Defining Probabilistic Models Using Decision Tables

Suppose I tell you I have a yellow object and ask you to identify it. It could be (among many other things)

• A banana
• A lemon
• A submarine (if you are old enough to remember the Beatles)

But its considerably less likely that it’s a submarine.

And if also tell you its long then its less likely to be a lemon. And if I say that its small, this adds more weight to it being a banana.

But at no point can we conclusively say what it is.

So how can we model rules that deal with this uncertainty

Each new piece of data about the object (eg color=yellow, size=small, shape=long) will increase or decrease the likelihood of the object being a particular thing (eg submarine or banana) So we need to be able to maintain a collection of things that the object might be (along with a measure of certainty that it is that thing) Then as other rules fire we need to be able to adjust our certainty.

If we know the color is red then its definitely NOT a banana If we know the color is yellow then it might be a banana with a certainty of .5 or a submarine with a certainty of 0.0001 But if we also know that its size is large then its more likely to be a submarine than a banana

What about Partial Evidence

If the only thing we know is that its yellow it could be a banana, a lemon or a submarine.

So is there a way we can accommodate the several possible for and given variable?

If we only know its yellow it could be a banana, a lemon or a submarine So how do we accommodate the several possibilities?

If We Know the Color Then we can assign some certainties about EACH of the things it might be. -1.0 means it cannot be that thing

• If we know the Shape
• Based on the object’s shape we can assign other certainties about what it might be
• If We Know The Size
• Then there are other certainties about what it might be
• Combining Certainties
• Different degrees of certainty that it might be a particular thing can be combined
• Choose the Most Likely Outcome
• Compare the certainty of two conclusions
• Remove the conclusion that’s less likely
• Display the remaining Conclusion(s)