D ISCRIMINATIVE A CTIVE L EARNING
Anonymous authors
Paper under double-blind review
A BSTRACT
We propose a new batch mode active learning algorithm designed for neural networks and large query batch sizes
The method Discriminative Active Learning (DAL) poses active learning as a binary classiﬁcation task , attempting to choose examples to label in such a way as to make the labeled set and the unlabeled pool indistinguishable.
Experimenting on image classiﬁcation tasks, we empiri- cally show our method to be on par with state of the art methods in medium and large query batch sizes , while being simple to implement and also extend to other domains besides classiﬁcation tasks
Our experiments also show that none of the state of the art methods of today are clearly better than uncertainty sampling, negating some of the reported results in the recent literature.
I NTRODUCTION
In the past few years deep neural networks achieved groundbreaking results in many machine learning tasks, ranging from computer vision to speech recognition and NLP.
While these successes can be attributed to the increase in computational power and to the expressiveness of neural networks, they are also a clear result of the use of massive datasets which contain millions of samples.
The collection and labeling of such datasets is highly time consuming and often expensive, and much research has been done to try and reduce the cost of this process.
Active learning is one ﬁeld of research which tries to address the difﬁculties of data labeling.
It assumes the collection of data is relatively easy but the labeling process is costly, which is the case in many language, vision and speech recognition tasks.
It tackles the question of which samples, if labeled, will result in the highest improvement in test accuracy under a ﬁxed labeling budget.
The most popular active learning setting is pool-based sampling (Settles, 2012), where we assume that we have a small labeled dataset L and access to a large unlabeled dataset U from which we choose the samples to be labeled next.
We then start an iterative process where in every step the active learning algorithm uses information in L and U to choose the best x ∈ U to be labeled.
x is then labeled by an oracle and added to L , and the process continues until we have reached the desired amount of samples or test accuracy.
Many heuristic methods have been developed over the years (Settles, 2012), mostly for classiﬁcation tasks, that have been shown to reduce the sample size by up to an order of magnitude.
These methods ﬁt a model to the labeled dataset and then choose a single sample to be labeled according to the performance of the model on the samples in U .
While these methods are very successful, they have a few shortcomings that make them less suited for large scale data collection for deep learning.
First, it is highly impractical to query a single sample from U in every iteration, since we need a human in the loop for every one of those iterations.
Adding to that the time needed to ﬁt a neural network, collecting a large dataset using this setting simply takes too long.
Second, many of these methods are designed solely for classiﬁcation tasks, and extending them to other domains is often non trivial.
To tackle the ﬁrst problem, the batch-mode active learning setting was introduced, allowing for the querying of a batch of examples at every iteration.
This change adds complexity to the problem since it might not be enough to greedily choose the top- K samples from U according to some score, since they may be very similar to each other.
Choosing a batch of diverse examples is often better than choosing one containing very similar examples, which may lead to performance that is worse than random sampling.
Several methods were developed with this problem in mind (Chen & Krause, 2013), (Guo & Schuurmans, 2008), (Azimi et al., 2012).
The second problem however has not been explicitly addressed to the best of our knowledge, and active learning solutions to other domains have had to be adapted separately (Settles, 2008), (Vezhnevets et al., 2012).
To address the second problem and make the method agnostic to the speciﬁc task being performed, we do not assume access to a classiﬁer trained on the labeled set when choosing the batch to query and instead only assume access to a learned representation of the data, Ψ( x ) .
We pose the active learning problem as a simple binary classiﬁcation problem and choose the batch to query according to a solution to said problem.
We compare our method empirically to today’s state-of-the-art active learning methods for image classiﬁcation, showing competitive results while being simple to implement and conceptually simple to transfer to new tasks.
R ELATED WORK
There has been extensive work on active learning prior to the advances in deep learning of the recent years.
This work is summarized in (Settles, 2012) which covers the many different heuristics developed for active learning, along with adaptation made for other tasks besides classiﬁcation.
A large empirical study of different heuristics applied to classiﬁcation using the logistic regression model can be found in (Yang & Loog, 2018).
This study shows uncertainty-based methods (Lewis &
Gale, 1994) perform well on a large and diverse set of datasets while being very simple to implement.
These methods score the unlabeled examples according to the classiﬁer’s uncertainty about their class, and choose the example with highest uncertainty.
While neural networks for classiﬁcation tasks output a probability distribution over labels, they have been shown to be over-conﬁdent and their softmax scores are unreliable measures of conﬁdence.
Recent work (Gal et al., 2017) shows an equivalence between dropout, a widely used neural network regularization method, and approximate Bayesian inference.
This allows for the use of dropout at test time in order to achieve better conﬁdence estimations of the network’s outputs.
Our empirical analysis shows this method performs very similarly to uncertainty sampling using the regular softmax scores.
In addition to uncertainty-based approaches to active learning, another approach that has been actively studied in the past is the margin-based approach, which has a similar ﬂavor.
Instead of scoring an example based on the output probabilities of the model, these methods choose the examples which are closest to the decision boundary of the model.
While in linear models like logistic regression for binary classiﬁcation problems these two approaches are equivalent, this isn’t the case for neural networks that have an intractable decision boundary.
(Ducoffe & Precioso, 2018) approximates the distance to the decision boundary using the distance to the nearest adversarial example (Szegedy et al., 2013).
Our empirical analysis shows that while this method is conceptually very different from uncertainty sampling, it ranks the unlabeled examples in a very similar way.
Another active learning approach is based on expected model change, choosing examples which will cause the biggest effect to our model when labeled.
(Settles et al., 2008) and (Huang et al., 2016) use this approach by calculating the expected gradient length (EGL) of the loss with respect to the model parameters, when the expectation is over the posterior distribution over the labels induced by the trained classiﬁer.
While their results show signiﬁcant improvements over random sampling for text and speech recognition tasks, our empirical analysis along with the analysis of (Ducoffe &
Precioso, 2018) show that this method is not suited for image classiﬁcation using CNNs.
Finally, (Sener & Savarese, 2018) and (Geifman & El-Yaniv, 2017) address the challenge posed by the batch-mode setting by formulating the active learning task as a core set selection problem, attempting to choose a batch which (cid:15) -covers the unlabeled set as closely as possible and obtains a diverse query in the process.
This is done robustly by formulating the (cid:15) -cover as an integer program which allows a small subset of the examples (outliers) not to be covered.
The metric space over which the (cid:15) -cover is optimized is the learned representation of the data.
While not discussed in their paper, the core set approach is similar to our method in that it only requires access to a learned representation of the data and not a trained classiﬁer, which allows their method to easily extend to other tasks as well.
However, their robust formulation is not as straightforward to implement as our method and does not scale as easily to large unlabeled datasets.
DAL - D ISCRIMINATIVE A CTIVE L EARNING
We motivate our proposed method with a simple idea - when building a labeled dataset out of a large pool of unlabeled examples, we would like our dataset to represent the true distribution of the data as well as possible.
In high dimensional and multi-modal data, this would ensure our labeled set has samples from all of the different modalities of the distribution.
A naive solution would be to model the distribution of the unlabeled pool and use the learned distribution to generate a subsample for labeling, but the generative models of today are either hard to train or break down in high dimensional problems, so a different solution is needed.
Assuming the unlabeled pool is large enough to represent the true distribution, we can instead ask for every example how certain we are that it came from the unlabeled pool as opposed to our current labeled set .
If the examples from the labeled set are indistinguishable from the unlabeled pool, then we have successfully represented the distribution with our labeled set.
Another intuitive motivation is that if we can say with high probability that an unlabeled example came from the unlabeled set, then it is different from our current labeled examples and labeling it should be informative.
This proposition allows us to pose the active learning problem as a binary classiﬁcation problem between the unlabeled class, U , and the labeled class, L .
Given a simple binary classiﬁcation task, we can now leverage powerful modern classiﬁcation models to solve our problem.
Formally, with Ψ : X → ˆ X being the mapping from the original input space to the learned representation, we deﬁne a binary classiﬁcation problem with ˆ X as our input space and Y = { l, u } as our label space, where l is the label for a sample being in the labeled set and u is the label for the unlabeled set.
For every iteration of the active learning process, we solve the classiﬁcation problem over U ∪ L by minimize the log loss and obtaining a model ˆ P ( y | Ψ
( x )) .
We then select the top- K samples that satisfy argmax
[Equation]
3. M OTIVATION FROM DOMAIN ADAPTATION
To give theoretical motivation for our method, we will show a connection to domain adaptation in the binary classiﬁcation setting.
The results and deﬁnitions in this section are taken from (Ben-David et al., 2010) unless stated otherwise.
Domain adaptation deals with the problem of bounding the error of a classiﬁer trained on a source distribution D S but then tested on a different target distribution D T .
If we assume U is large enough to represent the underlying distribution, but L is too small, we can treat L as coming from a biased source distribution and U as coming from the true target distribution.
(Ben-David et al., 2010) shows that we can use the total variation distance between D S and D T to bound the error of a classiﬁer trained on the source sample.
Assuming the labeling function is the same for both domains, we can write:
[Equation]
Since the total variation distance is an overly strict measure of distance, we may use the notion of
H -divergence (Kifer et al., 2004) to measure the distance between two distributions in the context of a hypothesis class.
Deﬁnition 3.1 Given a domain X with D and D (cid:48) distributions over X , let H be a hypothesis class on X and denote by I ( h ) the set of for which h ∈ H is a characteristic function; that is, x ∈
I ( h ) ⇐⇒ h ( x ) = 1 .
The H -divergence between D and D (cid:48) is
[Equation]
This divergence measure is upper bounded by the total variation distance and can be estimated from empirical data by the following lemma from (Ben-David et al., 2010):
[Equation]
Lemma 3.1 Let H be a hypothesis space on X with VC dimension d .
If S and S (cid:48) are samples of size m from D and D (cid:48) respectively and ˆ d H ( S, S (cid:48) ) is the empirical H -divergence between samples, then for any δ ∈ (0 , 1) , with probability at least 1 − δ ,
[Equation]
Finally, ˆ d H ( S, S (cid:48) ) can be calculated directly by solving the binary classiﬁcation task of distinguishing between S and S (cid:48) .
Labeling S as 0 and S (cid:48)
as 1 we have:
Lemma 3.2 For a symmetric hypothesis class H (one where for every h ∈ H , the inverse hypothesis 1 − h is also in H ) and samples S and S (cid:48) of size m ,
[Equation]
where I [ x ∈ S ] is the binary indicator variable which is 1 when x ∈ S .
This suggests that in order to minimize a bound on the generalization error of our task, we should attempt to minimize the H -divergence between D L and D U .
The H -divergence can be estimated by solving the binary classiﬁcation task of distinguishing between the two samples, then greedily minimized by choosing a sample which h correctly classiﬁes as being from U and moving it to L .
This procedure is precisely what is done in our method.
3.1. C ONNECTION TO DOMAIN ADAPTATION BY BACKPROPAGATION
It is interesting to compare our method to the unsupervised domain adaptation method introduced in (Ganin & Lempitsky, 2014).
Their method aims to learn a neural network that will generalize well to a target domain by demanding the representation both minimize the training loss on the source domain and maximize the binary classiﬁcation loss of a classiﬁer that distinguishes between the source and target representations.
Here, the classiﬁcation and domain adaptation objectives are trained jointly, while in DAL they are decoupled - the representation is learned by optimizing the classiﬁcation objective and the sample to query is then chosen using the domain adaptation objective given the learned representation. It would be interesting to use this domain adaptation framework in an active learning setting, as using the unlabeled pool in addition to the labeled set to learn the representation could be beneﬁcial. This can be seen as an extension of DAL, which we leave as future work. 3. R ELATION TO GAN S
Our method is reminiscent of generative adversarial networks (Goodfellow et al., 2014) in that it attempts to fool a discriminator which tries to distinguish between data coming from two different distributions.
However, while the distribution created by the generator in GANs is differentiable and changes according to the gradient of the discriminator in an attempt to maximize the discriminator loss, the active learning setting does not allow us to change the distribution of L in a differentiable way.
Rather, we may only change L by transferring examples from U , which is a discrete and non differentiable decision.
In that sense, DAL’s choice of example being the one which the discriminator is most conﬁdent came from U can be seen as a greedy maximization of the loss of the discriminator, extending the GAN objective to a non differentiable setting.
Instead of modeling the distribution of U with a neural network (the generator), we model the distribution using L which is a subset of U .
Since we train the discriminator until convergence before choosing the examples to label, it gets to observe all of the examples of L and U and more easily detect modes which exist only in U .
This aids in avoiding the problem of mode collapse often exhibited by GANs.
It should be noted that there have been direct attempts to use GANs for active learning (Zhu &
Bento, 2017) in the membership synthesis active learning setting (Settles, 2012), but the results so
1: procedure DAL Q UERY ( U , L , K, n ) (cid:46) K is the total budget, n is the amount of mini-queries 2: for i=1...
n do 3:
P ← TRAIN BINARY CLASSIFIER ( U , L ) 4: for j=1...
Kn do 5:
ˆ x ← argmax x ∈U
P ( y = u
| Ψ( x )) 6:
L ← L ∪ ˆ x 7:
U ← U\ ˆ x 8: end for 9: end for 10: return U , L 11: end procedure far have been preliminary and do not improve upon random sampling when evaluating the method on real datasets. Since so far GANs have been hard to train and unstable when working on real data, our method allows a simpler way of tackling the objective of GANs for active learning. 3. D IFFERENCE FROM THE CORE SET APPROACH It should be noted that similarly to the core set approach, our approach eventually covers the unlabeled data manifold with labeled examples, while not explicitly optimizing an (cid:15) -cover objective.
This could suggest a similarity between the two methods, but they differ on data manifolds which aren’t uniform in their density. The core set approach attempts to cover all of the points in the manifold without considering density, which leads it to over represent examples which come from sparse regions of the manifold. On the other hand, assuming DAL is able to represent ˆ P ( y | Ψ( x )) correctly, it will choose examples such that the ratio of labeled to unlabeled examples remains the same over the entire manifold. This means that L will not be biased towards sparse regions of the manifold, and will sample from U in proportion to the density.
Experiments comparing the two methods on synthetic data conﬁrm this intuition.
However, this does not guarantee our method should perform better than the core set approach, since a bias towards sparse regions of the manifold may be advantageous in certain situations.
P RACTICAL CONSIDERATIONS
We move to detailing some of the practical considerations that arise when implementing DAL.
4. T RADING OFF SPEED
As deﬁned above, our method is greedy and chooses the top- K examples to be labeled according to our score function, without consideration for the diversity of the batch.
Observe however that if we keep Ψ ﬁxed, we do not need a human to label the chosen examples in order to move an example from U to L and continue optimizing .
The representation of the chosen example stays the same and all we need to do is mark it as labeled.
If the sample size we want to query is K , we can split the query into n mini-queries by ﬁrst choosing only the top- Kn examples to be labeled using our method, moving those examples to L without actually labeling them yet, training a new classiﬁer on the new L and repeating the process.
This ensures the eventual chosen query is diverse, since consecutive mini queries will be less likely to contain similar instances.
n , the amount of times we split the query and repeat this process, gives us a parameter with which to trade-off between the running time of our algorithm and the amount of awareness it has for the diversity of its query.
The ﬁnal algorithm is detailed in 1.
In practice, we see an improvement in performance when using these kind of mini queries, but after a certain number of mini queries the improvement levels off.
For the datasets used in these experiments, we found 10-20 mini queries to perform well.
4. C HOOSING THE ARCHITECTURE FOR THE BINARY CLASSIFICATION
Since the learned representation isn’t structured in a way that should give a convolutional architecture any advantage, we chose to use a multi-layered perceptron as the architecture for solving the binary classiﬁcation task.
The chosen architecture was arbitrary, having three hidden layers with a width of 256 and ReLU activation functions.
4. H ANDLING OVERFITTING ISSUES
Note that we are not solving the binary classiﬁcation problem with generalization in mind, but rather we are trying to ﬁt the training set as well as possible and detect the examples which are harder to ﬁt.
A large neural network is often expressive enough to achieve a loss of zero on this kind of binary training set, but it would ﬁnd it harder to ﬁt samples which are nearby and of different labels.
This means that using a small neural network or using early stopping can ensure that the samples which don’t have a high probability of coming from U will have a lower ˆ P ( y = u | Ψ
( x )) .
In practice, we found that for an unlabeled pool 10 times the size of the labeled set, stopping the training process when the training accuracy reached 98% performed well, but changing this value slightly didn’t have a signiﬁcant effect on performance.
E MPIRICAL EVALUATION 5. D ATASETS AND MODELS
We evaluated our method on two datasets, MNIST (LeCun, 1998) and CIFAR-10 (Krizhevsky &
Hinton, 2009).
We used the same model to evaluate the labeled dataset of every method.
For the
MNIST task our classiﬁcation model was a simple LeNet architecture (LeCun et al., 1998), while for the CIFAR-10 task we used VGG-16 (Simonyan & Zisserman, 2014) as our architecture.
5. E XPERIMENTAL SETUP
There isn’t a standard methodology for evaluating active learning algorithms with neural networks today.
In reviewing the literature, an important factor which changes between algorithm evaluations is the query batch size, ranging from dozens of examples all the way up to thousands.
Since the query batch size is expected to have a signiﬁcant effect on the performance of the different methods, we evaluate the methods with query batch sizes of different orders of magnitude.
A single experiment for an algorithm entailed starting with an initial random batch which is identical for all algorithms.
We then select a batch to query using the algorithm, add it to the labeled dataset and repeat this process for a predetermined number of times.
In every intermediate step we evaluate the current labeled dataset by training the model on the dataset for many epochs and saving the weights of the epoch with the best validation accuracy, where a random 20% of the labeled set is reserved as the validation set.
The test accuracy of the best model is then recorded.
To reduce the variance from the stochastic training process of neural networks, we average our results over many experiments for every algorithm.
We optimize the model using the Adam optimizer (Kingma & Ba, 2014) with the default learning rate of 0.001.
The complete code used for these experiments is available online (Anonymous, 2018).
5. E VALUATED ALGORITHMS
We compare our method to the following baselines:
• Random : the query batch is chosen uniformly at random out of the unlabeled set.
• Uncertainty : the batch is chosen according to the uncertainty sampling decision rule.
We report the best performance out of the max-entropy and variation-ratio acquisition functions.
• DBAL (Deep Bayesian Active Learning): according to (Gal et al., 2017), we improve the uncertainty measures of our neural network with Monte Carlo dropout and report the best performance out of both the max-entropy and variation-ratio acquisition functions.
• DFAL (DeepFool Active Learning): according to (Ducoffe & Precioso, 2018), we choose the examples with the closest adversarial example.
We used cleverhans’ (Papernot et al., 2018) implementation of the DeepFool attack (Moosavi-Dezfooli et al., 2016).
• EGL (Expected Gradient Length): according to (Huang et al., 2016), we choose the examples with the largest expected gradient norm, with the expectation over the posterior distribution of labels for the example according to the trained model.
• Core-Set : we choose the examples that best cover the dataset in the learned representation space.
To approximate the (cid:15) -cover objective, we use the greedy farthest-ﬁrst traversal algorithm and use it to initialize the IP formulation detailed in (Sener & Savarese, 2018).
We use Gurobi (Gurobi Optimization, 2018) to iteratively solve the integer program.
• DAL (Discriminative Active Learning): our method, detailed above.
5. R ESULTS
In ﬁgure 1 and 2 we compare the different models on the MNIST and CIFAR-10 datasets, over a large range of query batch sizes.
A clear initial observation from the experiments is that, aside from EGL, all algorithms consistently outperform random sampling on a wide range of query batch sizes.
For Uncertainty Sampling, this comes in contrast to past results in (Ducoffe & Precioso, 2018) and (Sener & Savarese, 2018), which show uncertainty-based methods perform on par or worse than random sampling.
Those results were attributed to the batch-mode setting, causing the examples sampled by uncertainty sampling to be highly correlated.
However, our experiments show consistently that this isn’t the case even for very large batch sizes.
For (Ducoffe & Precioso, 2018), after reviewing the published code we believe this is due to an implementation error of the max-entropy acquisition function.
As for (Sener & Savarese, 2018), we are unable to offer a good explanation for the discrepancy in our result since their implementation of uncertainty-based methods was not published.
As for EGL, our result is consistent with (Ducoffe & Precioso, 2018) and an inspection of the queries made by EGL shows each query has a very high bias towards examples from a single class.
A possible explanation for the discrepancy between these results and the strong results of EGL in (Huang et al., 2016) may be the architecture used for the different tasks.
EGL was shown to perform well on text and speech tasks, which use recurrent architectures, while our implementation uses convolutional architectures.
Since EGL uses the gradient with respect to the model parameters as the score function, it is quite plausible that the architecture used can have a big effect on the performance of the method.
The next observation to be made is that once the batch size is large enough, all of the baseline methods are quite on par with each other, with results within the statistical margin of error.
When the query batch size is 100 we see a clear distinction between the performance of the uncertainty based methods and the performance of DAL and Core-Set.
As the batch size increases to 1000, the distinction still exists but DAL outperforms Core Set.
However, when we observe the results for
CIFAR-10, a more realistic dataset with larger query batch sizes, we see all of the methods having essentially the same performance with a slight advantage for our method in the batch size of 10000.
5. R ANKING COMPARISON
Following (Huang et al., 2016), we compare the rankings of the different algorithms on the MNIST unlabeled dataset in the ﬁrst iteration of the experiment.
For pairs of algorithms, we plot the rankings in a 2D ranking-vs-ranking coordinate system, such that a plot close to the diagonal implies the two algorithms score the unlabeled dataset in a similar way.
Figure 3 compares Uncertainty, DBAL, DFAL and DAL.
Core-Set is not compared since it does not output a ranking over the unlabeled set, but rather only outputs a query batch.
Unsurprisingly, we observe that Uncertainty and DBAL are similar since their acquisition function is the same and only the conﬁdence measures slightly changed.
On the other hand, while DFAL uses a very different method for ranking, we see that it ends up ranking the unlabeled set in a very similar way to DBAL and Uncertainty, suggesting that even in a very non-convex function like neural networks, a margin-based approach behaves similarly to an uncertainty-based one. [Figure] [Figure]
[Figure] When comparing DAL to the other methods however, we see a big difference in the ranking which is completely uncorrelated with the rankings of the other methods.
This suggests that DAL selects unlabeled examples in a completely different way than the baseline methods, due to the formulation of the active learning objective as a binary classiﬁcation problem.
C ONCLUSION
In this paper we propose a new active learning algorithm, DAL, which poses the active learning objective as a binary classiﬁcation problem and attempts to make the labeled set indistinguishable from the unlabeled pool.
We empirically show a strong similarity between the uncertainty and margin based methods in use today, and show our method to be completely different while obtaining results on par with the state of the art methods for image classiﬁcation on medium and large query batch sizes.
In addition, our method is simple to implement and can easily be extended to other domains, and so we see it as a welcome addition to the arsenal of methods in use today. [Figure]
R