ARA: accurate, reliable and active histopathological image classification framework with Bayesian deep learning

Abstract

Machine learning algorithms hold the promise to effectively automate the analysis of histopathological images that are routinely generated in clinical practice. Any machine learning method used in the clinical diagnostic process has to be extremely accurate and, ideally, provide a measure of uncertainty for its predictions. Such accurate and reliable classifiers need enough labelled data for training, which requires time-consuming and costly manual annotation by pathologists. Thus, it is critical to minimise the amount of data needed to reach the desired accuracy by maximising the efficiency of training. We propose an accurate, reliable and active (ARA) image classification framework and introduce a new Bayesian Convolutional Neural Network (ARA-CNN) for classifying histopathological images of colorectal cancer. The model achieves exceptional classification accuracy, outperforming other models trained on the same dataset. The network outputs an uncertainty measurement for each tested image. We show that uncertainty measures can be used to detect mislabelled training samples and can be employed in an efficient active learning workflow. Using a variational dropout-based entropy measure of uncertainty in the workflow speeds up the learning process by roughly 45%. Finally, we utilise our model to segment whole-slide images of colorectal tissue and compute segmentation-based spatial statistics.

Introduction

Histopathological images of cancer tissue samples are routinely inspected by pathologists for cancer type identification and prognosis. Hematoxylin-Eosin (H&E) stained slides have been used by pathologists for over a hundred years. With such long history and proven applicability, histopathological imaging is expected to stay in common clinical practice in the coming years1. With the advent of digital pathology, histopathological images became available for automated analysis at scale2. To this end, a rich catalogue of machine learning approaches to image classification and whole-slide segmentation has been developed3,4, promising to aid the effort of pathologists in interpreting the images5. Such machine learning models need to be perfectly accurate, as classification errors may result in faulty disease diagnosis and patient treatment. On top of that, we stipulate that in application to digital pathology, the models should also be reliable in their predictions. When performing the difficult task of automated classification or diagnosis based on histopathological images, they should state uncertainty in their predictions, indicating difficult cases for which human expert inspection is necessary. While accuracy is optimised by every machine learning method, reliability is another desired feature that is not delivered by many state of the art solutions.

Recent years brought particularly intensive development of deep-learning based approaches to image classification. In particular, Convolutional Neural Networks (CNNs) have served as a backbone for numerous breakthroughs in computer vision as a whole, specifically in image classification. Since 2012, when the groundbreaking AlexNet was created by Alex Krizevsky6, the state of the art has rapidly shifted from machine learning algorithms using manual feature engineering (henceforth referred to as ‘traditional’ machine learning approaches) to new deep learning ones7. Medical imaging in general8,9,10,11,12, and histopathological image classification in particular13,14,15,16,17,18,19,20, became important applications of these methods. Multiple machine learning methods go beyond the tasks of tissue type classification and whole-slide segmentation, confirming there is more information about the patients encrypted in histopathological images than immediately visible by eye5. For example, Wang et al.21 trained a CNN to predict survival of patients from their pathological images. Another deep learning model22 allowed prediction of mutations in several genes from non–small cell lung cancer histopathology. Finally, Bayesian measures of measuring uncertainty for deep-learning methods have been proposed23,24 and successfully applied to medical image analysis25. Those developments open the avenue to reliable image classification, where prediction uncertainty can be reported together with the predicted class.

All of these exciting methodological inventions would not be possible without training data that is numerous enough to train accurate models. Publicly available training data with annotated images such as the Breast Cancer Histopathological Database26 allow algorithm benchmarking and evaluation, sparkling new method developments27,28. Similarly, Kather et al.29 released a colorectal cancer dataset with H&E tissue slides, which were cut into 5000 small tiles (or patches), each of them annotated with one of eight tissue classes. They also devised an efficient classification method, with image-derived features serving as basis for a support vector machine model. Since its publication, this dataset was utilised several times to verify the performance of an array of methods. Ribeiro et al.30 developed a traditional method that uses multidimensional fractal techniques, curvelet transforms and Haralick descriptors. They tested its accuracy using the Kather et al. dataset in a binary classification scenario. Wang et al.31 developed a Bilinear CNN architecture that takes as input H&E stained images decomposed into H and E channels and used all eight classes from the Kather et al. dataset to verify its performance. Pham32 utilised this dataset to assess their autoencoder architecture. Sarkar et al.33 created a new saliency-based dictionary learning method and used the Kather et al. dataset for both training and testing. Finally, Ciompi et al.34 used it as an independent test set for an evaluation of two stain normalisation strategies. All traditional methods reported accuracy lower than the original classification method by Kather et al. The AUC value in the eight-class classification task obtained by Wang et al.31 was higher than the one achieved by Kather et al., confirming that a CNN is the method of choice for this dataset as well. Notably, none of these methods aimed for reliability, as they did not assess the uncertainty of their predictions.

Generation of datasets like the ones described above requires laborious workload of pathologists who process whole-slide images and assign labels to selected image regions. The requirement of meticulous pathological annotation limits the amount of data available for model training. Formally, this relates to the bias-variance trade-off in machine learning35. The effort to minimise bias on a small training set may result in high variance and low accuracy on unseen data, an effect known as overfitting. In order to minimise the expected test error, model regularisation techniques penalising model complexity can be applied. For CNNs, a technique called dropout has been proposed as a means of regularisation36. Another technique, called active learning, can be used to deal with the difficulty of laborious data annotation. Active learning is an iterative procedure, where in each step the model is re-trained on data expanded with new samples, which are added based on results from the previous steps in order to maximise the learning rate. Variants of active learning depend on the way the new samples are selected. One method of choice is selection which maximises the diversity of the training set37. Gal et al.38 proposed an active learning procedure for Bayesian deep learning models, where new samples are added in each iteration based on their uncertainty estimated using variational dropout. This technique can be conceptualised by an analogy to a diligent student, who while taking a course actively asks the teacher for more examples on topics which are hard for them to understand. There are several attempts at active learning for histopathological image classification in the literature, using both traditional machine learning37,39,40,41,42 and deep learning43,44,45,46. However, none of these approaches utilised uncertainty for selection of new samples in active training.

In this work, we introduce an accurate, reliable and active (shortly, ARA) learning framework for classification of histopathological images of colorectal cancer. To this end, we develop a new CNN model (called ARA-CNN) for classification of colorectal cancer tissues, trained on the Kather et al. dataset (Fig. 1). The model achieves stellar accuracy, higher than reported in the original publication of Kather et al.29 and in later studies. The key contribution of this work is an extensive analysis of the utility of two variational-dropout based uncertainty measures, Entropy H and BALD (Bayesian Active Learning by Disagreement; introduced by Houlsby et al.47), in their application to histopathological image classification. We demonstrate that the distribution of uncertainty is increased for tissue classes that are the most difficult to learn for the model. Moreover, images that are misclassified tend to have the highest uncertainties. We propose an active learning framework, where the model suggests the most uncertain classes for annotation by a pathologist and identifies the most certain misclassified images as potentially incorrectly annotated (Fig. 1A). We show that H outperforms random selection of images and BALD when applied to select samples in an active learning procedure, speeding up the learning process by roughly 45%. In-depth inspection indicates that correctly classified images with very low Entropy H are highly characteristic of each tissue class. We show that low Entropy H for misclassified images correctly identifies mislabelled data in the training dataset and that ARA-CNN is highly robust to such noise in the data. On the other hand, images with very high uncertainty H are atypical or show pathological features that could be shared by other classes, which makes them pathologically difficult to categorise. In addition to image classification and uncertainty estimation, the framework is successfully applied to image segmentation and provides segmentation-based statistics of tissue class abundance in whole tissue slides (Fig. 1B).

Figure 1
figure1

Overview of the proposed ARA framework. (A) Active histopathology workflow. Annotated whole-slide images (WSIs) are split into small image patches, which constitute a dataset. ARA-CNN is trained on that dataset. After the first round of training, the pathologist should be informed about i) which classes are the most uncertain and ii) which image patches are misclassified and highly certain, and thus identified as potentially mislabelled. The former should inform the pathologist about which classes to prioritise in the next round of annotation. The latter should inform about which image patches should be re-annotated with correct labels. We then take new annotated whole-slide images and continue the workflow until we reach a satisfying level of classification accuracy. (B) Segmentation workflow. Whole slide images are split into small image patches. Each of these is classified by trained ARA-CNN and is assigned a colour based on its classification result. These coloured tiles are merged together to form a segmented whole slide image and can be analysed in terms of their spatial relationships. Each resulting tile has a measured uncertainty value as well, so pathologists can make an informed decision whether to take the automated segmentation as-is or to inspect it manually.

Methods

Analysed data

The analysed dataset holds 5000 image patches belonging to eight balanced classes of histopathologically recognisable tissues29. The patches were pulled from ten anonymised and digitised tissue slides, stained with the H&E technique. After initial coarse-grained annotation, 625 non-overlapping tiles were extracted from contiguous tissue areas for each class. Each tile has the same size of 150 × 150 pixels (equivalent to 74 μm × 74 μm). The eight tissue classes are: tumour epithelium, simple stroma (homogeneous composition, includes tumour stroma, extra-tumoural stroma and smooth muscle), complex stroma (containing single tumour cells and/or few immune cells), immune cells (including immune-cell conglomerates and sub-mucosal lymphoid follicles), debris (including necrosis, haemorrhage and mucus), normal mucosal glands, adipose tissue, background (no tissue). Here, for the sake of brevity, these classes are labelled as: Tumour, Stroma, Complex, Lympho, Debris, Mucosa, Adipose and Empty. In addition, one tissue slide denoted by Kather et al.29 as a test image was used for the purpose of segmentation (see below).

ARA-CNN model

To automatically classify the images from the analysed dataset into their corresponding classes, we developed and trained a Convolutional Neural Network (CNN) model. The architecture of the model, called ARA-CNN, was inspired by many state of the art solutions, including Microsoft ResNet48 and DarkNet 1949. For normalisation and to reduce overfitting, we used a popular technique called Batch Normalisation50. In ARA-CNN, overfitting is also reduced by using dropout36. This in turn allowed us to apply variational dropout51 during testing. For every tested image, the model provides not only its predicted class, but also a measure of uncertainty estimated using variational dropout. The architecture of ARA-CNN is discussed in depth in Supplementary Information and presented in Fig. S1.

Dropout

Due to their size, deep learning models are especially prone to overfitting - they can inadvertently learn from sampling noise instead of actual non-linearities in the training data. One of the more popular and successful methods of combating this problem is dropout36. It works on the basis of randomly removing units in a neural network during training in order to simulate a committee of multiple different architectures. In our model, dropout is applied to two fully connected layers with 32 units preceding auxiliary and final output. Its rate is equal to 0.5, which means that during both inference and training approximately half of all units are turned off and set to 0.

Model training

The whole dataset of 5000 images was split into a training dataset and a test dataset used for evaluation. Their sizes varied depending on the experiment. In the 8-class case, we randomly divided the dataset into the training set with 4496 images (562 images per class) and the test set with 504 images (63 images per class). In the case of binary classification, the training set contained 1124 images, while the test set was comprised of 126 images (divided in half between Tumour and Stroma). These divisions were repeated ten times in the process of 10-fold cross-validation. Moreover, we also performed 5-fold cross-validation and 2-fold cross-validation, with the dataset split according to the number of folds.

Additionally, in each training epoch the training data was split into two datasets: the actual training data and a validation dataset. The latter was used for informing the learning rate reducer - we monitored the accuracy on the validation set and if it stopped improving, the learning rate was reduced by a factor of 0.1. In the task of evaluating model performance, this split was in proportion 90% to 10% between actual training data and the validation set, respectively, while in active learning the split was in proportion 70% to 30%. This is due to the fact that in active learning we start from a very small dataset and 10% was too small of a proportion to provide enough validation samples.

For parameter optimisation, we used the Adam52 optimiser. The training time differed depending on the experiment. In the cross-validation and mislabelled sample identification experiments we used 200 epochs, but in the active learning experiments it was 100 epochs instead (due to limited computational resources). In all cases, the training data was passed to the network in batches of 32, while the validation and test data was split into batches of 128 images.

Loss function

During training, the categorical cross-entropy loss function was applied to both (auxiliary and final) outputs. The final loss is a weighted sum of these two losses with weight 0.9 for the final output and 0.1 for the auxiliary output. For observation o, a set of M classes and class \({y}^{\ast }\in \{1\ldots M\}\), we denote the probability of assigning the observation to that class as \(P({y}^{\ast }|o,\hat{\omega })\), where \(\hat{\omega }\) represents the estimated parameters of the model. Categorical cross-entropy can then be defined as:

$$-\,\mathop{\sum }\limits_{{y}^{\ast }=1}^{M}\,\delta ({y}_{o}={y}^{\ast })\,\log (P({y}^{\ast }|o,\hat{\omega })),$$
(1)

where δ is the Dirac function and yo is the correct class for observation o.

Variational dropout for inference and uncertainty estimation

In order to provide more accurate classification as well as uncertainty prediction, we adopted a popular method called variational dropout51. The central idea of this technique is to keep dropout enabled by performing multiple model calls during prediction. Thanks to the fact that different units are dropped across different model calls, it might be considered as Bayesian sampling from a variational distribution of models24. In a Bayesian setting, the parameters (i.e. weights) \(\omega \) of a CNN model are treated as random variables. In variational inference, we approximate the posterior distribution P(ω|D) by a simpler (variational) distribution \(q(\omega )\), where D is the training dataset. Thus, we assume that \({\hat{\omega }}_{t}\sim q(\omega )\), where \({\hat{\omega }}_{t}\) is an estimation of \(\omega \) resulting from a variatonal dropout call t. With these assumptions, the following approximations can be derived24:

$$P({y}^{\ast }|o,D)={\int }^{}\,P({y}^{\ast }|o,\omega )P(\omega /D)d\omega \approx {\int }^{}\,P({y}^{\ast }|o,\omega )q(\omega )d\omega \approx \frac{1}{T}\,\mathop{\sum }\limits_{t=1}^{T}\,P({y}^{\ast }|o,{\hat{\omega }}_{t}),$$
(2)

where T is the number of variational samples. In our model we used \(T=50\).

Variational dropout has enabled us to measure the uncertainty of predictions. We implemented two uncertainty measures: Entropy H and BALD23. If the output of the model is a conditional probability distribution \(P({y}^{\ast }|o,D)\), then the measure H can be defined as entropy of the predictive distribution:

$$H[P({y}^{\ast }|o,D)]=-\,\,\,\sum _{{y}^{\ast }\in \{1\ldots M\}}\,P({y}^{\ast }|o,D)\,\log \,P({y}^{\ast }|o,D)$$
(3)

The second uncertainty measure, BALD, is based on mutual information and measures the information gain about the model parameters \(\omega \) obtained from classifying observation o with label y*. In the case of variational dropout, this can be expressed as the difference between entropy of the predictive distribution and the mean entropy of predictions across multiple model calls:

$$\begin{array}{rcl}I(\omega ,{y}^{\ast }|o,D) & = & H[P({y}^{\ast }|o,D)]-{{\mathbb{E}}}_{P(\omega /D)}[H[P({y}^{\ast }|o,\omega )]]\\ & \simeq & H[P({y}^{\ast }|o,D)]-\frac{1}{T}\,\mathop{\sum }\limits_{t=1}^{T}\,H[P({y}^{\ast }|o,{\hat{\omega }}_{t})].\end{array}$$
(4)

The difference between these two measures pertains to how they react to two different types of uncertainty in the data: epistemic and aleatoric53. The former type is caused by a lack of knowledge - in terms of machine learning, this is analogous to a lack of data, so the posterior probability over model parameters is broad. The latter uncertainty is a result of noise in the data - no matter how much data the model has seen, if there is inherent noise then the best possible prediction may be highly uncertain23. In general, the Entropy H measure cannot distinguish these two types of uncertainty. If uncertainty of a new observation is measured by H, then the value would not depend on the underlying uncertainty type. On the other hand, it is believed that BALD measures epistemic uncertainty of the model23, so it would not return a high value if there is only aleoratic uncertainty present. Depending on the dataset, one of these measures might work better than the other at catching and describing the uncertainty.

Image segmentation

To perform segmentation of test tissue slides from the Kather et al.29 dataset, each of these 5000 × 5000 px images was split into 10000 non-overlapping test samples with resolution of 50 × 50 pixels. These test images were then supplied as input to our model (by being upscaled to 128 × 128 pixels), which returned a classification into one of eight classes of colorectal tissue. Since the output of the model is a probability distribution, we selected the class with the highest value as the prediction for a given test image patch. We did not consider the measured uncertainty in this process. To get the final segmentation, we assigned a colour to each predicted class and generated a 50 × 50 pixels single-coloured patch for each test image. These patches were then stitched together to form the final images. Lastly, we applied a blurring Gaussian filter to smooth out the edges of tissue regions.

Finally, we performed a simple spatial analysis for each slide by counting the percentage of surface area taken by each class.

Active learning

Active learning is an iterative procedure, where the initial model is trained on a small dataset and in consecutive iterations it is re-trained on a dataset extended by new samples. At each step, the new samples are added according to some acquisition function evaluated using the current model. Intuitively, the uncertainty measures described above are a good basis for an acquisition function in deep learning. In a given iteration, the model should first choose the samples it is most uncertain of38.

In this work we implemented and compared effectively three different acquisition functions. Two were based on uncertainty measures H and BALD, whereas the third was a random selection and served as a baseline. We performed a series of experiments in order to determine if uncertainty-based active learning can speed-up training with the colorectal cancer dataset. To this end, we emulated the proposed active learning workflow (Fig. 1A) utilising the available data. We started from generating three random splits of the full dataset - this gave us three test sets of 504 images and three training sets of 4496 images. Then for each of these test-train pairs, we performed the active learning procedure for both uncertainty measures plus a baseline training process based on random selection of images. In each case, we started from selecting 40 images per class (so 320 in total) from the training dataset. We trained the model on that small dataset and then, based on a given acquisition function, we chose 160 images to add to the previous 320. This slightly larger set became a new training dataset. We repeated this process, adding 160 images in each step, until there were no more images to draw from the initial full training dataset, giving us 28 training steps in total. Additionally, in order to eliminate the effects of random weight initialisation, we pre-initialised the model 8 times for each step and used these initialisations for each of the 3 dataset splits. Thus, for each of the 28 steps we had to train the model 24 times.

For the random selection, the 160 new images in each step were sampled uniformly at random from the full training dataset. For the uncertainty-based functions, we performed inference on remaining images from the full training set in each step. We evaluated the uncertainty for each image using the H and BALD measures, according to Eqs (3) and (4). We sorted the results by uncertainty in descending order and selected the top 160. The results for each active learning step were averaged between initialisations and dataset splits.

Identification of mislabelled training samples

Identification of mislabelled training samples is an important problem in supervised learning54. Mislabelled training data is particularly likely to occur in our classification problem, where the training image patches are cut out from relatively large regions of WSIs annotated by the pathologist. In such a setup, the entire region labelled with a particular class may coincidentally include patches which in fact belong to a different class. Here, we show that such mislabelled training patches can be identified as those that were misclassified by ARA-CNN with low entropy H (i.e. with high certainty). Specifically, the identification of candidate mislabelled images using ARA-CNN proceeds as follows. Given the expected percentage of such mislabelled training images pm, separately for each class c we identify images misclassified by the model with uncertainty below a threshold \({H}_{t}^{c}={q}^{c}({p}_{m})\), where \({q}^{c}({p}_{m})\) is the pm-th percentile of the empirical distribution of H in class c. The final set of candidate mislabelled images is the union of the identified images across all classes.

Results

Model performance

To evaluate the performance of ARA-CNN, similarly to previous models trained on the same dataset, we measured its receiver operating characteristic (ROC) curves, area under the ROC curves (AUC) and error rates in 10-fold cross-validation for both 8-class and 2-class (Tumour vs Stroma) classification tasks. In addition, we also evaluated precision-recall curves. We used images with all colour information preserved. The results were compared to those of the original model by Kather et al. (Fig. 2), as well as to other methods that used the same dataset. Where necessary, we performed 5-fold or 2-fold cross-validation and used the results as a comparison point. In their work, Kather et al.29 tested the performance of several low-level image features in combination with four classification algorithms, applied to grayscale images from their dataset. Their approach is an example of a ‘traditional’ procedure, where image features have to be hand-crafted and chosen appropriately depending on the dataset. The best results were reported for a combination of features containing: pixel value histograms, local binary patterns, gray-level co-occurence matrix and perception-like features. The best performing classifier was a support vector machine (SVM) algorithm with the radial basis function (RBF) kernel.

Figure 2
figure2

Model performance in 10-fold cross-validation. (A) ROC and area under the ROC curve (AUC) for classification into eight tissue types. The model presented in this work achieved an average AUC of 0.995 (a mean was taken across all eight classes), (B) ROC and AUC for binary classification between Tumour and Stroma. ARA-CNN achieves AUC of 0.998. (C) Precision-recall curves for ARA-CNN in a multiclass classification setting. The mean AUC for these curves is 0.972. (D) Error comparison to previous work. With error rate 7.56% for eight class classification, our model substantially reduces the error (by 5.04%) compared to error rate 12.6% of the best model assessed by Kather et al.29. For binary (Tumour versus Stroma) classification, our model has error rate 0.89%, which is also lower than the 1.4% error rate of the Kather et al. model.

The ROC curves (generated with a one-vs-all method) for the 8-class experiment show excellent performance of ARA-CNN (Fig. 2A). The AUC values for the Tumour, Mucosa, Lympho, Adipose and Empty classes range from 0.997 to 0.999. Values for the Stroma, Complex and Debris classes are a little lower (from 0.988 to 0.992), which indicates that the model cannot always distinguish them from other classes. Still, the mean AUC value is 0.995, which is higher than the value of 0.976 obtained by Kather et al.29. The ROC curve for the 2-class problem (Fig. 2B) and its corresponding AUC value of 0.998 also illustrate near-perfect performance of ARA-CNN. It is important to note that performance evaluation using ROC curves for the multiclass classification task in a one-vs-all setting may be biased due to the fact that the classes are unbalanced. In such a setting, it is better to use precision-recall curves (Fig. 2C). The AUC values for these curves, as obtained by ARA-CNN, are a bit lower than for the ROC curves, but with the mean AUC of 0.972 are still indicative of excellent performance. The lowest AUC value (0.924) is obtained for the Complex versus all classification task. This indicates that the Complex class is the most difficult one to classify correctly for the model. We do not compare these results to other methods, as we are not aware of any other approaches that used precision-recall curves for performance evaluation on this dataset.

In terms of error rates, for the 8-class problem the ARA-CNN model reached an average rate of 7.56%, which is substantially lower, by 5.04%, than the best result reported by Kather et al.29 (Fig. 2D). Similarly, in the binary classification task, we obtained an error rate of 0.89%, lower than 1.4% obtained by Kather et al. Thus, our model is better than the best of standard approaches presented by Kather et al.29, especially in the multiclass classification scenario. One of the differences between deep learning and the standard approaches is that the former construct the features on the fly based on the data itself. Here, the features identified by ARA-CNN as part of the learning process outperform the set of features that were engineered by Kather et al.29 in the difficult task of decisively describing all classes in a multiclass image classification problem.

The classification performance of ARA-CNN is also superior or comparable to other published models that used the Kather et al. dataset, including both traditional and deep learning approaches that utilise CNNs (Table 1). ARA-CNN outperforms the traditional methods by a significant margin both in terms of AUC and accuracy. When it comes to CNN methods, Wang et al.31 performed 5-fold cross-validation and reported a mean AUC value of 0.985 (lower by 0.01 than ARA-CNN) and 92.6% accuracy (higher by 0.36% than ARA-CNN) for their BCNN in the multiclass task. Although BCNN and ARA-CNN achieve similarly high performance results, their architectures are very different. BCNN depends on an external method to perform stain decomposition of H&E images and is composed of two simple feed-forward CNNs, which take as input separate signals from the Eosin and Hematoxylin components and whose outputs are combined by bilinear pooling. We took a more typical deep-learning approach, with a deeper network with residual connections, where no independent feature extraction nor decomposition is needed, and the network itself is responsible for extracting important signals from raw image data. Pham32 used an autoencoder architecture to re-sample the images from the Kather et al. dataset and trained a small supervised network for different re-sampling factors. They reported at best an accuracy of 84.00% for binary classification, which is lower by 14.88% in comparison to our result. Ciompi et al.34 used the Kather et al. dataset for testing their model trained on an independent colorectal cancer dataset and reported relatively small accuracies of 50.96% and 75.55%, where the former was achieved without stain normalisation and the latter was an improvement resulting from having stain normalisation applied. However, since this model was trained on a different dataset, we do not directly compare our result to theirs. Overall, ARA-CNN’s achieves excellent performance on the Kather et al. dataset, and scores better than most other published methods that utilised the same data for training. Exceptional performance of our approach indicates that it successfully combines the flexibility typical for deep neural networks with strong regularisation resulting from dropout and Batch Normalisation.

Table 1 Comparison of different methods that used the Kather et al. dataset for training.

Finally, we present the excellent results of segmentation of whole slide images in Supplementary Information and in Fig. S2.

Uncertainty, active learning and identification of mislabelled images

Deep learning models are often criticised for being so-called black-boxes. Due to their complexity, it can be very hard to tell why a given test sample is classified to a certain class. The model presented in this work, thanks to its implementation of dropout and variational inference, has a few ways to measure the uncertainty of each prediction. These uncertainty measures allow the model predictions to be reliable. Consider an example image, which is classified by the model as Tumour with high probability 0.95, but the measured uncertainty is also high. This can mean that the prediction cannot be taken for granted and needs to be double-checked by a human. This additional indication of prediction uncertainty brings us one step closer to alleviating the problem of the black-box nature of deep learning and increases model-based understanding of the data. Here, we evaluated two uncertainty measures, Entropy H and BALD (see Uncertainty estimation), checking their distribution in each class and their performance as acquisition functions in active learning on the Kather et al.29 dataset.

First, we applied the trained model to 504 test images. For each image, we recorded the classification and the measured uncertainty. The results for Entropy H are presented in Fig. 3A. On average, the highest uncertainty values were reported for images from the Stroma and Complex classes. The biggest variance in uncertainty was measured for the Debris class. These three classes were also misclassified as each other, which indicates that they are similar in appearance and the model has a hard time differentiating them. This is in agreement with the precision-recall curves in Fig. 2D and with the analysis described below in Understanding uncertainty. In addition, it can be observed that misclassification occurred almost exclusively when the uncertainty was high. Thus, a high uncertainty is indeed a good indicator that the prediction may be faulty. The results for BALD are shown in Fig. 3B. On average, the most uncertain classes according to that measure are Stroma and Complex, in agreement with Entropy H. Interestingly, BALD measured much less variance in the Debris class, which makes Lympho the most variable class in this case. Moreover, the Empty class is relatively more certain according to BALD than in the Entropy H experiment. These differences may be a result of epistemic and aleatoric uncertainties present in the data, which are measured differently by BALD and Entropy H (see Active learning). Nevertheless, the BALD measure still captures the fact that misclassifications take place mainly for highly uncertain predictions.

Figure 3
figure3

The uncertainty of image classification. (A,B) Distribution of uncertainty for the colorectal cancer images used to train our model. The horizontal axis shows the actual class of these images, whereas the classification of each image is represented with coloured jitter. The y-axis value represents the amount of uncertainty. Our model is on average most uncertain when it comes to the Stroma and Complex classes. It also makes mistakes in classification mostly when it is uncertain. (A) Distribution of uncertainty for the Entropy H measure. (B) Distribution of uncertainty for the BALD measure. (C) Results of active learning experiments. Starting from a small training dataset with 320 images in total (step number 0, 40 images per class), the model was re-trained on the dataset increased in every iteration by 160 additional images. Three distinct acquisition functions were tested: Random, Entropy H and BALD. At each step, the average classification accuracy was measured (y-axis). (D,E) Microscopic images of tissues composing colorectal cancer. Samples were categorised by uncertainty measured with Entropy H. Columns correspond to different tissue classes. (D) Images with low uncertainty H. (E) Images with high uncertainty H.

Active learning

Active learning is a set of methods that try to minimise the amount of labelled data needed to fully train a classifier. They start from a small dataset and, as the training goes on, add new training samples according to some kind of acquisition function. We tested the effectiveness of using uncertainty measures as this function, effectively choosing most uncertain images as the ones the model should learn first. The idea here is that if the model learns first what it has the most trouble with, then it should achieve high accuracy at an earlier stage in the active learning process.

Here, we designed an active learning process with either the Entropy H or BALD measures acting as acquisition functions (see Active learning). We evaluated its efficiency on the Kather et al.29 dataset by analysing the resulting model accuracy as a function of the number of training samples (Fig. 3C). The Random acquisition function serves as a baseline. In initial active learning iterations the Entropy H measure performs very similarly to random selection, but from step 7 (which contained 1440 images) Entropy H achieves consistently higher accuracy (with on average 2% improvement in classification accuracy) until the very end of the process. The accuracy of the model trained on samples selected using the BALD measure is worse than the random one from the start of active learning until step 12. From step 13 (which contained 2400 images) it gets slightly better, but never eclipses the accuracy received using the Entropy H measure. This proves that the Entropy H uncertainty measure can be successfully used as an acquisition function in active learning scenarios utilising our ARA-CNN model. It can speed up the learning process by roughly 45%. The model reaches the classification accuracy equivalent to the full dataset already at step 15, in which the training set contained 2720 images. Thus, the fraction of images required for obtaining the full accuracy is only 2720 out of 5000 (54.4%), and the fraction of steps required is only 15 out of 27 (55.56%), both amounting to around 45% reduction. It means that this subset of images, chosen based on the Entropy H uncertainty measure, is large enough to accurately train the model.

Identification of mislabelled images

We propose that images that are misclassified by ARA-CNN with high certainty (i.e., low H) are good candidates for identifying mislabelled training samples (see Identification of mislabelled training samples). To demonstrate the performance of our identification approach, we artificially introduced increasing percentage of mislabelled images into the training set and measured sensitivity and specificity, while recording the overall model performance.

To this end, we randomly divided the dataset into a training set and a test set, with the the same proportions as during the model training (see Model training). Next, we took the training set, randomly sampled a given percentage pm of images and changed their assigned class at random. Finally, we trained the model on a training dataset with these mislabelled images reintroduced. We defined the set of positives P as candidate mislabelled images identified by our approach. The set of true positives TP is defined as all of the artificially mislabelled images. Sensitivity was evaluated as \(|TP|/|P|\) and specificity as \(|TN|/|N|\), with TN and N being the complement sets for TP and P, respectively.

Sensitivity of mislabelled image identification is overall very high, and is only slightly affected by the growing percentage of mislabelled samples (Fig. 4A). For \({p}_{m}\in \{0.1,0.5,1\}\), sensitivity is at 100%, meaning that all misclassified images with uncertainty below Ht are in fact mislabelled. For higher pm values, sensitivity is slightly lower, but it never dips below 88.82% (for \({p}_{m}=40\)). Specificity decreases with the increase of the percentage of mislabelled training samples, but remains at very high level even for substantial percentage pm, dropping below 80% only at pm around 20%. This demonstrates that uncertainty H can be used to find mislabelled training samples even when the noise in the training data is extremely high.

Figure 4
figure4

Identification of mislabelled images as a function of their percentage in the training set. (A) Sensitivity and specificity for the proposed mislabelled sample identification strategy. (B) Classification accuracy of ARA-CNN decreases only for very high fraction of mislabelled training images.

We also measured what effect an increasing pm has on the classification accuracy of ARA-CNN on the test set (Fig. 4B). Remarkably, up to and including 5% of artificially mislabelled training samples, the performance is not affected. From 10% up to and including 70%, it decreases, but only slightly. From 80%, the amount of mislabelled images is too large and the model cannot be trained properly, which results in a substantial drop in accuracy. Such a good classification performance even in the case when the majority of the training samples are mislabelled at random indicates that ARA-CNN is highly robust to noise in the training data.

Understanding the uncertainty of image classification

To investigate what pathological features of images are determinant for assigning specific uncertainty values measured by Entropy H, we selected test images with very low (\(H\le 0.2\)) and very high (\(H\ge 0.8\)) uncertainty and inspected them by eye. We focused on Entopy H due to its superior performance in active learning. There were no examples of the Empty class with high uncertainty, indicating this class is easy for the algorithm to recognise and classify properly. For each of the remaining seven tissue classes, images of lowest uncertainty display characteristic pathological features (Fig. 3D). Images of the Tumour class with low H display cells that have distinct changes in their nuclei: enlargement, hiperchromasia (dark violet colour), improper chromatin distribution (i.e. spots with higher and lower density) accompanied by multiplication of nucleoli, increased nuclear to cytoplasmic ratio, nuclear fusions and cell overlapping. The images of the Stroma class with lowest uncertainty display typical uniformly stained pink, eosinophilic fibres with elongated nuclei, and low nuclear to cytoplasmic ratio. For the images of the Complex class with low assigned H, the stroma is infiltrated by lymphatic or neoplastic cells with addition of erythrocytes. The highly certain images of the Lympho class show features typical for areas of lymphocytic dense infiltration - lymphocytes are intensively stained, monomorphic cells with round nucleus and very scarce thin, basophilic cytoplasm rim. Nucleoli are not visible. Images of the Debris class with low uncertainty H values are composed of various tissue samples. First, they contain a mucous, amorphic substance creating multiple, fine vesicles, white in the centre with violet contours. On top of that, features characteristic of the Debris class are mostly extravasated erythrocytes – red, round cell conglomerates presenting very dense collocation with blurred cell contours. Images of the Mucosa class with very low assigned uncertainty show typical features of mucosal glands in large intestine. They are composed of visible characteristic goblet cells that are cylindrical in shape and contain big, round areas filled with mucous - white with violet margin. Small, regular, dark nuclei are visible at the cell periphery. Goblet cells lay in linear or rosette–like formations. Finally, images of the Adipose class with low uncertainty show pathological features typical of the adipose tissue. They are composed of big, white polygonal areas with violet, wide contour, adhering to each other tightly. No nuclei are visible.

In contrast to low uncertainty images, the images with the highest uncertainty show features that are pathologically difficult to categorise (Fig. 3E). For very uncertain images of the Tumour class, the sparse cells visible within the stroma show fewer features of malignancy – most of them are small, regular in shape, with no visible nucleoli. No nuclear fusions or cell overlapping are observed. The pictures could be mistaken with complex stroma. For the images of the Stroma class that were assigned very high uncertainty H, the tissue has irregular structure without typical linear fibres and elongated nuclei. Empty spaces in both example images and very low colour intensity in the top one may be artefacts, although whole samples could be categorised as complex stroma or perchance debris because of listed alternations. Out of the two complex stroma example images with very high uncertainty, in the top image (Fig. 3E third column) there are no visible fibres. At the same time, the image contains many pale vesicular areas slightly similar to mucous. The bottom image could be interpreted as a normal stroma sample, because of its colour, fibrotic structure and shape of the nuclei. In the top image representative of very high uncertainty images of the Lympho class, cell arrangement is not very dense and there is a lot of stroma visible between nuclei – this could be categorised as complex stroma instead. The bottom picture shows many features of malignancy that should suggest diagnosis of tumour cells. From the two uncertain example images from the Debris class, the top consists of tissue residues with no particular structures visible. The bottom image shows structures very similar to mucosal glands – areas of mucous are bigger and well margined in comparison to amorphic mucous specific for this category. From the two high uncertainty images of the Mucosa class, the top image has heterogeneous composition. In the right part of the image, goblet cells with their nuclei can be seen. The left part is full of amorphic substance and could be categorised as debris. In the bottom example, only the lower left corner looks like mucosal glands forming rosette. The rest of the image contains stroma with lymphatic infiltration, thus pathologically could be categorised as complex stroma. In the top uncertain example of the Adipose class, although white, empty spaces are clearly visible and cell walls have more irregular margin than normally. In the bottom example, the characteristic polygonal shapes are not visible. The images do not suit any other category more than adipose tissue, however they do not share its typical features.

Discussion

In this article, we stipulated the necessity of an accurate, reliable and active (ARA) machine learning framework for histopathological image classifiction. We implemented this framework with a new Bayesian deep learning CNN model, called ARA-CNN. ARA-CNN was applied to the task of colorectal tissue classification and incorporated it into an uncertainty-based active pathology workflow. The classification accuracy achieved by our model exceeds the results reported by authors of the training dataset Kather et al.29 used in this work. The proposed CNN architecture shows outstanding performance in both binary and multiclass classification scenarios, reaching almost perfect accuracy (error rate of 0.89%) in the former case and best in class (error rate of 7.56%) in the latter. It also surpasses the classification performance of other methods that were trained with the same dataset by up to 18.78%.

To achieve reliability, the model measures the uncertainty of each prediction. As demonstrated by our active learning results (Fig. 3), it can be used to largely reduce the labour that trained pathologists need to put into image labelling and increase the efficiency of model training. In an active learning workflow involving interaction with a pathologist responsible for annotating whole slide images, the pathologist should be informed which classes are the most uncertain and prioritise them in subsequent annotation iterations (Fig. 1A). Our analysis involved a comparison of two different uncertainty measures, Entropy H, and BALD. The two measures agreed on which classes are most uncertain on average, pointing to classes which were most often misclassified by the model. The Entropy H, however, outperformed BALD as an acquisition function in the active learning workflow. Compared to random selection, H was able to speed-up the training process by a significant margin, while BALD performed only slightly better. Using H, the classification accuracy equal to that of the model trained with the full dataset was reached 45% faster. On top of that, we proposed a highly sensitive and specific approach for identification of mislabelled images in the training data as those which were misclassified by ARA-CNN with low uncertainty H. We showed that ARA-CNN is highly robust to such mislabelled training samples. To investigate how the pathological characteristics of images relate to their uncertainty measure H, we analysed pathological features of examples of highly certain and highly uncertain images. We observed that highly certain images are very good representatives of their class, while the highly uncertain ones are inconclusive and could have been annotated incorrectly when the dataset was constructed. This shows that measuring uncertainty is a good indicator of how well the model is trained and whether its predictions should be trusted without verification.

The excellent performance of ARA-CNN indicates that it is a step forward in establishing accurate and reliable machine learning models for histopathology. Based on such a model, further exciting avenues of research can be followed. As future work, we plan to apply our model to other histopathological tissue datasets. Due to its deep learning nature, our architecture should easily handle tissue types other than colorectal (potentially with the help of transfer learning). Furthermore, we plan more involved spatial analysis of segmented whole-slide images, especially in conjunction with clinical data. Our segmentation could facilitate application of methods that quantify spatial heterogeneity55 in histological samples of colorectal cancer, and improve our understanding of how tumour microenvironment influences the development of this disease. To this end, we plan to work on more precise segmentation algorithms, which will allow better understanding of spatial relations in analysed tissues.

Data Availability

The model definition is available as open-source Python code on GitHub: https://github.com/animgoeth/ARA-CNN.

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Acknowledgements

We thank Łukasz Koperski for guidelines in interpreting the histopatological images.

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Ł.R. performed all experiments and data analysis and contributed to the model. M.M. developed the model architecture. M.M. and Ł.R. developed the implementation of the approach and prepared the visualisations. J.Z. performed the inspection of images with low and high uncertainty. E.S. supervised the research. M.M. and E.S. conceptualised the project. Ł.R. and E.S. wrote the manuscript. All authors reviewed the manuscript.

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Correspondence to Ewa Szczurek.

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Rączkowski, Ł., Możejko, M., Zambonelli, J. et al. ARA: accurate, reliable and active histopathological image classification framework with Bayesian deep learning. Sci Rep 9, 14347 (2019). https://doi.org/10.1038/s41598-019-50587-1

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