How lime explains stuff
Behind the workings of lime lies the (big) assumption that every
complex model is linear on a local scale. While this is not justified in
the paper it is not difficult to convince yourself that this is
generally sound — you usually expect two very similar observations to
behave predictably even in a complex model. lime then takes
this assumption to its natural conclusion by asserting that it is
possible to fit a simple model around a single observation that will
mimic how the global model behaves at that locality. The simple model
can then be used to explain the predictions of the more complex model
locally.
The general approach lime takes to achieving this goal
is as follows:
- For each prediction to explain, permute the observation
n times.
- Let the complex model predict the outcome of all permuted
observations.
- Calculate the distance from all permutations to the original
observation.
- Convert the distance to a similarity score.
- Select
m features best describing the complex model
outcome from the permuted data.
- Fit a simple model to the permuted data, explaining the complex
model outcome with the
m features from the permuted data
weighted by its similarity to the original observation.
- Extract the feature weights from the simple model and use these as
explanations for the complex models local behavior.
It is clear from the above that there’s much wiggle-room in order to
optimize the explanation. Chief among the choices that influence the
quality of the explanation is how permutations are created, how
permutation similarity is calculated, how, and how many, features are
selected, and which model is used as the simple model. Some of these
choices are hard-coded into lime, while others can be
influenced by the user — all of them will be discussed below.
How to permute an observation
When it comes to permuting an observation, lime depends
on the type of input data. Currently two types of inputs are supported:
tabular and text
Tabular Data
When dealing with tabular data, the permutations are dependent on the
training set. During the creation of the explainer the statistics for
each variable are extracted and permutations are then sampled from the
variable distributions. This means that permutations are in fact
independent from the explained variable making the similarity
computation even more important as this is the only thing establishing
the locality of the analysis.
Text Data
When the outcome of text predictions are to be explained the
permutations are performed by randomly removing words from the original
observation. Depending on whether the model uses word location or not,
words occurring multiple times will be removed one-by-one or as a
whole.
Calculating similarities with permutations
Just as permutations are created differently based on the input data,
so the similarities are calculated in different ways. For text data the
cosine similarity measure is used, which is the standard in text
analysis (it effectively measures the angle difference between the two
feature vectors). For tabular data a bit more thought is required and
the optimal solution will depend on the type of input data. First, the
categorical features will be recoded based on whether or not they are
equal to the observation. Second, if continuous features are binned (the
default) these features will be recoded based on whether they are in the
same bin as the observation. Using the recoded data the distance to the
original observation is then calculated based on a user-chosen distance
measure (euclidean by default), and converted to a similarity using an
exponential kernel of a user defined width (defaults to 0.75 times the
square root of the number of features).
Selecting the features to use
Feature selection is a complete sub-field of modelling in itself and
lime has no silver bullet for this. Instead, it implements
a range of different feature selection approaches that the user is free
to choose from. First though, the number of features needs to be chosen.
The number must strike a balance between the complexity of the model and
the simplicity of the explanation, but try to keep it below 10 (personal
opinion). As for selecting the features, lime supports the
following algorithms:
- none: Use all features for the explanation. Not
advised unless you have very few features.
- forward selection: Features are added one by one
based on their improvements to a ridge regression fit of the complex
model outcome.
- highest weights: The
m features with
highest absolute weight in a ridge regression fit of the complex model
outcome are chosen.
- lasso: The
m features that are least
prone to shrinkage based on the regularization path of a lasso fit of
the complex model outcome is chosen.
- tree: A tree is fitted with
log2(m)
splits, to use at max m features. It may possibly select
less.
- auto: Uses forward selection if
m <= 6 and otherwise highest weights.
Fitting a model to the permuted and feature-reduced data
Once permutations have been created, similarities calculated and
features selected it is time to fit a model. If the complex model is a
regressor, the simple model will predict the output of the complex model
directly. If the complex model is a classifier, the simple model will
predict the probability of the chosen class (for classifiers it is
possible to either specify the classes to explain, or let
lime chose the top k most probable
classes).
The only requirement for the simple model is that it can work with
weighted input and that it is easy to extract understanding from the
resulting fit. While multiple types of models support this,
lime uses a ridge regression as the model of choice. In the
future this might be expanded to other types of models.
An example - Tabular Data
The following is a simple example which seeks to explain the outcome
of a model predicting cancer based on biopsy results:
library(MASS)
library(lime)
data(biopsy)
# First we'll clean up the data a bit
biopsy$ID <- NULL
biopsy <- na.omit(biopsy)
names(biopsy) <- c('clump thickness', 'uniformity of cell size',
'uniformity of cell shape', 'marginal adhesion',
'single epithelial cell size', 'bare nuclei',
'bland chromatin', 'normal nucleoli', 'mitoses',
'class')
# Now we'll fit a linear discriminant model on all but 4 cases
set.seed(4)
test_set <- sample(seq_len(nrow(biopsy)), 4)
prediction <- biopsy$class
biopsy$class <- NULL
model <- lda(biopsy[-test_set, ], prediction[-test_set])
If we use the model to predict the 4 remaining cases we get some
pretty solid predictions:
predict(model, biopsy[test_set, ])
## $class
## [1] benign benign benign benign
## Levels: benign malignant
##
## $posterior
## benign malignant
## 519 0.9999983 1.675271e-06
## 602 0.9999998 1.937210e-07
## 73 0.9999332 6.683463e-05
## 385 0.9999996 3.570728e-07
##
## $x
## LD1
## 519 -1.902036
## 602 -2.347318
## 73 -1.141160
## 385 -2.221096
But lets see how these predictions came to be, using lime.
explainer <- lime(biopsy[-test_set,], model, bin_continuous = TRUE, quantile_bins = FALSE)
explanation <- explain(biopsy[test_set, ], explainer, n_labels = 1, n_features = 4)
# Only showing part of output for better printing
explanation[, 2:9]
## # A tibble: 16 × 8
## case label label_prob model_r2 model_intercept model_prediction feature
## <chr> <chr> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 519 benign 1.00 0.558 0.0397 1.08 bare nuclei
## 2 519 benign 1.00 0.558 0.0397 1.08 clump thic…
## 3 519 benign 1.00 0.558 0.0397 1.08 uniformity…
## 4 519 benign 1.00 0.558 0.0397 1.08 bland chro…
## 5 602 benign 1.00 0.581 0.0225 1.07 bare nuclei
## 6 602 benign 1.00 0.581 0.0225 1.07 clump thic…
## 7 602 benign 1.00 0.581 0.0225 1.07 uniformity…
## 8 602 benign 1.00 0.581 0.0225 1.07 normal nuc…
## 9 73 benign 1.00 0.567 0.00495 1.08 bare nuclei
## 10 73 benign 1.00 0.567 0.00495 1.08 clump thic…
## 11 73 benign 1.00 0.567 0.00495 1.08 uniformity…
## 12 73 benign 1.00 0.567 0.00495 1.08 normal nuc…
## 13 385 benign 1.00 0.550 0.0185 1.08 bare nuclei
## 14 385 benign 1.00 0.550 0.0185 1.08 clump thic…
## 15 385 benign 1.00 0.550 0.0185 1.08 uniformity…
## 16 385 benign 1.00 0.550 0.0185 1.08 normal nuc…
## # … with 1 more variable: feature_value <int>
We can see that all the explanations for a benign outcome
have chosen the same features, strongly indicating that these are both
locally and globally important features. In order to get a more
intuitive representation, we can use the provided
plot_features() to get a visual overview of the
explanations.
plot_features(explanation, ncol = 1)
In this overview it is clear to see how case 195 and 416 behave
alike, while the third benign case (7) has an unusual large
bare nuclei which are detracting from its status as
benign without affecting the final prediction (indicating that
the values of its other features are making up for this odd one). To no
surprise it is clear that high values in the measurements are indicative
of a malignant tumor.
An example - text data
The following is a simple example which seeks to explain the outcome
of a model classifying sentences from 30 scientific papers as being
about (or not) the author’s own work, e.g. methods, results or
conclusions.
Most of the things written for data.frame can be applied
to textual data.
library(lime)
library(xgboost) # the classifier
library(text2vec) # used to build the BoW matrix
# load data
data(train_sentences)
data(test_sentences)
# Data are stored in a 2 columns data.frame, one for the sentences, one for the
# labels.
print(str(train_sentences))
## 'data.frame': 2517 obs. of 2 variables:
## $ class.text: chr "MISC" "MISC" "AIMX" "OWNX" ...
## $ text : chr "although the internet as level topology has been extensively studied over the past few years little is known a"| __truncated__ "an as node can represent a wide variety of organizations e g large isp or small private business univers"| __truncated__ "in this paper we introduce a radically new approach based on machine learning techniques to map all the ases i"| __truncated__ "we believe that this dataset will serve as an invaluable addition to further understanding of the structure and"| __truncated__ ...
## NULL
# The list of possible classes for a sentence
# We are only interested in the class "OWNX"
print(unique(train_sentences$class.text))
## [1] "MISC" "AIMX" "OWNX"
## [4] "BASE" "CONT" "MISC--the"
## [7] "AIMX--on" "OWNX--after" "MISC--in"
## [10] "MISC--specifically," "MISC--on" "MISC--several"
## [13] "CONT--these" "OWNX--we" "MISC--for"
# Tokenize data
get_matrix <- function(text) {
it <- itoken(text, progressbar = FALSE)
create_dtm(it, vectorizer = hash_vectorizer())
}
# BoW matrix generation
dtm_train = get_matrix(train_sentences$text)
dtm_test = get_matrix(test_sentences$text)
# Create boosting model for binary classification (-> logistic loss)
# Other parameters are quite standard
param <- list(max_depth = 7,
eta = 0.1,
objective = "binary:logistic",
eval_metric = "error",
nthread = 1)
xgb_model <- xgb.train(
param,
xgb.DMatrix(dtm_train, label = train_sentences$class.text == "OWNX"),
nrounds = 50
)
We will test our model on test data.
# We use a (standard) threshold of 0.5
predictions <- predict(xgb_model, dtm_test) > 0.5
test_labels <- test_sentences$class.text == "OWNX"
# Accuracy
print(mean(predictions == test_labels))
## [1] 0.8433333
Now we are sure that the model works, we may want to understand what
are the most important words for the predictions.
# We select 10 sentences from the label OWNX
sentence_to_explain <- head(test_sentences[test_labels,]$text, 5)
explainer <- lime(sentence_to_explain, model = xgb_model,
preprocess = get_matrix)
explanation <- explain(sentence_to_explain, explainer, n_labels = 1,
n_features = 2)
# Most of the words choosen by Lime
# are related to the team (we, our)
# or part of the paper (Section, in)
explanation[, 2:9]
## # A tibble: 10 × 8
## case label label_prob model_r2 model_intercept model_prediction feature
## <int> <chr> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 1 1 0.642 0.988 0.331 0.644 we
## 2 1 1 0.642 0.988 0.331 0.644 in
## 3 2 1 0.802 0.902 0.268 0.770 We
## 4 2 1 0.802 0.902 0.268 0.770 the
## 5 3 0 0.543 0.886 0.691 0.499 we
## 6 3 0 0.543 0.886 0.691 0.499 those
## 7 4 1 0.872 0.928 0.390 0.901 Section
## 8 4 1 0.872 0.928 0.390 0.901 we
## 9 5 1 0.732 0.468 0.274 0.719 our
## 10 5 1 0.732 0.468 0.274 0.719 We
## # … with 1 more variable: feature_value <chr>
# Another more graphical view of the same information (2 first sentences only)
plot_features(explanation)
The graph view gives lots of detailed information about the selected
words. Another approach to explain a text classification model is to see
the most important words in their context. This requires htmlwidgets and
will not be evaluated in this vignette, but you can run it locally and
examine the output
plot_text_explanations(explanation)
If you have run this locally you can see that for some sentences, the
prediction is wrong. For instance, look at the third sentence. The word
we is in red and the predicted label is 0 (with a low
probability), meaning the model thinks it’s not a sentence from the
category OWNX, mainly because of the presence of the word
those but the word we in red doesn’t support this
(false) prediction.
Interactive text model explanations
Text explanations are also available through shine to
explore interactively the model.
After loading the application, both text and parameters can be
modified. Prediction and selected words are updated in real time.
# Launching the application is done in one command
interactive_text_explanations(explainer)
