Guess-Averse Loss Functions for Cost Sensitive Multiclass Boosting
Oscar Beijbom, Mohammad Saberian, David Kriegman, Nuno Vasconcelos
Multiclass cost-sensitive learning
“good” surrogate loss properties:
Different errors have different cost:
Confusing image of cat with human is
more costly than confusing images of cat
and dogs.
Coral example:
Cost matrix
Several coral
Pocillopora
0
1
3
genera, but similar
ecological
function.
1
0
3
Porites
Cost is higher for
Macro algae
3
3
0
errors across
functional groups.
Classification calibration: The optimal
score function recovered from
minimizing the surrogate risk yields same
decisions as the Bayes decision rule.
Margin maximizing: A loss is margin
maximizing if minimizing the surrogate
risk also maximizes the margin
Losses with these properties may still
perform poorly in practice!!!
A new property: Guess-Aversion
How to incorporate cost of different
errors into Multiclass Boosting?
Problem Definition
A multiclass classifier is a set of score functions
which predicts class of largest score as the
label, i.e.
The optimal score function, minimizes
and implements Bayes decision rule
where
Many learning algorithms rely on a surrogate loss
function
and train score functions by minimizing
What is a good surrogate loss function for
cost-sensitive multiclass boosting?
non-guess-averse
guess-averse
loss surface for class 1
Lemma: Let :R ! R be a monotonically increasing function and : R ! R a
function satisfying
then
Define support sets
is a guess-averse loss function.
Experiments on UCI and Coral Data:
-a surrogate loss for a
sample (xi, zi) should have
low loss in
Performance Measure: empirical cost of classification,
Loss functions:
- when all scores are
equal, i.e. S = [0, 0, 0], the
classifier must resort to
arbitrary guessing.
loss surface for class 1
Definition: In a guess-averse loss, scores
that lead to correct classification have
lower loss than random guessing scores.
Most binary losses are guess-averse…
- Guess-averse losses
performed significantly better
that non-guess-averse ones!
- Code is available at
http://vision.ucsd.edu/~beijbom/f
iles/ICML_2014_guess_averse_co
de_data.zip