Posted by Eric Kidd Thu, 19 Apr 2007 20:43:00 GMT
Welcome to the 5th (and final) installment of Refactoring Probability Distributions! Today, let’s begin with an example from Bayesian Filters for Location Estimation (PDF), an excellent paper by Fox and colleagues.
In their example, we have a robot in a hallway with 3 doors. Unfortunately, we don’t know where in the hallway the robot is located:
The vertical black lines are “particles.” Each particle represents a possible location of our robot, chosen at random along the hallway. At first, our particles are spread along the entire hallway (the top row of black lines). Each particle begins life with a weight of 100%, represented by the height of the black line.
Now imagine that our robot has a “door sensor,” which currently tells us that we’re in front of a door. This allows us to rule out any particle which is located between doors.
So we multiply the weight of each particle by 100% (if it’s in front of a door) or 0% (if it’s between doors), which gives us the lower row of particles. If our sensor was less accurate, we might use 90% and 10%, respectively.
What would this example look like in Haskell? We could build a giant list of particles (with weights), but that would require us to do a lot of bookkeeping by hand. Instead, we use a monad to hide all the details, allowing us to work with a single particle at a time.
localizeRobot :: WPS Int localizeRobot = do -- Pick a random starting location. -- This will be our first particle. pos1 <- uniform [0..299] -- We know we're at a door. Particles -- in front of a door get a weight of -- 100%, others get 0%. if doorAtPosition pos1 then weight 1 else weight 0 -- ...
What happens if our robot drives forward?Read more...