-
Notifications
You must be signed in to change notification settings - Fork 8
/
connectomics19.html
413 lines (256 loc) · 9.56 KB
/
connectomics19.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
<!DOCTYPE html>
<html>
<head>
<title>Connectomics19</title>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/>
<link rel="stylesheet" href="fonts/quadon/quadon.css">
<link rel="stylesheet" href="fonts/gentona/gentona.css">
<link rel="stylesheet" href="slides_style.css">
<script type="text/javascript" src="assets/plotly/plotly-latest.min.js"></script>
</head>
<body>
<textarea id="source">
name:opening
## Statistical Foundations for Connectomics
Joshua T. Vogelstein
<img src="images/neurodata_purple.png" style="height:250px; float:right;"/>
<br><br><br><br><br><br><br><br><br><br>
<img src="images/funding/jhu_bme_blue.png" STYLE="HEIGHT:95px;"/>
<img src="images/funding/KNDI.png" STYLE="HEIGHT:95px;"/>
.foot[[jovo@jhu.edu](mailto:[email protected]) | <http://neurodata.io/talks/> | [@neuro_data](https://twitter.com/neuro_data)]
---
### Why do we rely on statistics for scientific evidence?
some (old dead) dudes/women:
0. had an interesting biological question (eg, lady tasting tea)
1. invented some wrong but useful models (eg, Gaussian, Poisson)
2. derived some estimators (eg, minimal mean squared error)
3. proved some theorems (eg, t-test works when data are Gaussian)
4. conducted extensive simulated and real data experiments substantiating theorems
---
.center[<img src="faces/cep.png" STYLE="width:90%"/>]
---
### while you guys were heroically
1. designing microscopes
2. getting better data
3. building computational infrastructure
4. developing machine vision
we've been doing statistics for networks,
and hopefully have enough stuff that some of it might be useful for you
---
### What are interesting biological questions?
Sydney Brenner the two questions are:
“.r[genetic specification of nervous systems] and ... .purple[nervous systems work to produce behavior].”
--
Formalizing the above, given that we model the brain as a network
- .r[ Pr[ Connectome | Genome ]]
- .purple[ Pr [ Behavior | Connectome]]
---
### Following Brenner from a stats perspective motivates:
0. have an interesting biological question (eg, bilateral homology)
1. invent some wrong but useful models (eg, DC-SBM)
2. derive some estimators (eg, minimal mean squared error)
3. prove some theorems (eg, two-sample tests work)
4. conduct extensive simulated and real data experiments
---
### Larval Drosophila Mushroom Body
<img src="images/drosophila_left_mb2.png" STYLE="width:70%"/>
---
### Erdős–Rényi
<img src="images/drosophila_left_mb2.png" STYLE="width:49%"/>
<img src="images/ERgraph.png" STYLE="width:49%"/>
- all edges are independent and identically distributed
---
### Stochastic Block Model (SBM)
<img src="images/drosophila_left_mb2.png" STYLE="width:49%"/>
<img src="images/SBMgraph.png" STYLE="width:49%"/>
- all edges are independent and identically distributed **within a block**
---
### Degree-Corrected SBM
<img src="images/drosophila_left_mb2.png" STYLE="width:49%"/>
<img src="images/DCSBMgraph.png" STYLE="width:49%"/>
- all edges are independent and identically distributed **within a block**, and
- each node has a *promiscuity* parameter
---
### Random Dot Product Graph
<img src="images/drosophila_left_mb2.png" STYLE="width:49%"/>
<img src="images/RDPGgraph.png" STYLE="width:49%"/>
- all nodes have a latent position in some d-dimensional space
- the probability of an edge between a pair of nodes is equal to the dot product of their latent positions
---
### Inhomogeneous Erdős–Rényi
<img src="images/drosophila_left_mb2.png" STYLE="width:49%"/>
<img src="images/drosophila_left_mb2.png" STYLE="width:49%"/>
- all edges are independent and **not identically distributed**
- a perfect (over-) fit
---
### Model Complexities
<img src="images/bar.png" STYLE="width:90%"/>
---
### Conclusions so far
- We have models, estimators, theorems, numerical experiments
- Questions we can ask next:
- are left and right different? if so how? where?
- are left and right independent?
- how does training change? where does it change?
### References
1. Vogelstein JT, et al. [*Connectal Coding: Discovering the Structures Linking Cognitive Phenotypes to Individual Histories.*](https://github.com/neurodata/neurodata.io/raw/deploy/source/docs/Connectal_Coding.pdf) Current Opinion in Neurobiology, April 2019.
2. Chung, J et al. [*GraSPy: Graph Statistics in Python.*](https://arxiv.org/abs/1904.05329) arXiv, 2019.
.center[https://neurodata.io/graspy/]
---
class: middle, inverse
### .center[your slide here!]
---
### Acknowledgements
<div class="small-container">
<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>
</div>
<div class="small-container">
<img src="faces/mim.jpg"/>
<div class="centered">Michael Miller</div>
</div>
<div class="small-container">
<img src="faces/dtward.jpg"/>
<div class="centered">Daniel Tward</div>
</div>
<div class="small-container">
<img src="faces/ebridge.jpg"/>
<div class="centered">Eric Bridgeford</div>
</div>
<div class="small-container">
<img src="faces/vikram.jpg"/>
<div class="centered">Vikram Chandrashekhar</div>
</div>
<div class="small-container">
<img src="faces/drishti.jpg"/>
<div class="centered">Drishti Mannan</div>
</div>
<div class="small-container">
<img src="faces/jesse.jpg"/>
<div class="centered">Jesse Patsolic</div>
</div>
<div class="small-container">
<img src="faces/falk_ben.jpg"/>
<div class="centered">Benjamin Falk</div>
</div>
<div class="small-container">
<img src="faces/kwame.jpg"/>
<div class="centered">Kwame Kutten</div>
</div>
<div class="small-container">
<img src="faces/perlman.jpg"/>
<div class="centered">Eric Perlman</div>
</div>
<div class="small-container">
<img src="faces/loftus.jpg"/>
<div class="centered">Alex Loftus</div>
</div>
<div class="small-container">
<img src="faces/bcaffo.jpg"/>
<div class="centered">Brian Caffo</div>
</div>
<div class="small-container">
<img src="faces/minh.jpg"/>
<div class="centered">Minh Tang</div>
</div>
<div class="small-container">
<img src="faces/avanti.jpg"/>
<div class="centered">Avanti Athreya</div>
</div>
<div class="small-container">
<img src="faces/vince.jpg"/>
<div class="centered">Vince Lyzinski</div>
</div>
<div class="small-container">
<img src="faces/dpmcsuss.jpg"/>
<div class="centered">Daniel Sussman</div>
</div>
<div class="small-container">
<img src="faces/youngser.jpg"/>
<div class="centered">Youngser Park</div>
</div>
<div class="small-container">
<img src="faces/cshen.jpg"/>
<div class="centered">Cencheng Shen</div>
</div>
<div class="small-container">
<img src="faces/shangsi.jpg"/>
<div class="centered">Shangsi Wang</div>
</div>
<div class="small-container">
<img src="faces/tyler.jpg"/>
<div class="centered">Tyler Tomita</div>
</div>
<div class="small-container">
<img src="faces/james.jpg"/>
<div class="centered">James Brown</div>
</div>
<div class="small-container">
<img src="faces/disa.jpg"/>
<div class="centered">Disa Mhembere</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>
</div>
<div class="small-container">
<img src="faces/gkiar.jpg"/>
<div class="centered">Greg Kiar</div>
</div>
<div class="small-container">
<img src="faces/jeremias.png"/>
<div class="centered">Jeremias Sulam</div>
</div> <span style="font-size:200%; color:red;">♥, 🦁, 👪, 🌎, 🌌</span>
<img src="images/funding/nsf_fpo.png" STYLE="HEIGHT:95px;"/>
<img src="images/funding/nih_fpo.png" STYLE="HEIGHT:95px;"/>
<img src="images/funding/darpa_fpo.png" STYLE=" HEIGHT:95px;"/>
<img src="images/funding/iarpa_fpo.jpg" STYLE="HEIGHT:95px;"/>
<img src="images/funding/KAVLI.jpg" STYLE="HEIGHT:95px;"/>
<img src="images/funding/schmidt.jpg" STYLE="HEIGHT:95px;"/>
---
class:center
<img src="images/lion_l2m.JPG" style="position:absolute; top:0px; left:0px; height:100%;"/>
---
### Drosophila Brain Networks
<img src="images/Fig15-new.png" style="width:800px;"/>
---
### Latent Structure Model
<img src="images/drosophila_left_mb2.png" STYLE="width:49%"/>
<img src="images/sbmlsm_graph.png" STYLE="width:49%"/>
---
### Geodesic Learning Drosophila Brain
<img src="images/drosphila_precision_recall.png" style="width:800px;"/>
---
### Drosophila Optic Medulla
<img src="images/hsbm.png" STYLE="width:80%"/>
.foot[Takemura et al., 2013]
</textarea>
<!-- <script src="https://gnab.github.io/remark/downloads/remark-latest.min.js"></script> -->
<script src="remark-latest.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.5.1/katex.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.5.1/contrib/auto-render.min.js"></script>
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.5.1/katex.min.css">
<script type="text/javascript">
var options = {};
var renderMath = function() {
renderMathInElement(document.body);
// or if you want to use $...$ for math,
renderMathInElement(document.body, {delimiters: [ // mind the order of delimiters(!?)
{left: "$$", right: "$$", display: true},
{left: "$", right: "$", display: false},
{left: "\\[", right: "\\]", display: true},
{left: "\\(", right: "\\)", display: false},
]});
}
var slideshow = remark.create(options, renderMath);
</script>
</body>
</html>