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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
None
None
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
None
None
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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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None
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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
None
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
None
None
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
None
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]