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Making Scores with HiScore
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Hakka Labs
February 13, 2015
Programming
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Making Scores with HiScore
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Hakka Labs
February 13, 2015
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Transcript
Making Scores with HiScore Abe Othman
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None
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HiScore is a python library for creating and maintaining scores
It uses a novel quasi-Kriging solution to a new methodology,
supervised scoring
What are scores?
Scores are a tool for domain experts to communicate their
expertise to a broad audience
88 51 27
} 58 Score Function Dimensions Score
There is no one correct scoring function
Scores are typically developed using the dual approach
1. Select a set of basis functions f(x ⃗) =
∑ γᵢφᵢ(x ⃗)
2. Adjust coefficients until things look right f(x ⃗) =
∑ γᵢφᵢ(x ⃗)
Dual scores ossify
Walkscore Problems Score of 100, but the highest crime in
SF
Supervised scoring: a primal approach
Experts start by labeling a reference set and the objects’
dimensions
Algorithm makes a scoring function that interpolates and obeys the
monotone relationship
Some nice features
Monotonicity is important for score acceptance and understanding
See a mis-scored point? Add it to the reference set
and re-run!
OK, but what algorithm?
Easy in one dimension
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Hard in many dimensions
Failed approach: simplical interpolation
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Failed approach: B-spline product bases
Supervised Scoring with Monotone Multidimensional Splines, AAAI 2014
Curse of dimensionality!
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Failed approach: RBF with monotone row generation constraints
Failed approach: Neural Networks
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Success: Beliakov
Reminder: Lipschitz Continuity |f(a)-f(b)| < C |a-b|
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Monotone Lipschitz continuity
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1. Project monotone Lipschitz cones from each point to generate
upper and lower bounds
2. Find the sup and inf constraints from the bounding
cones
3. Function value is halfway in-between the sup and inf
bounds
Beliakov example
Beliakov plateaux
Beliakov plateaux
How can we smooth and improve this?
Abandon Lipschitz, just project minimal cones from each point
None
`
HiScore solution
Using HiScore: Simplified Water Well Score
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Two factors: Distance from nearest latrine and platform size
Label a reference set by taking high, middle and low
values in each dimension
Distance: 0m, 10m, 50m Size: 1SF, 25SF, 100SF
Score Distance Size 0 0 1 5 0 25 10
0 100 20 10 1 50 10 25 60 10 100 65 50 1 90 50 25 100 50 100 Monotone Relationship: (+, +)
import hiscore reference_set = {(0,1): 0, (0,25): 5, (0,100): 10,
(10,1): 20, (10,25): 50, … } mono_rel = [1,1] hiscore.create(reference_set, mono_rel, minval=0, maxval=100)
None
Complicate the model with additional factors
Avoid curse of dimensionality by building a tree
None
Possible to easily construct and understand scores with dozens of
input dimensions
Making dimensions monotone: blood pressure
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S+ > 0 S- = 0 D+ > 0 D-
= 0 D+ = 0 D- > 0 S+ = 0 S- > 0
What do you want to score? github.com/aothman/ hiscore $ pip
install hiscore
Thanks!
[email protected]