Interpreting GMStrings: The characters after the final colon

The characters after the final colon in a GMString describe how much each input should be weighted. The standard format for this description uses the nth character in the sequence to specify the weighting for the nth input variable:

• `9': indicates that the input variable should be fully weighted.
• `8': indicates that this input variable should be given a weighting of a half.
• `7': indicates that this input variable should be given a weighting of a quarter.
• The weighting continues to halve each time the number is reduced by one, meaning less and less priority should be given to this input, until ...
• `0': indicates that the input variable should be left out of the distance metric, but included globally in the regression. What locally weighted regression will do is assign weights to all the datapoints using a distance metric that ignores this input variable. But once it has the weighted datapoints, the polynomial it fits to them will include this variable. What this buys you is the ability to have some variables (those with '0' in this feature) treated globally while other variables (with scale code '1' through '9') are treated locally.
• `-': indicates that the input variable should be completely ignored.

Thus we now see that the function approximator given by our example GMString, L24:SN:93-9, ignores the third and fourth inputs entirely, weakly weights the second input, and fully weights inputs one and five.

We have now almost completed our survey of GMStrings. The one remaining detail is that curly brackets may be used to shorten the description of the input weightings. Suppose we had a large number of inputs and a GMString of:

E35:FN:90000000000000090000000000000000009000000000002000000000000000000

We would like a shorter notation for the lengthy sequence after the second colon. We notice that the characters in this sequence are all zeroes except for 9's in positions 0, 15, and 34, and a 2 in position 46 (we count from zero in the coming short-hand). This can be denoted by the following notation: {0}9[0,15,34]2[46]. The value enclosed in the curly brackets is the default weighting to be given to inputs. Any inputs with a non-default weighting are specified afterwards by listing the value they take, then, within square brackets, all the inputs that take that value.

Hence a shorter legal notation for the lengthy GMString we saw above would be: E35:FN:{0}9[0,15,34]2[46].

We have now finished our survey of GMStrings. Phew!

Note that the EYE function Predict makes its prediction in accordance with the current GMString. See section 6.2.