Marco Capuccini introduces conformal prediction, a framework for assigning confidence levels to predictions from machine learning models. Conformal prediction produces a prediction set for new data instances rather than a single prediction. It guarantees the true label will be in the prediction set at least 1 - ε percent of the time, where ε is a user-specified significance level. The approach works by calibrating a model's "non-conformity measures" on labeled data, and using these to determine prediction set membership. Capuccini provides examples of applying conformal prediction to neural networks and other models. He describes using it in an application of AI-assisted pathology to generate prediction sets for histology slides with calibrated confidence.

1. How good is your prediction?
A gentle introduction to
Conformal Prediction.
Marco Capuccini
System-Software Development Group
RIKEN Center for Computational Science
marco.capuccini@riken.jp

2. Marco Capuccini
PhD
in
Scientific
C
om
puting
U
ppsala
U
niversity
Sw
eden
M
Sc
B
ioinform
atics
U
ppsala
U
niversity
Sw
eden
B
Sc
C
om
puterScience
La
Sapienza
R
om
e,Italy
Cloud / HPC
Computing
Data
Engineering
Machine
Learning
Bioinformatics
Postdoc
R
IKEN
(R
-C
C
S)
Kobe,Japan

3. RIKEN
▪ RIKEN is Japan's largest (government funded) research institution
▪ Established in 1917
▪ Research centers and institutes across Japan
…

4. Machine Learning (ML)
Machine Learning (ML) is a family of methods to derive knowledge or predictions
from data
Supervised learning:
● Given a set of objects x1
, x2
… xn
with known labels l1
, l2
…
● Goal: train a model M that can be used in order to predict unknown labels ln+1
,
ln+2
… for new objects xn+1
, xn+2
…
Application: spam filtering, text recognition, image analysis, financing, genomics,
song and movie recommendation …

5. How do we evaluate M?
Current (best) practices
1. Split x1
, x2
… xn
in a training set x1
, x2
… xk
and a test set xk+1
, xk+2
… xn
(1<k<n)
2. train M over the training set and evaluate it over the test set
What if performance changes with new objects?
How do we assign object-specific confidence to predictions?

6. Conformal Prediction
Mathematical framework (by Vovk et al.). Main idea:
● For an unseen object, instead of producing a single prediction l' a Conformal
Predictor (CP) produces a prediction set { l1
',l2
', … lK
' } according to a
user-specified significance level 𝜺
● Vovk et al. provide proof that ℙ( l ϵ { l1
',l2
', … lK
' } ) ≥ 1 - 𝜺, where l is the true label
for the unseen object
Can be applied to any ML predictor. How?
Vovk, Vladimir, Alex Gammerman, and Glenn Shafer. Algorithmic learning in a random world. Springer Science &
Business Media, 2005.

7. Neural network example
Binary classification
● The output sigmoid layer models the probability of positive class
CP wants the underlying predictor to assign a Non-Conformity Measure (NCM) to
examples; i.e. a strangeness measure for examples
● Given a labelled object (x, l)
NCM(x,l) = 1 - NN(x) if l is positive; NN(x) otherwise

8. More NCMs (1)
● Logistic regression?
● Linear Support Vector Machines?
● Random forests?
NCM(x,l) = 1 - LR(x) if l is positive; LR(x) otherwise
NCM(x,l) = -SVM(x) if l is positive, SVM(x) otherwise
NCM(x,l) = fraction of trees predicting the wrong label

9. Implementation
Idea
1. Given a new object. For each label:
● Compute “p-values” using a calibration set
2. Add label to prediction set if p-value > 𝜺. The p-values can also be used as a
measure confidence.
Details
● Shafer, Glenn, and Vladimir Vovk. "A tutorial on conformal prediction." Journal
of Machine Learning Research 9.Mar (2008): 371-421.
● http://jmlr.csail.mit.edu/papers/volume9/shafer08a/shafer08a.pdf

10. Example: AI-assisted pathology
~80K prostate biopsies from
~7.5K Swedish men
~80K slides ~5M
training tiles
Train CNN with
Inception-v3
Validation over ~500K tiles
Kaggle:
https://www.kaggle.com/c/prostate-cancer-grade-assessment

11. AI-assisted Pathology with Conformal Prediction
CNN
CP
Conformal
Predictor
For a user-defined 𝜺
CP(𝜺, x1
) = {Benignant}
CP(𝜺, x2
) = {Benignant, Cancer}
...
CP(𝜺, xn
) = {}
xk
, k=1...n is an unseen tile
By construction the true label of xk
is in the prediction set with probability at least 1- 𝜺
(Vovk et al. provide proof under exchangeability assumption)

12. Conformal Predictor Efficiency (AI-assisted Pathology)
Significance Level (𝜺)

13. Questions?
marco.capuccini@riken.jp