# Difference between revisions of ""Why Should I Trust You?": Explaining the Predictions of Any Classifier"

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− | Understanding why machine learning models behave the way they do helps users in model selection, feature engineering, | + | Understanding why machine learning models behave the way they do helps users in model selection, feature engineering, and finally trusting the model to deploy it. In many cases even though a non-interpretable model is more accurate on the validation data set than the interpretable one, an interpretable model is choses. But restricting the models to just interpretable model isn't the best option. In this paper the authors argue for explaining machine learning predictions using model-agnostic approaches and propose LIME (Local Interpretable Model-Agnostic Explanations), a novel explanation technique that explains the predictions of any classifier in an interpretable and faithful manner, by learning an interpretable model locally around the prediction. They also propose a method called sub-modular optimization to explain models globally by selecting a representative individual predictions. |

− | The | + | The experiments are conducted mainly on text data and image data, where models used are random forest (RF) and Convolutional Neural Networks (CNN). The experiments highlight utility of explanations in deciding between the models, which model is to be trusted and which is not and also improving the model based on the explanations. The main contributions of this paper are summarized as follows. |

− | + | * LIME, an algorithm to explain any prediction of any model (classifier or regressor) by approximating locally with an interpretable model that is faithful to the original model locally. | |

− | + | * SP-LIME, a method to select final set of representative samples using sub-modular optimization to show to the user that pretty much captures what the original model is doing globally. | |

− | |||

− | * SP-LIME, a method | ||

− | |||

− | |||

+ | * A detailed set of experiments with simulated subjects to prove the usefulness of LIME and SP-LIME. | ||

[[File:LIME.jpg|thumb|550px|Figure 1: Explaining individual predictions. A model predicts that a patient has the flu, and LIME highlights the symptoms in the patient’s history that led to the prediction. Sneeze and headache are portrayed as contributing to the “flu” prediction, while “no fatigue” is evidence against it. With these, a doctor can make an informed decision about whether to trust the model’s prediction.]] | [[File:LIME.jpg|thumb|550px|Figure 1: Explaining individual predictions. A model predicts that a patient has the flu, and LIME highlights the symptoms in the patient’s history that led to the prediction. Sneeze and headache are portrayed as contributing to the “flu” prediction, while “no fatigue” is evidence against it. With these, a doctor can make an informed decision about whether to trust the model’s prediction.]] |

## Revision as of 04:44, 13 November 2017

## Contents

## Introduction

Understanding why machine learning models behave the way they do helps users in model selection, feature engineering, and finally trusting the model to deploy it. In many cases even though a non-interpretable model is more accurate on the validation data set than the interpretable one, an interpretable model is choses. But restricting the models to just interpretable model isn't the best option. In this paper the authors argue for explaining machine learning predictions using model-agnostic approaches and propose LIME (Local Interpretable Model-Agnostic Explanations), a novel explanation technique that explains the predictions of any classifier in an interpretable and faithful manner, by learning an interpretable model locally around the prediction. They also propose a method called sub-modular optimization to explain models globally by selecting a representative individual predictions.

The experiments are conducted mainly on text data and image data, where models used are random forest (RF) and Convolutional Neural Networks (CNN). The experiments highlight utility of explanations in deciding between the models, which model is to be trusted and which is not and also improving the model based on the explanations. The main contributions of this paper are summarized as follows.

- LIME, an algorithm to explain any prediction of any model (classifier or regressor) by approximating locally with an interpretable model that is faithful to the original model locally.

- SP-LIME, a method to select final set of representative samples using sub-modular optimization to show to the user that pretty much captures what the original model is doing globally.

- A detailed set of experiments with simulated subjects to prove the usefulness of LIME and SP-LIME.

## The Case for Explanations

“Explaining a prediction” means presenting textual or visual artifacts that provide qualitative understanding of the relationship between the instance’s components (e.g. words in text, patches in an image) and the model’s prediction. Explaining predictions is an important aspect in getting humans to trust and use machine learning effectively, if the explanations are faithful and intelligible. The process of explaining individual predictions is illustrated in Figure 1. It is clear that a doctor is much better positioned to make a decision with the help of a model if intelligible explanations are provided. In this case, an explanation is a small list of symptoms with relative weights – symptoms that either contribute to the prediction (in green) or are evidence against it (in red).

There are several ways a model or its evaluation can go wrong. Data leakage, for example, defined as the unintentional leakage of signal into the training (and validation) data that would not appear when deployed, potentially increases accuracy. For example, for problem in Figure 1, what if the patient ID was found to be heavily correlated with the target class in the training and validation data. This issue would be incredibly challenging to identify just by observing the predictions and the raw data, but much easier if explanations such as the one in Figure 1 are provided, as patient ID would be listed as an explanation for predictions. Another particularly hard to detect problem is dataset shift, where training data is different than test data (an example,"20 newsgroups dataset" is given later on). The insights given by explanations are particularly helpful in identifying what must be done to convert an untrustworthy model into a trustworthy one – for example, removing leaked data or changing the training data to avoid dataset shift.

Machine learning practitioners often have to select a model from a number of alternatives, requiring them to assess the relative trust between two or more models. Figure 2 shows how individual prediction explanations can be used to select between models, in conjunction with accuracy. In this case, the algorithm with higher accuracy on the validation set is actually much worse, a fact that is easy to see when explanations are provided (again, due to human prior knowledge), but hard otherwise. Further, there is frequently a mismatch between the metrics that we can compute and optimize (e.g. accuracy) and the actual metrics of interest such as user engagement and retention. While we may not be able to measure such metrics, we have knowledge about how certain model behaviors can influence them. Therefore, a practitioner may wish to choose a less accurate model for content recommendation that does not place high importance in features related to “clickbait” articles (which may hurt user retention), even if exploiting such features increases the accuracy of the model in cross validation. We note that explanations are particularly useful in these (and other) scenarios if a method can produce them for any model, so that a variety of models can be compared.

### Desired Characteristics for Explainers

An essential criterion for explanations is that they must be interpretable, i.e., provide qualitative understanding between the input variables and the response. We note that interpretability must take into account the user’s limitations. For example, if hundreds or thousands of features significantly contribute to a prediction, it is not reasonable to expect any user to comprehend why the prediction was made, even if individual weights can be inspected. This requirement further implies that explanations should be easy to understand, which is not necessarily true of the features used by the model, and thus the “input variables” in the explanations may need to be different than the features. Finally, the notion of interpretability also depends on the target audience. Machine learning practitioners may be able to interpret small Bayesian networks, but laymen may be more comfortable with a small number of weighted features as an explanation.

Another essential criterion is local fidelity. Although it is often impossible for an explanation to be completely faithful unless it is the complete description of the model itself, for an explanation to be meaningful it must at least be locally faithful, i.e. it must correspond to how the model behaves in the vicinity of the instance being predicted. We note that local fidelity does not imply global fidelity: features that are globally important may not be important in the local context, and vice versa. While global fidelity would imply local fidelity, identifying globally faithful explanations that are interpretable remains a challenge for complex models. While there are models that are inherently interpretable such as simple linear models, decision trees, or falling rule lists [3], an explainer should be able to explain any model, and thus be model-agnostic (i.e. treat the original model as a black box).

In addition to explaining predictions, providing a global perspective is important to ascertain trust in the model. Building upon the explanations for individual predictions, a few explanations are selected to present to the user, such that they are representative of the model.

## Local Interpretable Model-Agnostic Explanations (LIME)

The overall goal of LIME is to identify an interpretable model over the interpretable representation that is locally faithful to the classifier. A possible interpretable representation for text classification is a binary vector (one-hot encoding) indicating the presence or absence of a word, even though the classifier may use more complex (and incomprehensible) features such as word embeddings. Likewise for image classification, an interpretable representation may be a binary vector (one-hot encoding) indicating the “presence” or “absence” of a contiguous patch of pixels (a super-pixel or a segment), while the classifier may represent the image as a tensor with three color channels per pixel. We denote $x ∈ R^d$ be the original representation of an instance being explained, and we use $x' ∈ \{0, 1\}^{d'}$ to denote a binary vector for its interpretable representation.

Formally, we define an explanation as a model $g ∈ G$, where $G$ is a class of potentially interpretable models, such as linear models, decision trees, or falling rule lists [3], i.e. a model $g ∈ G$ can be readily presented to the user with visual or textual artifacts. The domain of $g$ is $\{0, 1\}^{d'}$, i.e. $g$ acts over absence/presence of the interpretable components. As not every $g ∈ G$ may be simple enough to be interpretable - thus we let $Ω(g)$ be a measure of complexity (as opposed to interpretability) of the explanation $g ∈ G$. For example, for decision trees $Ω(g)$ may be the depth of the tree, while for linear models, $Ω(g)$ may be the number of non-zero weights. Let the model being explained be denoted $f : R^d → R$. In classification, $f(x)$ is the probability (or a binary indicator) that $x$ belongs to a certain class. We further use $π_x(z)$ as a proximity measure between an instance $z$ to $x$, so as to define locality around $x$. Finally, let $L(f, g, π_x)$ be a measure of how unfaithful $g$ is in approximating $f$ in the locality defined by $π_x$. In order to ensure both interpretability and local fidelity, we must minimize $L(f, g, π_x)$ while having $Ω(g)$ be low enough to be interpretable by humans. The explanation produced by LIME is obtained by the following:

- [math]\xi(x) = \underset{g\in\mathbb{G}}{\operatorname{argmin}}\, \mathcal{L}(f,g,\pi) + \Omega(g)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, Eq. (1)[/math]

This formulation can be used with different explanation families $G$, fidelity functions $L$, and complexity measures $Ω$. Here we focus on sparse linear models as explanations, and on creating local samples using perturbations of the sample being explained.

### Sampling for Local Exploration

We want to minimize the locality-aware loss $L(f, g, π_x)$ without making any assumptions about $f$, since we want the explainer to be model-agnostic. Thus, in order to learn the local behavior of $f$ as the interpretable inputs vary, we approximate $L(f, g, π_x)$ by drawing samples, weighted by $π_x$. We sample instances around $x'$ by setting few features of $x'$ to 0, uniformly at random (where the number of such features set to 0 is also uniformly sampled). Given a perturbed sample $z' ∈ \{0, 1\}^{d'}$ (which contains a fraction of the features of $x'$ set to 0), we recover the sample in the original representation $z ∈ R^d$ and obtain the prediction $f(z)$ from the original classifier, and is used as a label for the explanation model. Given this dataset $Z$ of perturbed samples with the associated labels, we optimize Eq. (1) to get an explanation $ξ(x)$. The primary intuition behind LIME is presented in Figure 3, where we sample instances both in the vicinity of $x$ (which have a high weight due to $π_x$) and far away from $x$ (low weight from $π_x$). Even though the original model may be too complex to explain globally, LIME presents an explanation that is locally faithful (linear in this case), where the locality is captured by weight factor, $π_x$. We now present a concrete instance of this general framework.

### Sparse Linear Explanations

For the rest of this paper, we let $G$ be the class of linear models, such that $g(z') = w_g · z'$ . We use the locally weighted square loss as $L$, as defined in Eq. (2), where we let $π_x(z) = exp(−D(x, z)^2 /σ^2 )$ be an exponential kernel defined on some distance function $D$ (e.g. cosine distance for text, L2 distance for images) with width $σ$.

- [math]\mathcal{L}(f,g,\pi_x) = \underset{z,z'\in\mathbb{Z}}{\operatorname{\Sigma}} \pi_x(z)\,(f(z) - g(z'))\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, Eq. (2)[/math]

For text classification, we ensure that the explanation is interpretable by letting the interpretable representation be a bag of words, and by setting a limit $K$ on the number of words, i.e. $Ω(g) = ∞1[||w_g||_0 > K]$. Potentially, $K$ can be adapted to be as big as the user can handle, or we could have different values of $K$ for different instances. In this paper we use a constant value for K, leaving the exploration of different values to future work. We use the same $Ω$ for image classification, using “super-pixels” (computed using any standard image segmentation algorithm, eg. quickshift() function in skimage python library [5]) instead of words, such that the interpretable representation of an image is a binary vector where 1 indicates the original super-pixel and 0 indicates a grayed out super-pixel. This particular choice of $Ω$ makes directly solving Eq. (1) intractable, but we approximate it by first selecting $K$ features with Lasso (using the regularization path [4]) (scikit lars_path method [6]) and then learning the weights via least squares (together a procedure we call K-LASSO in Algorithm 1). Since Algorithm 1 produces an explanation for an individual prediction, its complexity does not depend on the size of the dataset, but instead on time to compute $f(x)$ and on the number of samples $N$. In practice, explaining random forests with 1000 trees using scikit-learn (http://scikit-learn.org) on a laptop with N = 5000 takes under 3 seconds without any optimizations such as using gpus or parallelization. Explaining each prediction of the Inception network [7] for image classification takes around 10 minutes.

Any choice of interpretable representations and $G$ will have some inherent drawbacks. First, while the underlying model can be treated as a black-box, certain interpretable representations will not be powerful enough to explain certain behaviors. For example, a model that predicts sepia-toned images to be retro cannot be explained by presence of absence of super pixels. Second, our choice of $G$ (sparse linear models) means that if the underlying model is highly non-linear even in the locality of the prediction, there may not be a faithful explanation. However, we can estimate the faithfulness of the explanation on Z, and present this information to the user. This estimate of faithfulness can also be used for selecting an appropriate family of explanations from a set of multiple interpretable model classes (linear models, decision trees etc.), thus adapting to the given dataset and the classifier. We leave such exploration for future work, as linear explanations work quite well for multiple black-box models in our experiments.

## Examples

### Example 1: Text classification with SVMs

In Figure 2 (right side), we explain the predictions of a support vector machine with RBF kernel trained on unigrams to differentiate “Christianity” from “Atheism” (on a subset of the 20 newsgroup dataset). Although this classifier achieves 94% held-out accuracy, and one would be tempted to trust it based on this, the explanation for an instance shows that predictions are made for quite arbitrary reasons (words “Posting”, “Host”, and “Re” have no connection to either Christianity or Atheism). The word “Posting” appears in 22% of examples in the training set, 99% of them in the class “Atheism”. Even if headers are removed, proper names of prolific posters in the original newsgroups are selected by the classifier, which would also not generalize. After getting such insights from explanations, it is clear that this dataset has serious issues (which are not evident just by studying the raw data or predictions), and that this classifier, or held-out evaluation, cannot be trusted. It is also clear what the problems are, and the steps that can be taken to fix these issues and train a more trustworthy classifier.

### Example 2: Deep networks for images

When using sparse linear explanations for image classifiers, one may wish to just highlight the super-pixels with positive weight towards a specific class, as they give intuition as to why the model would think that class may be present. We explain the prediction of Google’s pre-trained Inception neural network [7] in this fashion on an arbitrary image (Figure 4a). Figures 4b, 4c, 4d show the super-pixels explanations for the top 3 predicted classes (with the rest of the image grayed out), having set $K = 10$. What the neural network picks up on for each of the classes is quite natural to humans - Figure 4b in particular provides insight as to why acoustic guitar was predicted to be electric: due to the fretboard. This kind of explanation enhances trust in the classifier (even if the top predicted class is wrong), as it shows that it is not acting in an unreasonable manner.

## Submodular Pick for Explaining Models

Although an explanation of a single prediction provides some understanding into the reliability of the classifier to the user, it is not sufficient to evaluate and assess trust in the model as a whole. We propose to give a global understanding of the model by explaining a set of individual instances. This approach is still model agnostic, and is complementary to computing summary statistics such as held-out accuracy. Even though explanations of multiple instances can be insightful, these instances need to be selected judiciously, since users may not have the time to examine a large number of explanations. We represent the time/patience that humans have by a budget $B$ that denotes the number of explanations they are willing to look at in order to understand a model. Given a set of instances $X$, we define the pick step as the task of selecting $B$ instances for the user to inspect.

The pick step should take into account the explanations that accompany each prediction. Moreover, this method should pick a diverse, representative set of explanations to show the user – i.e. non-redundant explanations that represent how the model behaves globally.

Given the explanations for a set of instances $X\,(|X| = n)$, we construct an $n × d'$ explanation matrix $W$ that represents the local importance of the interpretable components for each instance. When using linear models as explanations, for an instance $x_i$ and explanation $g_i = ξ(x_i)$, we set $W_{ij} = |w_{gij}|$. Further, for each component (column) $j$ in $W$, we let $I_j$ denote the global importance of that component in the explanation space. Intuitively, we want $I$ such that features that explain many different instances have higher importance scores. In Figure 5, we show a toy example $W$, with $n = d' = 5$, where $W$ is binary (for simplicity). The importance function $I$ should score feature $f2$ higher than feature $f1$, i.e. $I_2 > I_1$, since feature $f2$ is used to explain more instances. Concretely for the text applications, we set $I_j = \sqrt{\sum_{i=1}^nW_{ij}}$ . For images, $I$ must measure something that is comparable across the super-pixels in different images, such as color histograms or other features of super-pixels; we leave further exploration of these ideas for future work.

While we want to pick instances that cover the important components, the set of explanations must not be redundant in the components they show the users, i.e. avoid selecting instances with similar explanations. In Figure 5, after the second row is picked, the third row adds no value, as the user has already seen features $f2$ and $f3$ - while the last row exposes the user to completely new features. Selecting the second and last row results in the coverage of almost all the features. We formalize this non-redundant coverage intuition in Eq. (3), where we define coverage as the set function $c$ that, given $W$ and $I$, computes the total importance of the features that appear in at least one instance in a set $V$ .

- [math]c(V, W, I) = {{\sum_{j = 1}^{d'}}}\mathbb{1}_{[\exists i\in V:W_{ij}\gt 0]}I_j\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, Eq. (3)[/math]

The pick problem, defined in Eq. (4), consists of finding the set $V, |V| ≤ B$ that achieves highest coverage.

- [math]Pick(W, I) = \underset{V,|V|\leq B}{\operatorname{argmax}}\, c(V,W, I)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, Eq. (4)[/math]

The problem in Eq. (4) is maximizing a weighted coverage function, and is NP-hard [10]. Let $c(V\cup\{i\}, W, I)−c(V, W, I)$ be the marginal coverage gain of adding an instance $i$ to a set $V$ . Due to sub-modularity, a greedy algorithm that iteratively adds the instance with the highest marginal coverage gain to the solution offers a constant-factor approximation guarantee of $1−1/e$ to the optimum [8]. We outline this approximation in Algorithm 2, and call it sub-modular pick.

## Simulated User Experiments

In this section, we present simulated user experiments to evaluate the utility of explanations in trust-related tasks. In particular, we address the following questions: (1) Are the explanations faithful to the model, (2) Can the explanations aid users in ascertaining trust in predictions, and (3) Are the explanations useful for evaluating the model as a whole. Code and data for replicating our experiments are available at https://github.com/marcotcr/lime-experiments.

### Experiment Setup

We use two sentiment analysis datasets (books and DVDs, 2000 instances each) where the task is to classify product reviews as positive or negative [9]. We train decision trees (DT), logistic regression with L2 regularization (LR), nearest neighbors (NN), and support vector machines with RBF kernel (SVM), all using bag of words as features. We also include random forests (with 1000 trees) trained with the average word2vec embedding (RF), a model that is impossible to interpret without a technique like LIME. We use the implementations and default parameters of scikit-learn, unless noted otherwise. We divide each dataset into train (1600 instances) and test (400 instances). To explain individual predictions, we compare our proposed approach (LIME), with parzen [10], a method that approximates the black box classifier globally with Parzen windows, and explains individual predictions by taking the gradient of the prediction probability function. For parzen, we take the $K$ features with the highest absolute gradients as explanations. We set the hyper-parameters for parzen and LIME using cross validation, and set $N = 15000$. We also compare against a greedy procedure in which we greedily remove features that contribute the most to the predicted class until the prediction changes (or we reach the maximum of $K$ features), and a random procedure that randomly picks K features as an explanation. We set $K$ to 10 for our experiments. For experiments where the pick procedure applies, we either do random selection (random pick, RP) or submodular pick, SP. We refer to pick-explainer combinations by adding RP or SP as a prefix.

### Are explanations faithful to the model?

We measure faithfulness of explanations on classifiers that are by themselves interpretable (sparse logistic regression and decision trees). In particular, we train both classifiers such that the maximum number of features they use for any instance is 10, and thus we know the gold set of features that the are considered important by these models. For each prediction on the test set, we generate explanations and compute the fraction of these gold features that are recovered by the explanations. We report this recall averaged over all the test instances in Figures 6 and 7. We observe that the greedy approach is comparable to parzen on logistic regression, but is substantially worse on decision trees since changing a single feature at a time often does not have an effect on the prediction. The overall recall by parzen is low, likely due to the difficulty in approximating the original high-dimensional classifier. LIME consistently provides > 90% recall for both classifiers on both datasets, demonstrating that LIME explanations are faithful to the models.

### Should I trust this prediction?

In order to simulate trust in individual predictions, we first randomly select 25% of the features to be “untrustworthy”, and assume that the users can identify and would not want to trust these features (such as the headers in 20 newsgroups, leaked data, etc). We thus develop oracle “trustworthiness” by labeling test set predictions from a black box classifier as “untrustworthy”if the prediction changes when untrustworthy features are removed from the instance, and “trustworthy” otherwise. In order to simulate users, we assume that users deem predictions untrustworthy from LIME and parzen explanations if the prediction from the linear approximation changes when all untrustworthy features that appear in the explanations are removed (the simulated human “discounts” the effect of untrustworthy features). For greedy and random, the prediction is mistrusted if any untrustworthy features are present in the explanation, since these methods do not provide a notion of the contribution of each feature to the prediction. Thus for each test set prediction, we can evaluate whether the simulated user trusts it using each explanation method, and compare it to the trustworthiness oracle.

Using this setup, we report the score, F1 (average of precision and recall) on the trustworthy predictions for each explanation method, averaged over 100 runs, in Table 1. The results indicate that LIME dominates others (all results are significant at p = 0.01) on both datasets, and for all of the black box models. The other methods either achieve a lower recall (i.e. they mistrust predictions more than they should) or lower precision (i.e. they trust too many predictions), while LIME maintains both high precision and high recall. Even though we artificially select which features are untrustworthy, these results indicate that LIME is helpful in assessing trust in individual predictions.

### Can I trust this model?

In the final simulated user experiment, we evaluate whether the explanations can be used for model selection, simulating the case where a human has to decide between two competing models with similar accuracy on validation data. For this purpose, we add 10 artificially “noisy” features. Specifically, on training and validation sets (80/20 split of the original training data), each artificial feature appears in 10% of the examples in one class, and 20% of the other, while on the test instances, each artificial feature appears in 10% of the examples in each class. This recreates the situation where the models use not only features that are informative in the real world, but also ones that introduce spurious correlations. We create pairs of competing classifiers by repeatedly training pairs of random forests with 30 trees until their validation accuracy is within 0.1% of each other, but their test accuracy differs by at least 5%. Thus, it is not possible to identify the better classifier (the one with higher test accuracy) from the accuracy on the validation data.

The goal of this experiment is to evaluate whether a user can identify the better classifier based on the explanations of $B$ instances from the validation set. The simulated human marks the set of artificial features that appear in the $B$ explanations as untrustworthy, following which we evaluate how many total predictions in the validation set should be trusted (as in the previous section, treating only marked features as untrustworthy). Then, we select the classifier with fewer untrustworthy predictions, and compare this choice to the classifier with higher held-out test set accuracy.

We present the accuracy of picking the correct classifier as $B$ varies, averaged over 800 runs, in Figure 8. We omit SP-parzen and RP-parzen from the figure since they did not produce useful explanations, performing only slightly better than random. LIME is consistently better than greedy, irrespective of the pick method. Further, combining sub-modular pick with LIME outperforms all other methods, in particular it is much better than RP-LIME when only a few examples are shown to the users. These results demonstrate that the trust assessments provided by SP-selected LIME explanations are good indicators of generalization.

## Conclusion and Future Work

In this paper, we argued that trust is crucial for effective human interaction with machine learning systems, and that explaining individual predictions is important in assessing trust. We proposed LIME, a modular and extensible approach to faithfully explain the predictions of any model in an interpretable manner. We also introduced SP-LIME, a method to select representative and non-redundant predictions, providing a global view of the model to users. Our experiments demonstrated that explanations are useful for a variety of models in trust-related tasks in the text and image domains, with both expert and non-expert users: deciding between models, assessing trust, improving untrustworthy models, and getting insights into predictions. There are a number of avenues of future work that we would like to explore. Although we describe only sparse linear models as explanations, our framework supports the exploration of a variety of explanation families, such as decision trees; it would be interesting to see a comparative study on these with real users. One issue that we do not mention in this work was how to perform the pick step for images, and we would like to address this limitation in the future. The domain and model agnosticism enables us to explore a variety of applications, and we would like to investigate potential uses in speech, video, and medical domains, as well as recommendation systems. Finally, we would like to explore theoretical properties (such as the appropriate number of samples) and computational optimizations (such as using parallelization and GPU processing), in order to provide the accurate, real-time explanations that are critical for any human-in-the-loop machine learning system.

## Remarks and Critique

This paper is by far the best paper I have read on model interpretability. The paper is full of new ideas and the authors clearly explain the approaches used with reasons as to why they picked it and also highlight both weaknesses and strong points of the approaches. Even though some of the tricks used are a little ambiguous on paper such as K-Lasso, super-pixels, but going through the code on GitHub, it becomes more clear. The code is also very well documented and easy to install and run to reproduce the results published. I tried running it on CIFAR-10 dataset and found it to be useful in understanding my model better.

There are few minor details that are unanswered in the paper.

- To interpret prediction for an image classifier, authors use super-pixels (segments) as features, but they don't give any reason as to why they picked this approach. One of the reasons I can think of for this to make sense is that convolutional neural networks learn shapes from layer to layer that become more complete moving from top to lower layers,. So in a way you can say, the classifier classifies on the basis of set of groups of pixels close to each other (as in the case of segments) than just the pixels that are spread apart far away from each other.

- The authors don't say how locally faithful the interpretable model should be to the classifier with constraints on maximum number of features to be used, i.e, what is the sort of error (mean squared error in case of linear interpretable models) we are content with?

- It seems that LIME can easily extended to regression cases and is not just limited to classification tasks, but the paper doesn't discuss anything in this regard.

## References

[1] Marco Tulio Ribeiro, Sameer Singh, Carlos Guestrin, Model-Agnostic Interpretability of Machine Learning, presented at 2016 ICML Workshop on Human Interpretability in Machine Learning (WHI 2016), New York, NY

[2] Marco Tulio Ribeiro, Sameer Singh, Carlos Guestrin, “Why Should I Trust You?” Explaining the Predictions of Any Classifier, KDD 2016 San Francisco, CA, USA

[3] F. Wang and C. Rudin. Falling rule lists. In Artificial Intelligence and Statistics (AISTATS), 2015.

[4] B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani. Least angle regression. Annals of Statistics, 32:407–499, 2004.

[5] http://scikit-image.org/docs/dev/api/skimage.segmentation.html#skimage.segmentation.quickshift

[6] http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.lars_path.html

[7] C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke, and A. Rabinovich. Going deeper with convolutions. In Computer Vision and Pattern Recognition (CVPR), 2015.

[8] A. Krause and D. Golovin. Submodular function maximization. In Tractability: Practical Approaches to Hard Problems. Cambridge University Press, February 2014.

[9] J. Blitzer, M. Dredze, and F. Pereira. Biographies, bollywood, boom-boxes and blenders: Domain adaptation for sentiment classification. In Association for Computational Linguistics (ACL), 2007.

[10] D. Baehrens, T. Schroeter, S. Harmeling, M. Kawanabe, K. Hansen, and K.-R. Muller. How to explain individual classification decisions. Journal of Machine Learning Research, 11, 2010.