Post on 18-Feb-2018
transcript
What is bigdata inference?
Carey E. Priebe Department of Applied Mathematics & Statistics
Johns Hopkins University
October 30, 2012
DARPA Big Data Colloquium 2012
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 –
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.”
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
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
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
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
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
sensors bigdata
bigdataprocessing
bigdatainference
decisions /decision makers
collection management /sensor deployment
(MMDDDDS)
universe
sensors bigdata
bigdataprocessing
bigdatainference
decisions /decision makers
collection management /sensor deployment
DARPAXDATA
universe
sensors bigdata
bigdataprocessing
bigdatainference
decisions /decision makers
collection management /sensor deployment
universe
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
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
h: �
Fusion and Inference from Multiple and Massive Disparate Distributed
Dynamic Data Sets
⌅1 ⇥ · · ·⇥ ⌅K
Extract {Vi, xi, ti }i∈I
professorstudent
time
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
< > - +
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
synapsedetection
computer vision tracking of axon & dendrite to
neurons associated with synapse
graphconstruction
volume synapses neurons graph
Connectome Example
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 –