hilbert space of stationary ergodic processesdml.cs.byu.edu/icdm17ws/ishanu.pdfhilbert space of...
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Hilbert Space of Stationary Ergodic Processes
Ishanu chattopadhyay
University of Chicago
D3M Workshop ICDM 2017
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Angle?
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WhyAngles
● Intrinsic Geometry● Riemannian Structure● Projections, optimizations
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Classification Prediction
Features
Samples
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Time Series
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Time Series
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Time Series
● Prediction● Classification● Understanding
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Time Series
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Time Series
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Time Series
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Stochastic Processes
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Random Walk
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Random Walk
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Probabilistic Finite Automata
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Learning Probabilistic Finite Automata
I. Chattopadhyay and H. Lipson , "Abductive learning of quantized stochastic processes with probabilistic finite automata.", Philosophical Transactions of The Royal Society A, Vol. 371(1984), Feb 2013, pp 20110543.
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Probabilistic Finite Automata
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Probabilistic Finite Automata
Ergodic stationaryFinite Valued process
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Algebraic Structures on Model Space
Abelian Group19
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Zero Machine
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Algebraic Structures on Model Space
Multiplication by scalars
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Algebraic Structures on Model Space
Multiplication by scalars
System of Equations
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Data smashing
I. Chattopadhyay and H. Lipson , "Data Smashing: Uncovering Lurking Order In Data", Royal Society Interface, 11: 20140826
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where X,Y are probabilistic finite automata
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TangentsNormalsInner Product
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TangentsNormalsInner Product
iid processes26
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ConstructionFor prob.vectors
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Inner Product
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Geodesicspace
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GeodesicSpace:
Every noise corruption is a spiral
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Resistance To Noise Corruption
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Identify Intrinsic geometry of dataNew Classification Algorithms
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