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CFU REU: Week 1

CFU REU: Week 1. Lam Tran. Brief Introduction. Home town: San Diego, CA University of Rochester, Rochester, NY Class 2009 Research Interest: Probability and Machine Learning. Stereo Vision (Big Picture). Learn. θ. Stereo Vision 2(Big Picture). θ. Gradient Descent.

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CFU REU: Week 1

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  1. CFU REU: Week 1 Lam Tran

  2. Brief Introduction • Home town: San Diego, CA • University of Rochester, Rochester, NY • Class 2009 • Research Interest: Probability and Machine Learning

  3. Stereo Vision (Big Picture) Learn θ

  4. Stereo Vision 2(Big Picture) θ

  5. Gradient Descent • How to get out of local minimal • Δ energy = old energy - new energy (negative) • Climb out of hill • Climb when • Rand < Exp(beta*(Δ energy )) • Rand ~ Gauss Distribution and Exp(beta* Δ energy ) ~ [0 .. 1] • When beta = 0, always move to new states. • When beta = large, move only when new energy < old energy (stuck at local minimal, similar to gradient descent).

  6. Gradient Descent • Worst case scenario • Energy gained ~ height of the hill climbed. • Avoid climbing hills with high energy change • Exp(beta*(Δ energy )) ~ inv proportional to Δ energy • Hills with higher Δ energy has a smaller probability of being climbed.

  7. Experimentation • F(x) = alpha*sin(x) with beta = 3. • 1000 trails with 100 sample sizes • Alpha = 1, mean = 99.70% • Alpha = 2, mean = 88.45% • Alpha = 4, mean = 45.11%

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