Week6-1Probabilities

Probabilistic reasoning

peech recognition

recognize speech and wreck a nice beach

machine translation

l’avocat general: the attorney general and the general avocado

probabilities make it possible to combine evidence from multiple sources in a systematic way.

Meaning of probabilities

Frequentist

I threw the coin 10 times and it turned up heads 5 times

Subjective

I believe the coin is fair

The chain rule

P(w1,w2,...,wn)=P(wm∣w1,...,wn−1)...P(w2∣w1)P(w1)

Independence

Two events are independent if

P(A∩B)=P(A)P(B)P(A∣B)=P(A)

Adding vs. removing constraints

Adding constraints

P(walk = yes | weather = nice, freetime = yes, …)

more accurate

more difficult to estimate

Removing constraints(back off)

P(walk = yes | weather = nice, freetime = yes, …)

P(walk = yes | weather = nice, freetime = yes)

P(walk = yes | weather = nice)

less accurate but more statistically feasibile