Merge pull request #338 from aai-institute/259-implement-class-wise-shapley

Implement class wise shapley

Author: mdbenito

CHANGELOG.md

@@ -2,6 +2,8 @@
 
 ## Unreleased
 
+- New method: Class-wise Shapley values
+  [PR #338](https://github.com/aai-institute/pyDVL/pull/338)
 - No longer using docker within tests to start a memcached server
   [PR #444](https://github.com/aai-institute/pyDVL/pull/444)
 - Faster semi-value computation with per-index check of stopping criteria (optional)
@@ -43,6 +45,9 @@ randomness.
   `compute_beta_shapley_semivalues`, `compute_shapley_semivalues` and
   `compute_generic_semivalues`.
   [PR #428](https://github.com/aai-institute/pyDVL/pull/428)
+- Added classwise Shapley as proposed by (Schoch et al. 2021)
+  [https://arxiv.org/abs/2211.06800]
+  [PR #338](https://github.com/aai-institute/pyDVL/pull/338)
 
 ### Changed
 

README.md

@@ -71,6 +71,11 @@ methods from the following papers:
   Efficient Data Value](https://proceedings.mlr.press/v202/kwon23e.html). In
   Proceedings of the 40th International Conference on Machine Learning, 18135–52.
   PMLR, 2023.
+- Schoch, Stephanie, Haifeng Xu, and Yangfeng Ji. [CS-Shapley: Class-Wise
+  Shapley Values for Data Valuation in
+  Classification](https://openreview.net/forum?id=KTOcrOR5mQ9). In Proc. of the
+  Thirty-Sixth Conference on Neural Information Processing Systems (NeurIPS).
+  New Orleans, Louisiana, USA, 2022.
 
 Influence Functions compute the effect that single points have on an estimator /
 model. We implement methods from the following papers:

docs/api/pydvl/value/shapley/classwise/img/classwise-shapley-discounted-utility-function.svg

@@ -0,0 +1,269 @@
+---
+title: Class-wise Shapley
+---
+
+# Class-wise Shapley
+
+Class-wise Shapley (CWS) [@schoch_csshapley_2022] offers a Shapley framework
+tailored for classification problems.  Given a sample $x_i$ with label $y_i \in
+\mathbb{N}$, let $D_{y_i}$ be the subset of $D$ with labels $y_i$, and
+$D_{-y_i}$ be the complement of $D_{y_i}$ in $D$. The key idea is that the
+sample $(x_i, y_i)$ might improve the overall model performance on $D$, while
+being detrimental for the performance on $D_{y_i},$ e.g. because of a wrong
+label. To address this issue, the authors introduced
+
+$$
+v_u(i) = \frac{1}{2^{|D_{-y_i}|}} \sum_{S_{-y_i}}
+\left [
+\frac{1}{|D_{y_i}|}\sum_{S_{y_i}} \binom{|D_{y_i}|-1}{|S_{y_i}|}^{-1}
+\delta(S_{y_i} | S_{-y_i})
+\right ],
+$$
+
+where $S_{y_i} \subseteq D_{y_i} \setminus \{i\}$ and $S_{-y_i} \subseteq
+D_{-y_i}$ is _arbitrary_ (in particular, not the complement of $S_{y_i}$). The
+function $\delta$ is called **set-conditional marginal Shapley value** and is
+defined as
+
+$$
+\delta(S | C) = u( S_{+i} | C ) − u(S | C),
+$$
+
+for any set $S$ such that $i \notin S, C$ and $S \cap C = \emptyset$.
+
+In practical applications, estimating this quantity is done both with Monte
+Carlo sampling of the powerset, and the set of index permutations
+[@castro_polynomial_2009]. Typically, this requires fewer samples than the
+original Shapley value, although the actual speed-up depends on the model and
+the dataset.
+
+
+!!! Example "Computing classwise Shapley values"
+    Like all other game-theoretic valuation methods, CWS requires a
+    [Utility][pydvl.utils.utility.Utility] object constructed with model and
+    dataset, with the peculiarity of requiring a specific
+    [ClasswiseScorer][pydvl.value.shapley.classwise.ClasswiseScorer]. The entry
+    point is the function
+    [compute_classwise_shapley_values][pydvl.value.shapley.classwise.compute_classwise_shapley_values]:
+
+    ```python
+    from pydvl.value import *
+    
+    model = ...
+    data = Dataset(...)
+    scorer = ClasswiseScorer(...)
+    utility = Utility(model, data, scorer)
+    values = compute_classwise_shapley_values(
+        utility,
+        done=HistoryDeviation(n_steps=500, rtol=5e-2) | MaxUpdates(5000),
+        truncation=RelativeTruncation(utility, rtol=0.01),
+        done_sample_complements=MaxChecks(1),
+        normalize_values=True
+    )
+    ```
+
+
+### The class-wise scorer
+
+In order to use the classwise Shapley value, one needs to define a
+[ClasswiseScorer][pydvl.value.shapley.classwise.ClasswiseScorer]. This scorer
+is defined as
+
+$$
+u(S) = f(a_S(D_{y_i})) g(a_S(D_{-y_i})),
+$$
+
+where $f$ and $g$ are monotonically increasing functions, $a_S(D_{y_i})$ is the
+**in-class accuracy**, and $a_S(D_{-y_i})$ is the **out-of-class accuracy** (the
+names originate from a choice by the authors to use accuracy, but in principle
+any other score, like $F_1$ can be used). 
+
+The authors show that $f(x)=x$ and $g(x)=e^x$ have favorable properties and are
+therefore the defaults, but we leave the option to set different functions $f$
+and $g$ for an exploration with different base scores. 
+
+!!! Example "The default class-wise scorer"
+    Constructing the CWS scorer requires choosing a metric and the functions $f$
+    and $g$:
+
+    ```python
+    import numpy as np
+    from pydvl.value.shapley.classwise import ClasswiseScorer
+    
+    # These are the defaults
+    identity = lambda x: x
+    scorer = ClasswiseScorer(
+        "accuracy",
+        in_class_discount_fn=identity,
+        out_of_class_discount_fn=np.exp
+    )
+    ```
+
+??? "Surface of the discounted utility function"
+    The level curves for $f(x)=x$ and $g(x)=e^x$ are depicted below. The lines
+    illustrate the contour lines, annotated with their respective gradients.
+    ![Level curves of the class-wise
+    utility](img/classwise-shapley-discounted-utility-function.svg){ align=left width=33%  class=invertible }
+
+## Evaluation
+
+We illustrate the method with two experiments: point removal and noise removal,
+as well as an analysis of the distribution of the values. For this we employ the
+nine datasets used in [@schoch_csshapley_2022], using the same pre-processing.
+For images, PCA is used to reduce down to 32 the features found by a pre-trained
+`Resnet18` model. Standard loc-scale normalization is performed for all models
+except gradient boosting, since the latter is not sensitive to the scale of the
+features.
+
+??? info "Datasets used for evaluation"
+    | Dataset        | Data Type | Classes | Input Dims | OpenML ID |
+    |----------------|-----------|---------|------------|-----------|
+    | Diabetes       | Tabular   | 2       | 8          | 37        |
+    | Click          | Tabular   | 2       | 11         | 1216      |
+    | CPU            | Tabular   | 2       | 21         | 197       |
+    | Covertype      | Tabular   | 7       | 54         | 1596      |
+    | Phoneme        | Tabular   | 2       | 5          | 1489      |
+    | FMNIST         | Image     | 2       | 32         | 40996     |
+    | CIFAR10        | Image     | 2       | 32         | 40927     |
+    | MNIST (binary) | Image     | 2       | 32         | 554       |
+    | MNIST (multi)  | Image     | 10      | 32         | 554       |
+
+We show mean and coefficient of variation (CV) $\frac{\sigma}{\mu}$ of an "inner
+metric". The former shows the performance of the method, whereas the latter
+displays its stability: we normalize by the mean to see the relative effect of
+the standard deviation. Ideally the mean value is maximal and CV minimal. 
+
+Finally, we note that for all sampling-based valuation methods the same number
+of _evaluations of the marginal utility_ was used. This is important to make the
+algorithms comparable, but in practice one should consider using a more
+sophisticated stopping criterion.
+
+### Dataset pruning for logistic regression (point removal)
+
+In (best-)point removal, one first computes values for the training set and then
+removes in sequence the points with the highest values. After each removal, the
+remaining points are used to train the model from scratch and performance is
+measured on a test set. This produces a curve of performance vs. number of
+points removed which we show below.
+
+As a scalar summary of this curve, [@schoch_csshapley_2022] define **Weighted
+Accuracy Drop** (WAD) as:
+
+$$
+\text{WAD} =  \sum_{j=1}^{n} \left ( \frac{1}{j} \sum_{i=1}^{j} 
+a_{T_{-\{1 \colon i-1 \}}}(D) - a_{T_{-\{1 \colon i \}}}(D) \right)
+= a_T(D) - \sum_{j=1}^{n} \frac{a_{T_{-\{1 \colon j \}}}(D)}{j} ,
+$$
+
+where $a_T(D)$ is the accuracy of the model (trained on $T$) evaluated on $D$
+and $T_{-\{1 \colon j \}}$ is the set $T$ without elements from $\{1, \dots , j
+\}$.
+
+We run the point removal experiment for a logistic regression model five times
+and compute WAD for each run, then report the mean $\mu_\text{WAD}$ and standard
+deviation $\sigma_\text{WAD}$.
+
+![Mean WAD for best-point removal on logistic regression. Values
+computed using LOO, CWS, Beta Shapley, and TMCS
+](img/classwise-shapley-metric-wad-mean.svg){ class=invertible }
+
+We see that CWS is competitive with all three other methods. In all problems
+except `MNIST (multi)` it outperforms TMCS, while in that case TMCS has a slight
+advantage.
+
+In order to understand the variability of WAD we look at its coefficient of
+variation (lower is better):
+
+![Coefficient of Variation of WAD for best-point removal on logistic regression.
+Values computed using LOO, CWS, Beta Shapley, and TMCS
+](img/classwise-shapley-metric-wad-cv.svg){ class=invertible }
+
+CWS is not the best method in terms of CV. For `CIFAR10`, `Click`, `CPU` and
+`MNIST (binary)` Beta Shapley has the lowest CV. For `Diabetes`, `MNIST (multi)`
+and `Phoneme` CWS is the winner and for `FMNIST` and `Covertype` TMCS takes the
+lead. Besides LOO, TMCS has the highest relative standard deviation.
+
+The following plot shows accuracy vs number of samples removed. Random values
+serve as a baseline. The shaded area represents the 95% bootstrap confidence
+interval of the mean across 5 runs.
+
+![Accuracy after best-sample removal using values from logistic 
+regression](img/classwise-shapley-weighted-accuracy-drop-logistic-regression-to-logistic-regression.svg){ class=invertible }
+
+Because samples are removed from high to low valuation order, we expect a steep
+decrease in the curve.
+
+Overall we conclude that in terms of mean WAD, CWS and TMCS perform best, with
+CWS's CV on par with Beta Shapley's, making CWS a competitive method.
+
+
+### Dataset pruning for a neural network by value transfer
+
+Transfer of values from one model to another is probably of greater practical
+relevance: values are computed using a cheap model and used to prune the dataset
+before training a more expensive one.
+
+The following plot shows accuracy vs number of samples removed for transfer from
+logistic regression to a neural network. The shaded area represents the 95%
+bootstrap confidence interval of the mean across 5 runs.
+
+![Accuracy after sample removal using values transferred from logistic
+regression to an MLP
+](img/classwise-shapley-weighted-accuracy-drop-logistic-regression-to-mlp.svg){ class=invertible }
+
+As in the previous experiment samples are removed from high to low valuation
+order and hence we expect a steep decrease in the curve. CWS is competitive with
+the other methods, especially in very unbalanced datasets like `Click`. In other
+datasets, like `Covertype`, `Diabetes` and `MNIST (multi)` the performance is on
+par with TMCS.
+
+
+### Detection of mis-labeled data points
+
+The next experiment tries to detect mis-labeled data points in binary
+classification tasks. 20% of the indices is flipped at random (we don't consider
+multi-class datasets because there isn't a unique flipping strategy). The
+following table shows the mean of the area under the curve (AUC) for five runs.
+
+![Mean AUC for mis-labeled data point detection. Values computed using LOO, CWS,
+Beta Shapley, and 
+TMCS](img/classwise-shapley-metric-auc-mean.svg){ class=invertible }
+
+In the majority of cases TMCS has a slight advantage over CWS, except for
+`Click`, where CWS has a slight edge, most probably due to the unbalanced nature
+of the dataset. The following plot shows the CV for the AUC of the five runs.
+
+![Coefficient of variation of AUC for mis-labeled data point detection. Values
+computed using LOO, CWS, Beta Shapley, and TMCS
+](img/classwise-shapley-metric-auc-cv.svg){ class=invertible }
+ 
+In terms of CV, CWS has a clear edge over TMCS and Beta Shapley.
+
+Finally, we look at the ROC curves training the classifier on the $n$ first
+samples in _increasing_ order of valuation (i.e. starting with the worst):
+
+![Mean ROC across 5 runs with 95% bootstrap
+CI](img/classwise-shapley-roc-auc-logistic-regression.svg){ class=invertible }
+
+Although at first sight TMCS seems to be the winner, CWS stays competitive after
+factoring in running time. For a perfectly balanced dataset, CWS needs on
+average fewer samples than TCMS.
+
+### Value distribution
+
+For illustration, we compare the distribution of values computed by TMCS and
+CWS.
+
+![Histogram and estimated density of the values computed by TMCS and
+CWS on all nine datasets](img/classwise-shapley-density.svg){ class=invertible }
+
+For `Click` TMCS has a multi-modal distribution of values. We hypothesize that
+this is due to the highly unbalanced nature of the dataset, and notice that CWS
+has a single mode, leading to its greater performance on this dataset.
+
+## Conclusion
+
+CWS is an effective way to handle classification problems, in particular for
+unbalanced datasets. It reduces the computing requirements by considering
+in-class and out-of-class points separately.
+