Monthly Archives: February 2014

Boots: New Machine Learning Approaches to Modeling Dynamical Systems

Large streams of data, mostly unlabeled.

Machine learning approach to fit models to data. How does it work? Take the raw data, hypothesize a model, use a learning algorithm to get the model parameters to match the data.

What makes a good machine learning algorithm?

  • Performance guarantees: \(\theta \approx \theta^*\) (statistical consistency and finite sample bounds)
  • Real-world sensors, data, resources (high-dimensional, large-scale, ...)

For many types of dynamical systems, learning is provably intractable. You must choose the right class of model, or else all bets are off!

Look into:

  • Spectral Learning approaches to machine learning

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Basener: Topological and Bayesian Methods in Data Science

  • Topology: Encompasses the global shape of the data, and the relations between data points or groups within the global structure
    • Google Pagerank Algorithm
    • Example: Cosmic Crystallography
      • Torus universe (zero curvature)
      • Spherical universe (positive curvature)
      • Other universe (negative curvature)
  • Data: Hyperspectral Imagery
  • Gradient Flow Algorithm
    • identify neighbor with highest density for each data point (arrow points from that point to that particular neighbor)
      • gives a data field
    • follow the arrows to identify clusters

people.rit.edu/wfbsma/data/NINJA_MAIN_self_test_refl_RX.img.html

 

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