How SVMs can Estimate Quantiles and the Median
I. Steinwart and A. Christmann, Poster W4 Fact: Minimizing the risk of absolute loss yields the median. Q1: When is this efficient? A1: If there is enough mass around the median. Q1: Can we use the -insensitive loss? A2: Only sometimes.
efficient with | . |
0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -4 0.5

not efficient with | . |
0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -4

median 

median 

-3

-2

-1

0

1

2

3

4

-3

-2

-1

0

1

2

3

4

0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -4

OK with -loss
median  - 
1

-loss not suitable
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1



median   estimate -   smallest estimate  largest  estimate

-3

-2

-1

0

1

2

3

4

0 -4

-3

-2

-1

0

1

2

3

4

Consequence: Rates for estimating quantiles and the median with SVMs.