Many different measurement techniques are used to record neural activity in the brains of different organisms, including fMRI, EEG, MEG, lightsheet microscopy and direct recordings with electrodes. Each of these measurement modes have their advantages and disadvantages concerning the resolution of the data in space and time, the directness of measurement of the neural activity and which organisms they can be applied to. For some of these modes and for some organisms, significant amounts of data are now available in large standardized open-source datasets. I will report on our efforts to apply causal discovery algorithms to, among others, fMRI data from the Human Connectome Project, and to lightsheet microscopy data from zebrafish larvae. In particular, I will focus on the challenges we have faced both in terms of the nature of the data and the computational features of the discovery algorithms, as well as the modeling of experimental interventions.

1. Causal Discovery in Neuro Imaging Data
Frederick Eberhardt
SAMSI Causal Inference Workshop, Dec 9-11, 2019

2. Overview
2
causaldiscovery
resting state brain causal graph of brain regions

3. 3
Human Connectome Project

4. resting state fMRI data in the HCP
4
• The subjects are asked to lie with eyes open, with “relaxed” fixation
on a white cross (on a dark background), think of nothing in
particular, and not to fall asleep.
• Four ~15-minute rfMRI runs are acquired in two separate fMRI
sessions
• Acquisition parameters: 1200 volumes, TR = 720 ms, voxel size =
2mm isotropic, 72 slices

5. Anatomical Parcelation
anatomical parcelationvoxel level resting state fMRI

6. Parcel Activation over Time
time points
parcels

7. 7
10-100ms interactions
~100billionneurons
What are we measuring?

8. 7
10-100ms interactions
~100billionneurons
~90,000voxelsBOLDsignal 720ms measurement interval
What are we measuring?

9. 7
10-100ms interactions
~100billionneurons
5-6s hemodynamic delay
~90,000voxelsBOLDsignal 720ms measurement interval
What are we measuring?

10. 7
10-100ms interactions
~100billionneurons
5-6s hemodynamic delay
~90,000voxelsBOLDsignal 720ms measurement interval
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parcel 1
parcel 405
…
What are we measuring?

11. 7
10-100ms interactions
~100billionneurons
5-6s hemodynamic delay
• indirect measurement of neural activity by
BOLD signal
• aggregation in space from voxel to parcel
• aggregation in time by an order of magnitude
~90,000voxelsBOLDsignal 720ms measurement interval
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parcel 1
parcel 405
…
What are we measuring?

12. Fast Greedy Equivalence Search (FGES)
8
Chickering (2002) JMLR
Ramsey (2017) IJDSA
• greedy local search for a DAG
• uses Bayesian Information Criterion (BIC) to determine which edge to
add/delete at any stage in the algorithm
• one free “sparsity” parameter that regulates fit vs. model complexity
• is consistent: given its assumptions it will identify the Markov
equivalence class of the true DAG in the large sample limit

13. Fast Greedy Equivalence Search (FGES)
8
• Assumptions
- acyclic causal structure
- no confounding
- linear Gaussian structural equation model
- iid data
Chickering (2002) JMLR
Ramsey (2017) IJDSA
• greedy local search for a DAG
• uses Bayesian Information Criterion (BIC) to determine which edge to
add/delete at any stage in the algorithm
• one free “sparsity” parameter that regulates fit vs. model complexity
• is consistent: given its assumptions it will identify the Markov
equivalence class of the true DAG in the large sample limit

14. Fast Greedy Equivalence Search (FGES)
8
• Assumptions
- acyclic causal structure
- no confounding
- linear Gaussian structural equation model
- iid data
Chickering (2002) JMLR
Ramsey (2017) IJDSA
• greedy local search for a DAG
• uses Bayesian Information Criterion (BIC) to determine which edge to
add/delete at any stage in the algorithm
• one free “sparsity” parameter that regulates fit vs. model complexity
• is consistent: given its assumptions it will identify the Markov
equivalence class of the true DAG in the large sample limit
• scales to >100,000 variables
- implementation in java in the Tetrad code
package
- our python implementation here: https://
github.com/eberharf/fges-py/

15. resting state fMRI
880
subjects
single
subject
correlations

16. resting state fMRI
880
subjects
single
subject
correlations
880
subjects
single
subject
left
hemisphere
right
hemisphere
causal connections
between
hemispheres

17. causal connections
880
subjects
single
subject
left
hemisphere
right
hemisphere
resting state fMRI

18. causal connections
880
subjects
single
subject
left
hemisphere
right
hemisphere
resting state fMRI

19. causal connections
880
subjects
single
subject
left
hemisphere
right
hemisphere
example structure for illustration
resting state fMRI

20. causal connections
between
hemispheres
880
subjects
single
subject
resting state fMRI

21. causal connections
between
hemispheres
880
subjects
single
subject
example structure for illustration
resting state fMRI

22. HUMAN
causal connections
MOUSE
causal connections
Cross-species Analysis

23. Fast Greedy Equivalence Search
• acyclic causal structure
• no unmeasured confounding
• very scalable
Causal Orientation

24. Fast Greedy Equivalence Search
• acyclic causal structure
• no unmeasured confounding
• very scalable
Answer Set Programming for Causality
• cyclic or acyclic causal structure
• unmeasured confounding permitted
• does not scale
Causal Orientation

25. 56
59
81
82108
109
110
Fast Greedy Equivalence Search
• acyclic causal structure
• no unmeasured confounding
• very scalable
Answer Set Programming for Causality
• cyclic or acyclic causal structure
• unmeasured confounding permitted
• does not scale
Causal Orientation

26. true causal structure
Observation to Intervention
x y
z

27. true causal structure
Observation to Intervention
x y
z
equivalence class of causal
structures that we learned
x y
z

28. true causal structure
Observation to Intervention
x y
z
equivalence class of causal
structures that we learned
x y
z
intervened causal structure
x y
z

29. 15
3.0 s
EPI scan EPI scan
Stimulation
period (30 s)
Electrical stimulation
Stimulus
isolator
Waveform
generation
computer
+ -
B
100 ms
a,b = 0.25 ms
c = 0.75 ms
a b c
d
e
R
(-2.4, -8.2,Subj.292)
L
electrical stimulation fMRI

30. 16
simple contrast (GLM) causal discovery
Effect of stimulating the right amygdala

31. peak activation
depletion
-10 -5 0 5
-40-200204060
run 1, mean of 10 stimulus blocks stacked
timesteps before and after onset of stimulus
activation
-10 -5 0 5
-40-2002040
run 2, mean of 10 stimulus blocks stacked
timesteps before and after onset of stimulus
activation
-10 -5 0 5
-60-40-20020406080
run 3, mean of 10 stimulus blocks stacked
timesteps before and after onset of stimulus
activation
-10 -5 0 5
-60-40-2002040
run 4, mean of 10 stimulus blocks stacked
timesteps before and after onset of stimulus
activation
stimulation stimulation
stimulation stimulation

32. 18
parcel intervention On/Off on first 5 observation
alL_AngularGyrus x
R_InsularCortex x x
R_TemporalPole x x x
R_SuperiorTemporalGyrusPosterior x
R_MiddleTemporalGyrusAnterior x
R_MiddleTemporalGyrusTemporoOccipital x
R_InferiorTemporalGyrusAnterior x
R_InferiorTemporalGyrusTemporoOccipital x
R_FrontalOrbitalCortex x
R_ParahippocampalGyrusAnterior x
R_ParahippocampalGyrusPosterior x
R_TemporalFusiformCortexPosterior x
R_PlanumPolare x
LeftCaudate x
LeftAmygdala x
RightHippocampus x x x
After adjusting for hemodynamic delay and depletion…

33. 18
parcel intervention On/Off on first 5 observation
alL_AngularGyrus x
R_InsularCortex x x
R_TemporalPole x x x
R_SuperiorTemporalGyrusPosterior x
R_MiddleTemporalGyrusAnterior x
R_MiddleTemporalGyrusTemporoOccipital x
R_InferiorTemporalGyrusAnterior x
R_InferiorTemporalGyrusTemporoOccipital x
R_FrontalOrbitalCortex x
R_ParahippocampalGyrusAnterior x
R_ParahippocampalGyrusPosterior x
R_TemporalFusiformCortexPosterior x
R_PlanumPolare x
LeftCaudate x
LeftAmygdala x
RightHippocampus x x x
—— one subject —— | population
After adjusting for hemodynamic delay and depletion…

34. Population Prior to Improve Learning for Single Subject
BIC(H) = − 2log(ℒ) + λ log(n)Bayesian Information Criterion

35. Population Prior to Improve Learning for Single Subject
BIC(H) = − 2log(ℒ) + λ log(n)Bayesian Information Criterion
Prior probability on the presence
of an edge
ϕij

36. Population Prior to Improve Learning for Single Subject
BIC(H) = − 2log(ℒ) + λ log(n)Bayesian Information Criterion
Prior probability on the presence
of an edge
ϕij
Effect of the prior probability
when adding an edge i—j
BIC(Hij) − BIC(H) − α log(
ϕij
1 − ϕij
)

37. Population Prior to Improve Learning for Single Subject
BIC(H) = − 2log(ℒ) + λ log(n)Bayesian Information Criterion
Prior probability on the presence
of an edge
ϕij
Effect of the prior probability
when adding an edge i—j
BIC(Hij) − BIC(H) − α log(
ϕij
1 − ϕij
)
sparsity
prior weight

38. Evaluation without ground truth
20

39. Evaluation without ground truth
20
• single-subject connectivity = high-confidence edges inferred on
MyConnectome data (84 scanning sessions of one individual)
- distinct from HCP data; different scanner

40. Evaluation without ground truth
20
• single-subject connectivity = high-confidence edges inferred on
MyConnectome data (84 scanning sessions of one individual)
- distinct from HCP data; different scanner
• human-generic edges = high-confidence edges learned from
Human Connectome population data

41. Evaluation without ground truth
20
• single-subject connectivity = high-confidence edges inferred on
MyConnectome data (84 scanning sessions of one individual)
- distinct from HCP data; different scanner
• human-generic edges = high-confidence edges learned from
Human Connectome population data
• subject-specific edges = high-confidence edges from single
subject that are not human-generic edges

42. Evaluation without ground truth
20
• single-subject connectivity = high-confidence edges inferred on
MyConnectome data (84 scanning sessions of one individual)
- distinct from HCP data; different scanner
• human-generic edges = high-confidence edges learned from
Human Connectome population data
• subject-specific edges = high-confidence edges from single
subject that are not human-generic edges
‣ single-subject connectivity = 60% human-generic, 40%
subject-specific

43. Evaluation without ground truth
20
• single-subject connectivity = high-confidence edges inferred on
MyConnectome data (84 scanning sessions of one individual)
- distinct from HCP data; different scanner
• human-generic edges = high-confidence edges learned from
Human Connectome population data
• subject-specific edges = high-confidence edges from single
subject that are not human-generic edges
‣ single-subject connectivity = 60% human-generic, 40%
subject-specific
• test data: two sessions (~1,000 timepoints) of single-subject
MyConnectome data

44. Evaluation without ground truth
20
• single-subject connectivity = high-confidence edges inferred on
MyConnectome data (84 scanning sessions of one individual)
- distinct from HCP data; different scanner
• human-generic edges = high-confidence edges learned from
Human Connectome population data
• subject-specific edges = high-confidence edges from single
subject that are not human-generic edges
‣ single-subject connectivity = 60% human-generic, 40%
subject-specific
• test data: two sessions (~1,000 timepoints) of single-subject
MyConnectome data
➡ How much does the prior help to learn the single-subject
connectivity from the test data?

45. Recall for human-generic and subject-specific Connectivity
human-generic edges,
recall for different
sparsities and prior weights

46. Recall for human-generic and subject-specific Connectivity
human-generic edges,
recall for different
sparsities and prior weights
subject-specific edges,
recall for different
sparsities and prior weights

47. video from Fetcho lab: http://pages.nbb.cornell.edu/neurobio/Fetcho/what-we-do-overview/; image from https://grants.nih.gov/sites/default/files/150312_zebrafish_slides.pdf
Zebrafish Larvae

48. video from Fetcho lab: http://pages.nbb.cornell.edu/neurobio/Fetcho/what-we-do-overview/; image from https://grants.nih.gov/sites/default/files/150312_zebrafish_slides.pdf
Zebrafish Larvae

49. GIF from video Ahrens M.B. et al. Nat. Methods 10, 413–420 (2013)
https://www.sfari.org/2018/09/11/sfari-workshop-discusses-zebrafish-as-experimental-systems-to-study-autism/#ref
Lightsheet Microscopy

50. GIF from video Ahrens M.B. et al. Nat. Methods 10, 413–420 (2013)
https://www.sfari.org/2018/09/11/sfari-workshop-discusses-zebrafish-as-experimental-systems-to-study-autism/#ref
Lightsheet Microscopy

51. Causal Discovery
Connections in the Brain of a Zebrafish Larva
~100,000 neurons
~250,000 direct
connections

52. Known Connections from Anatomical Studies
inferior olivecerebellum

53. inferior olivecerebellum inferior olivecerebellum
Recovered reliably across different larvae
fish 1 fish 2

54. image credit: Hildebrand et al, 2017; Janelia
The Aim: From Functional to Anatomical Connections
Anatomical Studies
Hypotheses
Causal Discovery

55. Open Questions
28

56. Open Questions
28
• What are appropriate coarse-grained parcelations of a brain?

57. Open Questions
28
• What are appropriate coarse-grained parcelations of a brain?
- How can we discover them?

58. Open Questions
28
• What are appropriate coarse-grained parcelations of a brain?
- How can we discover them?
• How do we handle time delays?

59. Open Questions
28
• What are appropriate coarse-grained parcelations of a brain?
- How can we discover them?
• How do we handle time delays?
- (sampling rate)

60. Open Questions
28
• What are appropriate coarse-grained parcelations of a brain?
- How can we discover them?
• How do we handle time delays?
- (sampling rate)
- slower vs. faster causal effects

61. Open Questions
28
• What are appropriate coarse-grained parcelations of a brain?
- How can we discover them?
• How do we handle time delays?
- (sampling rate)
- slower vs. faster causal effects
• How to model the interventions?

62. Open Questions
28
• What are appropriate coarse-grained parcelations of a brain?
- How can we discover them?
• How do we handle time delays?
- (sampling rate)
- slower vs. faster causal effects
• How to model the interventions?
- (soft vs. hard)

63. Open Questions
28
• What are appropriate coarse-grained parcelations of a brain?
- How can we discover them?
• How do we handle time delays?
- (sampling rate)
- slower vs. faster causal effects
• How to model the interventions?
- (soft vs. hard)
- time course of the intervention

64. Open Questions
28
• What are appropriate coarse-grained parcelations of a brain?
- How can we discover them?
• How do we handle time delays?
- (sampling rate)
- slower vs. faster causal effects
• How to model the interventions?
- (soft vs. hard)
- time course of the intervention
- electric stimulation vs. task fMRI vs. magnetic stimulation

65. Open Questions
28
• What are appropriate coarse-grained parcelations of a brain?
- How can we discover them?
• How do we handle time delays?
- (sampling rate)
- slower vs. faster causal effects
• How to model the interventions?
- (soft vs. hard)
- time course of the intervention
- electric stimulation vs. task fMRI vs. magnetic stimulation
• What is the relation between the observational network and
the stimulated network?

66. Open Questions
28
• What are appropriate coarse-grained parcelations of a brain?
- How can we discover them?
• How do we handle time delays?
- (sampling rate)
- slower vs. faster causal effects
• How to model the interventions?
- (soft vs. hard)
- time course of the intervention
- electric stimulation vs. task fMRI vs. magnetic stimulation
• What is the relation between the observational network and
the stimulated network?
• [scalability of methods with weaker assumptions: fast non-
parametric independence tests; non-Gaussian / non-linear
methods etc.]

67. Caltech:
• Ralph Adolphs
• Julien Dubois
• Lynn Paul
• Mike Tyszka
• Krzysztof
Chalupka
• Pietro Perona
• Yusuke Tomina
• Daniel Wagenaar
Undergraduates:
• RJ Antonello
• Lin Lin Lee
• Samuel Liebana
• John Moss
• Ethan Pronovost
• Amy Xiong
• Mark Xu
• Dan Xu
Funding:
• Chen Institute Director Award
• Caltech Carver Mead seed
grant
• AWS credit award
• NSF 1564330
• NSF 1845958
• NIH U01 NS103780-01
Janelia:
• Misha Ahrens
• Yu Mu
• Mikail Rubinov
• Greg Fleischman
UCLA / LA
Biomed:
• Paul Mathews
• Neil Harris
• Katrina Choe
• Joshua
Schoenfield
Collaborators
Thank you!