The document discusses methods for communicating classification uncertainty to end-users. It presents the misclassification method and reclassification method for estimating classification errors. The misclassification method bases error rates on true class sizes and is robust to changes in class proportions, while the reclassification method can be biased by such changes. Additional methods are proposed to estimate variance and handle multiclass problems and shifting feature distributions. The goal is to help non-experts intuitively understand uncertainty in automated classification.

1. Assessing Classification Uncertainty
From the Perspective of End-Users
Emma Beauxis-Aussalet
May 2018 1

2. Use Case
2
We count animals
to study ecosystems

3. Use Case
3
We count animals
to study ecosystems
Which species
live here?

4. Use Case
4
We count animals
to study ecosystems
Which species
live here?
How many animals
per species?

5. Use Case
5
Use computer vision!
You won’t disturb us
and you’ll save money…

6. Use Case
6
...but we need to assess
its scientific validity
Use computer vision!
You won’t disturb us
and you’ll save money…

7. Classification Problem
7
Collect examples of animals
(Ground-Truth)

8. Classification Problem
8
Collect examples of animals
(Ground-Truth)
Construct models
for each species

9. Classification Problem
9
Collect examples of animals
(Ground-Truth)
Construct models
for each species
Classify animals’ species
as the most similar model

10. Classification Problem
10
What can
go wrong?

11. Classification Problem
11
Some species
are misclassified

12. Classification Problem
12
Some species
are misclassified
Some fish
are not detected

13. Classification Problem
13
Some species
are misclassified
Other objects are
classified as fish
Some fish
are not detected

14. Classification Problem
14
Some species
are misclassified
Other objects are
classified as fish
Some fish
are not detected
Why?
When?
How many?

15. How to communicate
the uncertainty?
15
Here the Octopus appeared.
(½Φ )-(π√⅞)
How precise is this?
May 2018

16. Communication Problems
16
Why should we communicate the uncertainty?
Make informed decisions when
choosing and tuning classifiers
Estimate noise and biases in
classification results

17. Communication Problems
17
Why should we communicate the uncertainty?
Make informed decisions when
choosing and tuning classifiers
Estimate noise and biases in
classification results

18. Issues with Classifier Evaluation
18

19. Issues with Classifier Evaluation
19
It’s very tedious

20. Issues with Classifier Evaluation
20
It’s very tedious
I’m not confident
in my decisions

21. Issues with Classifier Evaluation
21
It’s very tedious
I’m not confident
in my decisions
The terminology
confuses me

22. Issues with Classifier Evaluation
22
It’s very tedious
I’m not confident
in my decisions
The terminology
confuses me
I often confuse
FP and FN

23. Issues with Classifier Evaluation
23
It’s very tedious
I’m not confident
in my decisions
The terminology
confuses me
I don’t understand
the impact on
end-results
I often confuse
FP and FN

24. Simplified Visualization
24

25. Simplified Visualization
25

26. Simplified Visualization
26

27. Simplified Visualization
27

28. Simplified Visualization
28

29. Simplified Visualization
29

30. Simplified Visualization
30

31. Simplified Visualization
31

32. Simplified Visualization
32

33. Interpretation
Numbers Proportions
33

34. Interpretation
Numbers Proportions
Sources of bias
34

35. Interpretation
Numbers Proportions
Collect more
groundtruth?
35

36. Interpretation
Numbers Proportions
Improve
classifier?
36

37. Classee Project & Online Tool
37
http://classee.project.cwi.nl
ADS project with:
Joost van Doorn
Max Welling
Lynda Hardman

38. Potential Use
38
Improve internal communication
and decision making
Build trust with partners or clients

39. Communication Problems
39
Why should we communicate the uncertainty?
Make informed decisions when
choosing and tuning classifiers
Estimate noise and biases in
classification results

40. Communication Problems
40
Why should we communicate the uncertainty?
Make informed decisions when
choosing and tuning classifiers
Estimate noise and biases in
classification results

41. Issues with Estimating Classification Errors
Time
Count of Items per Class over time
NumberofItems

42. Issues with Estimating Classification Errors
Time
Count of Items per Class over time
NumberofItems
Class A
Class A increases a lot

43. Issues with Estimating Classification Errors
Time
Count of Items per Class over time
NumberofItems
Class A
Class B
Class A increases a lot
Minority Class B increases too

44. Issues with Estimating Classification Errors
Time
Count of Items per Class over time
NumberofItems
Class A
Class B
Class A increases a lot
Minority Class B increases too
Class A items misclassified as
Class B increase too

45. Issues with Estimating Classification Errors
Time
Count of Items per Class over time
NumberofItems
Class A
Class B
Class A increases a lot
Minority Class B increases too
Class A items misclassified as
Class B increase too
Does Class B increase only
because of errors from Class A?

46. Issues with Estimating Classification Errors
Time
Count of Items per Class over time
NumberofItems
Class A
Class B
Class A increases a lot
Does Class B increase only
because of errors from Class A?
Minority Class B increases too
Class A items misclassified as
Class B increase too
Within the items classified as Class B,
how many truly belong to Class A?

47. Reclassification Method

48. Reclassification Method
Error rates based on
output class size
(e.g., Precision)

49. Reclassification Method
Number of items
Error rates based on
output class size
(e.g., Precision)

50. Reclassification Method
Number of items
truly belonging to Class X
Error rates based on
output class size
(e.g., Precision)

51. Reclassification Method
Number of items
truly belonging to Class X
and classified as Class Y
Error rates based on
output class size
(e.g., Precision)

52. Reclassification Method
Number of items
truly belonging to Class X
and classified as Class Y
Error rates based on
output class size
(e.g., Precision)
Total mumber of items
classified as Class Y
(output class size)

53. Reclassification Method
AssA
Assumption

54. Reclassification Method
AssA
Assumption
Target set

55. Reclassification Method
Error
Decomposition
for the target set

56. Reclassification Method
Class Size
for the target set

57. Reclassification Method
This method is biased
if class proportions
change

58. Reclassification Method
This method is biased
if class proportions
change
Time
Count of Items per Class over time
NumberofItems

59. Misclassification Method
This method is robust
to changes in class
proportions

60. Misclassification Method
Total number of items
truly belonging to Class X
(true class size)
Error rates based on
true class size
(e.g., Recall)

61. Results with UCI datasets
Class size estimates for 100 random splits in training, test and target sets
(Naïve bayes classifier with 10-fold cross validation)

62. Results with UCI datasets
Classifier
Output

63. Results with UCI datasets
Misclassification
method

64. Results with UCI datasets
Reclassification
method

65. Results with UCI datasets
The Misclassification method
is robust to changes in class proportions

66. Results with UCI datasets
The Misclassification method
is robust to changes in class proportions
But its results have
higher variance

67. Results with UCI datasets

68. Results with UCI datasets

69. Variance Estimation
Methods exist to estimate the variance
of the Reclassification & Misclassification methods

70. Variance Estimation
Methods exist to estimate the variance
of the Reclassification & Misclassification methods
They are applicable for test sets randomly sampled
within the target sets
Target Set
Test Set

71. Variance Estimation
Methods exist to estimate the variance
of the Reclassification & Misclassification methods
They are applicable for test sets randomly sampled
within the target sets
They are not applicable for disjoint test and target sets
Target Set
Test Set
Target Set
Test Set

72. Sample-to-Sample Method
The Sample-to-Sample method addresses disjoint test and target set
Target Set
Test Set

73. Sample-to-Sample Method
The Sample-to-Sample method addresses disjoint test and target set
randomly sampled within the same population
Target Set Test Set
Population
with actual Class X

74. Sample-to-Sample Method
Population’s
Error Rates
Target Set’s
Error Rates Test Set’s
Error Rates

75. Sample-to-Sample Method
Sample-to-Population
variance estimates
Population’s
Error Rates
Target Set’s
Error Rates Test Set’s
Error Rates

76. Sample-to-Sample Method
Sample-to-Population
variance estimates
Population-to-Sample
variance estimates
Population’s
Error Rates
Target Set’s
Error Rates Test Set’s
Error Rates

77. Sample-to-Sample Method
Sample-to-Sample
variance estimates
Target Set’s
Error Rates
Population’s
Error Rates
Test Set’s
Error Rates

78. Sample-to-Sample Method
Distribution of target set’s error rates
estimated from test set’s error rates

79. Sample-to-Sample Method
Distribution of target set’s error rates
estimated from test set’s error rates
Normal distribution
explainable with the
Central Limit Theorem

80. Sample-to-Sample Method
Distribution of target set’s error rates
estimated from test set’s error rates
Same mean for
test and target sets

81. Sample-to-Sample Method
Distribution of target set’s error rates
estimated from test set’s error rates
Variance w.r.t. test set

82. Sample-to-Sample Method
Distribution of target set’s error rates
estimated from test set’s error rates
Variance w.r.t. target set

83. Sample-to-Sample Method
Distribution of target set’s error rates
estimated from test set’s error rates
We use the class size estimates
from the Misclassification method
Variance w.r.t. target set

84. Sample-to-Sample Method
Evaluation using known n’x. to derive

85. Sample-to-Sample Method
We estimated 68% CI because
we can observe more variations than with 95% CI

86. Application of Sample-to-Sample Method

87. Application of Sample-to-Sample Method
?!

88. Application of Sample-to-Sample Method
Let’s start with binary problems,
we can expressing their solutions in a simpler form

89. Application of Sample-to-Sample Method
Let’s start with binary problems,
we can expressing their solutions in a simpler form
These are ratios of random variables…
(Cauchy distribution)

90. Application of Sample-to-Sample Method
Let’s start with binary problems,
we can expressing their solutions in a simpler form
These are ratios of random variables…
(Cauchy distribution)
...but they are correlated
(Fieller’s theorem)

91. Application of Sample-to-Sample Method
Fieller’s Theorem estimates confidence intervals’ limits
for ratios of correlated random variables

92. Application of Sample-to-Sample Method
Evaluation of Sample-to-Sample applied with Fieller’s theorem
using estimated to derive

93. Application of Sample-to-Sample Method
Evaluation of Sample-to-Sample applied with Fieller’s theorem
using estimated to derive
We achieve
accurate confidence intervals
for class size estimates

94. Application of Sample-to-Sample Method
Evaluation of Sample-to-Sample applied with Fieller’s theorem
using estimated to derive
…but intervals can be
very large for small class sizes
We achieve
accurate confidence intervals
for class size estimates

95. Application of Sample-to-Sample Method
Evaluation of Sample-to-Sample applied with Fieller’s theorem
using estimated to derive
We achieve
accurate confidence intervals
for class size estimates
…but intervals can be
very large for small class sizes
…and inaccurate for very small
class sizes or error rates

96. Application of Sample-to-Sample Method
Multiclass problems are difficult to express as a ratio
compatible with Fieller’s theorem
…but bootstrapping and simulations can address multiclass problems

97. Potential Use
97
Handle classification errors
in traffic predictions,
or computer vision systems …

98. Future Work
98May 2018

99. Future Work
99
Variance estimation for multiclass problems

100. Future Work
100
Variance estimation for multiclass problems
Guidelines for balancing the sizes of test and target sets
(smaller training sets but larger test sets may improve error estimation)

101. Future Work
101
Variance estimation for multiclass problems
Predict variance magnitude without knowledge of the target sets
(Maximum Determinant method)
Guidelines for balancing the sizes of test and target sets
(smaller training sets but larger test sets may improve error estimation)

102. Future Work
102
Variance estimation for multiclass problems
Handle shifts of error rates and feature distributions
(domain adaptation, e.g., with Bayesian classifiers)
Predict variance magnitude without knowledge of the target sets
(Maximum Determinant method)
Guidelines for balancing the sizes of test and target sets
(smaller training sets but larger test sets may improve error estimation)

103. Future Work
103
Variance estimation for multiclass problems
Fully-specified guidelines for choosing between
Reclassification or Misclassification methods. Or none.
(depending on number of classes, class sizes in test and target sets,
error rate magnitude, shifts of features distribution)
Handle shifts of error rates and feature distributions
(domain adaptation, e.g., with Bayesian classifiers)
Predict variance magnitude without knowledge of the target sets
(Maximum Determinant method)
Guidelines for balancing the sizes of test and target sets
(smaller training sets but larger test sets may improve error estimation)

104. Future Work
104
Visualizations of variance estimates
e.g., for potential target sets

105. Future Work
105
Visualizations of variance estimates
e.g., for potential target sets
Uncertainty propagation in pipelines of classifiers
e.g., with different test sets

106. Future Work
106
Visualizations of variance estimates
e.g., for potential target sets
Uncertainty propagation in pipelines of classifiers
e.g., with different test sets
Identify individual misclassifications

107. 107May 2018
Thank you!
Questions?

108. 108May 2018
Thank you!
Questions?
Other uncertainty factors?
Shift of feature distributions?
Predic variance magnitude?
Misclassification method
explained?

109. 109May 2018

110. October 2017 IEEE Conference on Data Science and Advanced Analytics (DSAA)
Varying Feature Distributions

111. Varying Feature Distributions
If the feature distributions vary between test and target set,
classifiers may behave differently

112. Varying Feature Distributions
The error rates may systematically differ between test and target sets,
and the Misclassification and Reclassification Methods
can greatly worsen the classification biases
If the feature distributions vary between test and target set,
classifiers may behave differently

113. Varying Feature Distributions
Examples with simulated data

114. Varying Feature Distributions
Future work is required to handle varying feature distributions

115. Varying Feature Distributions
Regressions can be fit to infer error rates from feature values,
but this approach is more complex with the Misclassification Method
Future work is required to handle varying feature distributions

116. Varying Feature Distributions
Regressions can be fit to infer error rates from feature values,
but this approach is more complex with the Misclassification Method
Future work is required to handle varying feature distributions
…but the Misclassification Method can be used to
refine priors in Bayesian classifiers
(i.e., the unconditional class probabilities)

117. 117May 2018

118. Ratio-to-TP Method
This method gives
exactly the same results as
the Misclassification
method

119. Ratio-to-TP Method
Atypical Ratio
(Cauchy distribution)

120. Ratio-to-TP Method
Number of
True Positives (TP)
Atypical Ratio
(Cauchy distribution)

121. Ratio-to-TP Method
Number of TP
for the target set

122. Ratio-to-TP Method

123. May 2018
Predicting the Results Variance
Maximum Determinant Method
123

124. Maximum Determinant Method
When starting an application, several classifiers may be available
with no knowledge of the potential target sets

125. Maximum Determinant Method
To choose a classifier, the Maximum Determinant Method aims at
predicting which classifier yields the smallest variance
when applying the Misclassification Method
When starting an application, several classifiers may be available
with no knowledge of the potential target sets

126. Maximum Determinant Method
Hypothesis: The higher the determinant of the error rate matrix,
the lower the results variance.

127. Maximum Determinant Method
Hypothesis: The higher the determinant of the error rate matrix,
the lower the results variance.

128. Maximum Determinant Method
Hypothesis: The higher the determinant of the error rate matrix,
the lower the results variance.
Inspired by
Cramer’s rule

129. Evaluation with UCI datasets
Maximum Determinant Method

130. Maximum Determinant Method
Comparison between Misclassification & Ratio-to-TP error rate matrices

131. Maximum Determinant Method
Initial results are promising but theory must be established

132. Maximum Determinant Method
What are the parameters of relationship between the determinant
and the variance of misclassification results?
(number of classes, class sizes in test and target sets, error rate magnitude)
Initial results are promising but theory must be established

133. Maximum Determinant Method
Initial results are promising but theory must be established
Binary problems for which the method is irrelevant?
What are the parameters of relationship between the determinant
and the variance of misclassification results?
(number of classes, class sizes in test and target sets, error rate magnitude)

134. Maximum Determinant Method
Initial results are promising but theory must be established
Problems for which Misclassification or Ratio-to-TP error rates
provide better predictors?
Binary problems for which the method is irrelevant?
What are the parameters of relationship between the determinant
and the variance of misclassification results?
(number of classes, class sizes in test and target sets, error rate magnitude)

135. 135May 2018

136. Misclassification Method
Assumption

137. Misclassification Method
Error
Decomposition

138. Misclassification Method
Class size estimates
are needed
Error
Decomposition

139. Misclassification Method

140. Misclassification Method

141. Misclassification Method

142. Misclassification Method
Solution of the
linear equations

143. Misclassification Method
True class size
estimates
for the target set

144. Ratio-to-TP Method
Assumption

145. Ratio-to-TP Method
Error
Decomposition

146. Ratio-to-TP Method
Error
Decomposition
TP estimates
are needed

147. Ratio-to-TP Method
Always invertible if all
c = number of classes

148. 148May 2018

149. Interactions of Uncertainty Factors
149
Classification
Errors

150. Interactions of Uncertainty Factors
150
Poor ground-truth
yields poor models
Ground-Truth
Quality
Classification
Errors

151. Interactions of Uncertainty Factors
151
Poor images
yield more errors
Ground-Truth
Quality
Classification
Errors
Image Quality

152. Interactions of Uncertainty Factors
152
Typhoons yield poor images? (bias)
What confidence intervals? (noise)
Ground-Truth
Quality
Classification
Errors
Biases & Noise
in Specific Output
Image Quality

153. Interactions of Uncertainty Factors
153
Missing videos?
Sampling
Coverage
Ground-Truth
Quality
Classification
Errors
Biases & Noise
in Specific Output
Image Quality

154. Interactions of Uncertainty Factors
154
Some species often move
in & out the field of view
Sampling
Coverage
Duplicated
Individuals
Ground-Truth
Quality
Classification
Errors
Biases & Noise
in Specific Output
Image Quality

155. Interactions of Uncertainty Factors
155
Fields of view
target specific habitats
Sampling
Coverage
Duplicated
Individuals
Field of View
Ground-Truth
Quality
Classification
Errors
Biases & Noise
in Specific Output
Image Quality

156. Interactions of Uncertainty Factors
156
Fields of view
target specific habitats
and shift overtime
Sampling
Coverage
Duplicated
Individuals
Field of View
Ground-Truth
Quality
Classification
Errors
Biases & Noise
in Specific Output
Image Quality

157. Interactions of Uncertainty Factors
157
Sampling
Coverage
Duplicated
Individuals
Field of View
Ground-Truth
Quality
Classification
Errors
Biases & Noise
in Specific Output
Image Quality

158. Interactions of Uncertainty Factors
158

159. Lessons Learned
159
Uncertainty factors arise from the system
and its deployement conditions

160. Lessons Learned
160
Uncertainty factors arise from the system
and its deployement conditions
Investigations should include
domain experts and technical experts
…and non-experts!

161. Lessons Learned
161
Uncertainty factors arise from the system
and its deployement conditions
Investigations should include
domain experts and technical experts
…and non-experts!
People need to feel comfortable
to engage in criticism

162. 162May 2018

163. Classee: Experimental Results
163

164. Classee: Experimental Results
164

165. Existing Metrics & Visualizations
165
Confusion
Matrix

166. Existing Metrics & Visualizations
166
Typical
Visualization

167. Existing Metrics & Visualizations
167

168. Existing Metrics & Visualizations
168

169. Existing Metrics & Visualizations
169
Diagonals are correct animals.
(TP)
The rest are errors.

170. Existing Metrics & Visualizations
170
Columns are missed animals.
(FN)

171. Existing Metrics & Visualizations
171
Rows are added animals.
(FP)

172. Existing Metrics & Visualizations
172

173. Existing Metrics & Visualizations
173
Rows & Columns
are cumulated

174. Existing Metrics & Visualizations
174
Advanced
measurements
are repeated

175. 175
Issues Tackled

176. 176
Issues Tackled
Some metrics
conceal uncertainty

177. 177
Issues Tackled
Using one single type of curve
can hide differences
Some metrics
conceal uncertainty

178. 178
Issues Tackled
Some metrics
conceal uncertainty
The metrics omit which species
are confused with another
Using one single type of curve
can hide differences

179. 179
Issues Tackled
Some metrics
conceal uncertainty
Using one single type of curve
can hide differences
…and omit species proportions
The metrics omit which species
are confused with another