Presentation on theme: "CFU REU: Week 1 Lam Tran. Brief Introduction Home town: San Diego, CA University of Rochester, Rochester, NY – Class 2009 – Research Interest: Probability."— Presentation transcript:
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).
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.
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%