darpa big data colloquium 2012 - department of applied ...priebe/.files/cep-xdata-keynote.pdf ·...
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What is bigdata inference?
Carey E. Priebe Department of Applied Mathematics & Statistics
Johns Hopkins University
October 30, 2012
DARPA Big Data Colloquium 2012
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Kronecker Quote
“The wealth of your practical experience with sane and interesting problems
will give to mathematics a new direction and a new impetus.”
– Leopold Kronecker to Hermann von Helmholtz –
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What is mathematics?
“The wealth of your practical experience with sane and interesting problems
will give to mathematics a new direction and a new impetus.”
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What is mathematics?
“The wealth of your practical experience with sane and interesting problems
will give to mathematics a new direction and a new impetus.”
With appologies toRichard Courant
andHerbert Robbins
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What is mathematics?
“The wealth of your practical experience with sane and interesting problems
will give to mathematics a new direction and a new impetus.”
Mreality
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What is mathematics?
“The wealth of your practical experience with sane and interesting problems
will give to mathematics a new direction and a new impetus.”
Mreality
Mmathematics
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What is mathematics?
“The wealth of your practical experience with sane and interesting problems
will give to mathematics a new direction and a new impetus.”
Applied
^Mreality
Mmathematics
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What is mathematics?
“The wealth of your practical experience with sane and interesting problems
will give to mathematics a new direction and a new impetus.”
Applied
^Mreality
Mmathematics
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sensors bigdata
bigdataprocessing
bigdatainference
decisions /decision makers
collection management /sensor deployment
(MMDDDDS)
universe
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sensors bigdata
bigdataprocessing
bigdatainference
decisions /decision makers
collection management /sensor deployment
DARPAXDATA
universe
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sensors bigdata
bigdataprocessing
bigdatainference
decisions /decision makers
collection management /sensor deployment
universe
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Extract {Vi, xi, ti }i∈I
time
h:
Fusion and Inference from Multiple and Massive Disparate Distributed
Dynamic Data Sets
Generate Time Series of Attributed Graphs
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time
h:
Fusion and Inference from Multiple and Massive Disparate Distributed
Dynamic Data Sets
�Generate Time Series of Attributed Graphs
⌅1 ⇥ · · ·⇥ ⌅K
Extract {Vi, xi, ti }i∈I
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h: �
Fusion and Inference from Multiple and Massive Disparate Distributed
Dynamic Data Sets
⌅1 ⇥ · · ·⇥ ⌅K
Extract {Vi, xi, ti }i∈I
professorstudent
time
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Anomaly Detection in Time Series of Attributed Graphs
h: �
Fusion and Inference from Multiple and Massive Disparate Distributed
Dynamic Data Sets
time
⌅1 ⇥ · · ·⇥ ⌅K
Extract {Vi, xi, ti }i∈I
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< > - +
The curse of dimensionality
g!
M(d)
!gn(d)
g!(d)
L(!gn(d)) "#d#$
12
L(g!(d)) "#d#$ 0
d0
12
L(!gn(d))
doptn
October 2003 – p.5/35
The Curse of Dimensionality
Dennis M. Healy
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synapsedetection
computer vision tracking of axon & dendrite to
neurons associated with synapse
graphconstruction
volume synapses neurons graph
Connectome Example
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Kronecker Quote
“The wealth of your practical experience with sane and interesting problems
will give to mathematics a new direction and a new impetus.”
– Leopold Kronecker to Hermann von Helmholtz –