matrix of expected weights
Notes
- directed vs. undirected
- loopy vs. no loops
---
## Continuous Conditionally Independent Edge Models
Random Dot Product Graphs (RDPG): akin to latent state models in population coding
- edges are binary
- edges are conditionally independent
- each node has a .r[latent position in d-dimensions]
- P[ A(i,j) ] = f(latent position i, latent position j)
- for example, P[ A(i,j) ] is the product of latent positions
Notes
- directed vs. undirected
- no loops is ickier
- generalizes previous models
---
## Connectome RDPGs
<img src="images/fig_ase.png" style="width: 750px;"/>
---
## Generalized RDPG
- Weighted RDPG: edges have weights
- Zero-Inflated Weighted RDPG: edges have probabilities and expected weights
---
## Latent Structure Models
- Special case of RDPG, where latent positions are organized into .r[structures]
- Examples
- each node class has a distribution of latent positions, eg, Gaussian
- latent positions are hierarchical, eg, multiscale atlas
- repeated motif, eg, cortical columns
- latent positions are curved
---
## Drosophila Mushroom Bodies
<img src="images/Fig15-new.png" style="width: 750px;"/>
---
## Population Graph Models
- Mixture of RDPG
- Joint Heterogeneous RDPG
<!-- <img src="images/rerf_perf.png" style="width: 800px;"/> -->
<!-- <img src="images/Fig4_benchmark_ranks.png" style="height: 600px;"/> -->
---
## .k[Discussion]
---
## Summary and Next Steps
- Connectomes are the mechanistic link:
.center[.r[genotype --> phenotype]]
- Extend ideas from coding theory to support these analyses
- Connectomes, genetic and phenotypic data are available
---
### Acknowledgements
<div class="small-container">
<img src="faces/ebridge.jpg"/>
<div class="centered">Eric Bridgeford</div>
</div>
<div class="small-container">
<img src="faces/pedigo.jpg"/>
<div class="centered">Ben Pedigo</div>
</div>
<div class="small-container">
<img src="faces/jaewon.jpg"/>
<div class="centered">Jaewon Chung</div>
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<img src="faces/cep.png"/>
<div class="centered">Carey Priebe</div>
</div>
<div class="small-container">
<img src="faces/randal.jpg"/>
<div class="centered">Randal Burns</div>
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<div class="small-container">
<img src="faces/mim.jpg"/>
<div class="centered">Michael Miller</div>
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<div class="small-container">
<img src="faces/dtward.jpg"/>
<div class="centered">Daniel Tward</div>
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<div class="small-container">
<img src="faces/vikram.jpg"/>
<div class="centered">Vikram Chandrashekhar</div>
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<div class="centered">Drishti Mannan</div>
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<div class="centered">Jesse Patsolic</div>
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<div class="centered">Benjamin Falk</div>
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<div class="centered">Kwame Kutten</div>
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<div class="centered">Eric Perlman</div>
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<div class="centered">Alex Loftus</div>
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<div class="centered">Brian Caffo</div>
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<div class="centered">Minh Tang</div>
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<div class="centered">Avanti Athreya</div>
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<div class="centered">Vince Lyzinski</div>
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<div class="centered">Daniel Sussman</div>
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<div class="centered">Youngser Park</div>
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<div class="small-container">
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<div class="centered">Cencheng Shen</div>
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<div class="centered">Shangsi Wang</div>
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<div class="centered">Tyler Tomita</div>
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<div class="centered">James Brown</div>
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<div class="centered">Disa Mhembere</div>
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<div class="centered">Greg Kiar</div>
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</div><span style="font-size:200%; color:red;">♥, 🦁, 👪, 🌎, 🌌</span>
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---
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