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Active Learning in an Information-rich Age

Active Learning in an Information-rich Age. Early 20 th century, how do you study physics? Early 21 st century, how do you study wavelets?. Use Tools Like Caveman Did. Publish or Perish (a good tool for scientific research). http://www.harzing.com/resources.htm#/pop.htm.

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Active Learning in an Information-rich Age

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  1. Active Learning in an Information-rich Age • Early 20th century, how do you study physics? • Early 21st century, how do you study wavelets?

  2. Use Tools Like Caveman Did Publish or Perish (a good tool for scientific research) http://www.harzing.com/resources.htm#/pop.htm

  3. Small-World Phenomenon Schröder Morlet, Grossmann Mayer Sweldens Daubechies Vaidyanathan Mallat DeVore Vertteli Donoho Coifman Johnstone

  4. Signal Denoising Studyby Toy Examples taken from Donoho’s paper “Translation-invariant Denoising”

  5. Four Classes of Signals

  6. Noisy Observations Y=X+W W~N(0,1)

  7. An Easy Attack • Use a Low-Pass filter such as moving averaging • Why low-pass? • What if noise is periodic? • How far are we from the optimal performance?

  8. A Different Class of Signal

  9. A Different Class of Noise ECG signal

  10. Signal in Nature • Self-similar property (Global) • 1/f noise is a signal or process with a frequency spectrum such that the power spectral density is proportional to the reciprocal of the frequency • Transient/nonstationary property (Local) • Changes in space and time • Motivate the study of wavelet transforms

  11. Noise in Nature • Always Gaussian? • Stationary or transient? • Random or structural (perceptually meaningful)?

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