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

2. 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).

3. The Probablisitic Library Model

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

5. 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

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

7. Multiplexer