Byoung-Tak Zhang Summarized by HaYoung Jang Probabilistic Computation with DNA Molecules: The Probabilistic Library model Byoung-Tak Zhang Summarized by HaYoung Jang

Introduction Probabilistic library model How to represent the joint probability of data variables in DNA molecules (representation). How to calculate conditional probabilities of variables (inference). How to update the probability distribution from observed data (learning).

The Probablisitic Library Model

Computing Probabilities Marginal probability of A Marginal probability of B Joint probability Conditional probability

Updating Probabilty Distributions 1. Let the library L represent the current empirical distribution P(X, Y) 2. Get a training example (x, y). 3. Classify x using L as described in the previous slide. Let this class be y* 4. Update L If y* = y, then Ln  Ln-1 + {Δc(u, v)} for u = x and v = y for (u, v) ∈ Ln-1 If y* ≠ y, then Ln  Ln-1 – {Δc(u, v)} for u = x and v ≠ y for (u, v) ∈ Ln-1 5. Goto Step 2 if not terminated

Majority Function Why does it work? x1 x2 x3 y 1

Multiplexer