In the traditional supervised learning, each training instance is typically associated with one label. With the rapid development of deep learning, such single-instance single-label classification problem is nearly solved, given abundant well-labelled training data. For example, for single object recognition tasks, such as ILSVRC, several methods have already achieved super-human performance [7, 8, 10]. However, in many real-world applications, instead of training instances, we often encounter the problem of training bags, each of which usually contains many instances, e.g., frames in a video clip, object proposals of an image, which is referred as multi-instance setting. In addition, to accurately describe a bag, we often need to associate multiple labels or tags to it, which is referred as multi-label setting. Such multi-instance multi-label (MIML) learning setting  is more general, but more challenging.
MIML learning has many applications in computer vision. For example, in multi-object recognition and automatic image tagging problems, an image can be decomposed into many object proposals, where we can treat each image as a bag and each of its proposals as an instance in the bag, as illustrated in Fig.1. The MIML learning problem essentially is, given training bags with only bag-level labels, how to learn an effective model that can accurately assign multiple labels to new bags. MIML learning problems have attracted significant attentions in the past few years [25, 32, 21, 2]. With the release of large scale multi-label datasets such as YFCC100M  and Google Open Images , it will stimulate more large-scale MIML learning studies.
On the other hand, in many applications, additional information is often available in the training phrase. Vapnik and Vashist  referred such additional information as privileged information (PI) and showed that PI can be utilized as a teacher to train more effective models in traditional supervised learning problems. This motivates us to incorporate PI into MIML learning problem. However, there are two main obstacles hinging us from applying learning using privileged information (LUPI) paradigm to MIML problems.
First of all, existing works on privileged information only consider instance-level PI [28, 27, 17, 14]. This might not be a problem for traditional supervised learning, but for most MIML tasks, instance-level PI, where each training instance in each training bag must have a corresponding privileged instance, is hard to obtain. In contrast, bag-level PI is much easier to acquire, and is often already available. Take the aforementioned multi-object recognition problem as an example. It is hard to obtain privileged information for each object proposal we extract, but for images, there are bounding-boxes, captions, descriptions, which can all be used as bag-level PI. Another example could be video recognition, where each clip can be viewed as a bag and frames or sub-clips in each clip, containing different objects, activities, can be viewed as instances in the bag. It is clear that bag-level PI such as video descriptions are much easier to obtain. Therefore, in MIML learning with privileged information, it is more general and meaningful to consider bag-level PI, which is lacking in the current literature.
Secondly, most existing works on PI are still based on the original SVM+ formulation, where PI is used as slack functions. Although this formulation has many theoretical and practical merits 
, it is hard to incorporate it into state-of-the-art deep learning paradigm in an end-to-end fashion as the SVM+ formulation is not stochastic gradient descent (SGD) compatible. Thus, existing PI works fail to benefit from rapid developments of deep learning.
In this paper, we address these two problems by proposing a two-stream fully convolutional network, which we refer as MIML-FCN+. In the proposed framework, each stream handles one source of information, namely training bags and privileged bags, respectively. The two-stream networks are unified by a novel PI loss, which follows the high level idea of SVM+  but with a totally different realization oriented for deep learning. Specifically, we propose to utilize privileged bags to model training losses and use it as a convex regularization term, which facilitates SGD-compatible loss and end-to-end training. In addition, motivated by the work , which shows exploiting structured correlations among instances can help MIML learning, we further propose to construct a graph for each bag and incorporate the structured correlations into our MIML-FCN+ framework, thanks to the structure of fully convolutional networks, where filter sizes and step sizes of the convolutional layers can be easily adjusted.
The major contributions of this paper are threefold. First, we propose and formulate a new problem of MIML learning with privileged bags, which is a much more practical setting in real world applications. To the best of our knowledge, this is the first work exploiting privileged bags instead of privileged instances. Second, we propose a two-steam fully convolution network with a novel PI loss, MIML-FCN+, to solve the MIML+PI learning problem. Our solution is fully SGD-compatible and can be easily integrated with other state-of-the-art deep learning networks such as CNN and RNN. Our MIML-FCN+ is flexible to combine different types of information, e.g. images as training bags and texts as privileged bags. It can also be easily extended to make use of privileged instances if available. Third, we further propose a way to incorporate graph-based inter-instance correlations into our MIML-FCN+.
2 Related Works
Multi-instance Multi-label Learning: During the past decade, many MIML algorithms have been proposed [18, 36, 37, 20, 19]. For example, MIMLSVM  degenerates the MIML problem into solving the single-instance multi-label problem while MIMLBoost  degenerates MIML into multi-instance single-label learning, which suggest that MIML is closely related to both multi-instance learning and multi-label learning. Ranking loss had been shown to be effective in multi-label learning, and thus Briggs et al.  proposed to optimize ranking loss for MIML instance annotation. In terms of generative methods, Yang et al.  proposed a Dirichlet-Bernoulli alignment based model for MIML learning problem. In contrast, in this work we consider using privileged information to help MIML learning under the deep learning paradigam, which has not been explored before.
Many computer vision applications such as scene classification, multi-object recognition, image tagging, and action recognition, can be formulated as MIML problelms. For instance, Zha et al. proposed a hidden conditional random field model for MIML image annotation. Zhou et al.  applied MIML learning for scene classification. Several works [21, 32, 2] also implicitly exploited the MIML nature of multi-object recognition problem.
Learning Using Privileged Information (LUPI): LUPI assumes there are additional data available during training, i.e. privileged information (PI), which are not available in testing. Vapnik and Vashist  proposed an SVM+ formulation that exploits PI as slack variables during training to “teach” students to learn better classification model. The idea was later developed into two schemes: similarity control and knowledge transfer . LUPI has also been utilized in metric learning , learning to rank  and multi-instance learning . A few works have applied PI to computer vision applications. For example, Li et al.  applied PI for web images recognition. Sharmanska et al.  applied PI for image ranking and retrieval. However, most of the existing PI works consider only instance-level PI, are still based on SVM+ formulation, which is hard to be incorporated into a deep learning framework in an end-to-end fashion. In this work, we address all these limitations by a two-stream fully convolutional network and a new PI loss.
3 Proposed Approach
In the context of multi-instance and multi-label (MIML) learning, assume there are bags in the training data, denoted by , where each bag has instances and contains the labels associated with . We represent
as a binary vector of length, where is the number of labels. The -th dimension if -th label is associated with at least one instance in ; otherwise . In other words, denoting as the label vector of instance , if and only if . Note that in common MIML setting, the instance-level labels are usually assumed not available.
In learning using privileged information (LUPI) paradigm, we further assume that for each training bag, there exists a privileged bag . and are two views of the same real world image. can contain instances . Here is generally different with , and there is no instance-level correspondence between training data and privileged information. This is one fundamental difference between our work and previous LUPI studies that always assume each training instance has a corresponding privileged instance .
3.1 MIML Learning through FCN
MIML: We start with reviewing the general MIML learning pipeline. Given a bag , the goal of MIML learning is essentially to learn a model such that the difference between and the true label is small. An MIML system generally consists of two components: a non-linear feature mapping component and a classification component. In the feature mapping component, each -dimensional training instance is mapped from the input space to the feature space, where training data could be linearly separable, by a non-linear mapping function .
In the classification component, each instance is first mapped from the feature space to the label space by
where is a
weight matrix classifying the-dim mapped instance to a label vector. Then, the predicted instance-level labels is transferred to the bag-level labels. According to the MIML learning definition, the relation between instance-level labels and bag-level labels can be expressed either as:
where is the per-dimension max operation, or alternatively as a set of linear constraints :
Let us consider the first case, i.e., using Eq.(2) to map instance-level labels to bag-level labels. With this relation, the bag-level label prediction becomes
Thus, the objective function for MIML learning can be written as
where is a suitable multi-label loss such as square loss or ranking loss.
It is not difficult to see that the above formulated MIML learning can be realized via a neural networks. First, in terms of feature mapping, the previous MIML studies usually project the data from input space into feature space by pre-defined project functions, such as kernels and Fisher vectors , or learned linear projections 
, which are incompatible with neural networks. On the other hand, the combination of multiple layers of fully connected layers and non-linear activation functions has proven to be a powerful non-linear feature mapping[4, 22]
. Thus, in our framework, we employ multiple convolutional layers and ReLU layers as our feature mapping component. The reason that we use fully convolutional networks (FCN) without including any fully connected layers is that FCN is more flexible and can handle any spatial resolution, which is needed for the considered MIML problem since the number of instances in each bag varies.
Particularly, with denoting the -th convolutional layer, where is the input, is the convolution operation, is the parameters and is the bias, and denoting the non-linearity, the feature mapping component of our framework can be expressed as:
if there are in total layers. For filters, the convolution operator is just a dot-product.
Other operations in MIML can also be easily mapped into FCN. Specifically, the classification component in (4) is realized by a convolutional layer with filter size and parameters
to project the learned feature to the label space, followed by a pooling layer to extract per-bag prediction. The loss function in (5) is realized by a loss layer with appropriate SGD-compatible multi-label loss such as square loss [29, 31] and ranking loss [29, 32]. Fig. 2 shows an example of our proposed MIML-FCN architecture, which typically consists of a few layer-pairs (e.g. 2 layer-pairs here) of conv layer and ReLu layer for feature mapping, one
conv layer for classification, one global pooling layer (e.g. max pooling here) and one loss layer.
We would like to point out that similar network structure has been used in several previous works on multi-object recognition and weakly supervised object detection [21, 2], while we explicitly use such structure for MIML and more importantly we will extend it to incorporate privileged information as well as structured correlations among instances.
3.2 MIML-FCN with Privileged Bags
Training the proposed MIML-FCN might not be as easy and straightforward as training a single-label CNN, as the MIML learning itself is by definition non-convex. As a result, the framework might not reach optimal classification accuracies even if the hyperparameters are carefully tuned. Fortunately, in many applications there often exists additional information, referred as privileged information (such as image captions in multi-object recognition), in training stage that can help us learn a better model.
SVM+: Learning using privileged information (LUPI) paradigm was first introduced by Vapnik and Vashist . They utilized privilege information as the slack variables in the SVM formulation, called SVM+. Specifically, their (linear) SVM+ objective function is:
where and are the trade-off parameters, is the classification model, is the slack function, replacing the slack variables in the original SVM formulation. This slack function acts as a teacher by correcting the concepts of similarity of original training data by privileged information during training process.
Although LUPI paradigm has many good theoretical and practical merits [28, 27, 17], directly applying this formula to MIML learning setting is not plausible due to two main problems. Firstly, in most MIML problems, instance-level PI, or privileged instances, is difficult to obtain. The previous work  that extends SVM+ directly to MISVM+ requires privileged instances, which greatly limits its applicable areas. In contrast, bag-level privileged information, or privileged bags, is much easier to get and often readily available. Secondly, Eq.(7) is relatively difficult to solve compared to traditional SVM. Although there are efforts on developing new dual coordinate descent algorithm to improve the training efficiency , unifying LUPI and deep learning in an end-to-end fashion is still not tackled.
MIML-FCN+: To overcome the obstacles, we construct a two-stream network, named MIML-FCN+. The first stream models training bags (same as MIML-FCN), and the second stream models the privileged bags. With this configuration, our framework not only effectively utilizes privileged bags, but also allows the flexibility to deal with different types of data. For instance, if the training bags are images and privileged bags are texts, we clearly need to map these data to different feature spaces in order to effectively extract knowledge, for which our two-stream networks can be configured accordingly. We could even employ RNN if the privileged information is text.
With MIML-FCN+, we need an SGD-compatible PI loss to replace the original loss so that we can utilize privileged bags as “teachers” during training. Since dealing with slack variables is difficult, inspired by the high level idea of , we propose to utilize privileged information to model the loss of training data, penalize the difference of PI modelled loss and true loss, and add the difference as a regularization term to Eq.(5).
Specifically, assume that for each training bag , we have a privileged bag . We use a second stream of network (called slack-FCN) to model privileged bags. Compared to the first stream of network (called loss-FCN), which models the training bags, the goal of the second stream is not to learn a classification model, but to model the loss of the first stream. Denote the output of the second stream for an input privileged bag as , the two streams share the same loss layer defined by:
where is the L norm.
In SVM+, privileged information is used to model slack variables, which can be viewed as a set of tolerance functions that allows the margin constraints to be violated. In the proposed MIML-FCN+, we make use of this idea and utilize privileged information to approximate classification error of original training data. On one hand, slack-FCN models the difficulty of classifying training bags with privileged information. On the other hand, slack-FCN can provide a way to regularize the classification errors to avoid over-fitting.
The proposed MIML-FCN+ can be optimized in an alternating fashion. Specifically, we update the loss-FCN while fixing the parameters of slack-FCN until it converges, and subsequently update slack-FCN while fixing the parameters of loss-FCN. This process is repeated for several times until the whole system converges.
3.3 Utilizing Structured Correlations among Instances
In the previous sections, we treat instances in a bag as independently and identically distributed (i.i.d) samples by using filter in the convolutional layers. The assumption ignores the fact that instances in a bag are rarely independent , and correlations among instances often contain structured information. Considering object proposals from an image as an example, these proposals are clearly correlated as there exist large overlaps among them. Zhou et al.  showed that treating instances as non-i.i.d samples could be helpful for learning more effective classifier. Their MIGraph and miGraph methods explicitly or implicitly use graph to exploit the structured correlations among instances in each bag.
Our MIML-FCN+ framework is flexible to incorporate such structured correlations among instances since our framework is based on FCN, where the filter sizes of convolutional layers can be easily adjusted to accommodate graph input. Specifically, we first construct a Nearest-Neighbour (NN) graph for each bag, which is a simple and effective way to capture correlations among instances in each bag. Assume for each vertex in the graph, i.e., each instance, there exist edges connecting to other vertices, i.e., its nearest neighbours. We can organize this graph as a
D tensor and use it as the input to our system. The dimensionality of the tensor will be, where is the number of instances in bag , and is the dimension of each instance. Instead of using filter for the first convolutional layer, we use filters. In this way, we essentially utilize not only each instance itself, but also its nearest neighbours in the graph. By treating each instance as a connected vertex in the graph, we could potentially learn a more robust network.
4 Multi-object Recognition: A Practical Example
In this section, we use multi-object recognition as a practical example to show how to apply our proposed MIML-FCN+ framework. We also validate the performance of the proposed MIML-FCN+ on this application in the experiment section.
Multi-object recognition refers to recognizing multiple objects from one single image. As the objects could be from different locations, scales and categories, it is natural to extract object proposals from training images. Thus, for training data, we refer each image as a bag
and feature extracted from the proposals in the image as instances in the bag. Particularly, we utilize ROI-pooled CNN features as features for proposals as in. We stack our MIML-FCN+ framework on top of ROI-pooled CNN and train the entire system end-to-end.
Bounding boxes as PI: For privileged bags, we utilize two different types of privileged information. The first type of privileged information is bounding boxes for objects. In order to make of use of this information, we propose a PI pooling layer to replace the global max pooling in the slack-FCN, as shown in Fig. 3(a). This PI pooling layer identifies true positive proposals that have IoU with ground truth bounding boxes and average-pool the scores of these proposals so as to better exploit the key instances in the bag. For negative proposals, PI pooling layer sticks with max-pooling. Mathematically, this PI pooling layer can be defined as:
where is the set of proposals that have IoU with ground truth bounding boxes of -th category, is the predicted instance or proposal level scores in the slack-FCN for the -th proposal and -th category, is the predicted bag level score in the slack-FCN for the -th category, and is the corresponding ground-truth for the loss-FCN.
Note that the proposed PI pooling can only be used in slack-FCN, since it is only available in training but not in testing. Considering only the pooling layer is changed in slack-FCN, both loss-FCN and slack-FCN can share the same feature extraction network, i.e. VGG-16 with ROI pooling as shown in Fig. 3(a). Also, only one conv and Relu layer-pair is used in both loss-FCN and slack-FCN for feature mapping, compared with the two layer-pairs used in Fig. 2. This is because empirically we find one conv and Relu layer-pair performs better.
Image captions as PI: The second type of privileged information is image captions. Considering one image contains multiple captions, we refer all captions of an image as a privileged bag and each individual caption as one instance. To better represent these captions, we extract work2vec features from each word and use the weighted-averaged feature as the representation for each sentence. Subsequently, we feed these features into our slack-FCN, as shown in Fig. 3(b). Note that it is also possible to use a RNN to encode each caption and then append our slack-FCN, which will allow the whole system end-to-end trainable.
We also need to decide what type of loss is suitable for training the proposed networks for multi-object recognition. In this research, we consider two losses: square loss and label ranking loss.
Square Loss: The previous works [29, 32] have shown that square loss can be a very strong baseline for multi-label learning. Thus, we employ square loss as one configuration for our framework. Specifically, the general cost function in (8) now becomes
for which the gradients with respect to and are straightforward to compute.
Label Ranking Loss: Huang et al.  proposed an approximated label ranking loss for the triplet , where is an input bag, is one of its relevant labels, and is one of its irrelevant label. The key idea of this loss is to learn a model so that for every training bag, its relevant labels rank higher than its irrelevant labels by a margin. Specifically, the loss is defined by :
) can be easily calculated and backpropagated.
For our MIML-FCN+, instead of the triplet , we sample a quadruplet at each iteration, and optimize:
Lastly, after training the proposed MIML-FCN+, we use only the loss-FCN during testing.
In this section, we validate the effectiveness of the proposed MIML-FCN+ framework on three widely used multi-label benchmark datasets.
5.1 Datasets and Baselines
We evaluate our method on the PASCAL Visual Object Calssess Challenges (VOC) 2007 and 2012 datasets  and Microsoft Common Objects in COtext (COCO) dataset . The details of these datasets are listed in Table 1. We use the train and validation sets of VOC datasets for training, and test set for testing. For MS COCO, we use the train2014 set for training, and val2014 for testing. For VOC datasets, we use bounding boxes as privileged information with the PI pooling layer as discussed in 4. For MS COCO
dataset, we use two types of PI, bounding boxes and image captions. The evaluation metric used is average precision (AP) and mean average precision (mAP).
|Dataset||#Train Bags||#Test Bags||#Train Instances||#Labels||#Avg Labels|
We compare against several state-of-the-art methods for MIML learning,
MIMLfast : A fast and effective MIML learning method based on approximate label ranking loss as described in the previous section. MIMLfast first projects each instance to a shared feature space with linear projection, then learns sub-concepts for each label and selects the sub-concept with maximum score. MIMLfast also employs global max to obtain bag-level score. The main difference between their method and our baseline MIML-FCN is that our feature mapping can be non-linear.
miFV : A Fisher vector (FV) based MIL learning method that encodes each bag to a single Fisher vector, and then uses the ranking loss or square loss to train a multi-label classifier on the FVs.
RankLossSIM : an MIML learning extension of the ranking SVM formulation.
There exist other MIML learning methods such as MIMLSVM, MIMLBoost  and KISAR , but they are too slow for our large-scale applications. Other than the MIML learning methods, we also compare our MIML-FCN+ framework with the state-of-the-art approaches for multi-object recognition that do not formulate the task as MIML learning problem, including VeryDeep , WSDDN , and the MVMI framework . However, we did not compare with the existing PI methods such as SVM+  and sMIL+ , since they can only deal with privileged instances but not privileged bags. As far as we know, our proposed MIML-FCN+ is the only method that can make use of privileged bags.
For our own MIML-FCN+ framework, we consider three different variations:
MIML-FCN: Basic network without PI.
MIML-FCN+: Two stream networks, loss-FCN and slack-FCN, using either bounding boxes as PI, denoted as MIML-FCN+BB, or image captions as PI, denoted as MIML-FCN+CP.
G-MIML-FCN+: Two stream networks utilizing NN graphs. It also has two versions: G-MIML-FCN+BB and G-MIML-FCN+CP.
5.2 Settings and Parameters
Following the discussions in Section 4, we consider each image from the datasets as a bag. For each image, we extract maximum proposals using Regional Proposal Network (RPN) , each of which is considered as one instance in the bag. This results in millions of training instances even for the relatively small VOC 2007 dataset.
For feature extraction, we utilize the network architecture of Faster R-CNN . Basically, our feature extraction network is the VGG-16 network  with ROI pooling layer, with the removal of all the classification / detection related layers. For fair comparison, all methods we compare are using these same features, although some methods likes our MIML-FCN+ and WSDDN  can be integrated with the feature extraction network and trained end-to-end.
Our basic MIML-FCN consists of one convolutional layer, one ReLU layer, one classification layer, one pooling layer and one loss layer, as shown in Fig. 3. The convolutional layer contains filters in total. We tested a few possible numbers of filters, such as and found out that achieves slightly better accuracies. We also study the effects of different number of convolution and ReLu layer-pairs, effects of dropout, as well as the differences between square loss and label ranking loss. The results are presented in Fig.4. From these results, we decide to choose one convolutional-ReLU layer-pair with square loss.
Our main hyperprameter is the tradeoff parameter , which is tune by cross-validation in a small subset of the training data. The other important hyperparameter is the nearest neighour number in G-MIML-FCN+, which we set to in all our experiments. For other methods, we follow the parameter tuning specified in their papers if available.
5.3 Classification Results
|VOC 2007||VOC 2012||MS COCO|
Table 2 reports our experimental results compared with state-of-the-art methods on the three benchmark datasets.
Comparing our basic network MIML-FCN with state-of-the-art MIML methods (upper part of the table), we can see that our MIML-FCN achieves significantly better accuracies. Specifically, MIML-FCN achieves around performance gain over miFV, which uses Fisher vector as a holistic representation for bags. This suggests that using neural networks for MIML problem can better encode holistic representation. One interesting observation is that, if we remove the first convolutional and ReLU layers of our MIML-FCN, it becomes worse than miFV. This phenomenon confirms the effectiveness of non-linear mapping component in our system. For MIMLFast, the main difference is that we employ square loss instead of label ranking loss and we have a non-linear ReLU function. Our MIML-FCN obtains more than accuracy gain over MIMLFast, which once again confirms the effectiveness of non-linear mapping over linear mapping.
For comparisons with other state-of-the-art recognition methods (middle part of the table), it can be seen that our basic MIML-FCN achieves similar results as WSDDN, as the principles behind both methods are similar. In contrast, instead of treating the task as MIML problem, VeryDeep  just treats it as multiple single label problems, where it uses multiple images at different scales as network input, concatenates all the features from different scales as the final representations and then learns multiple binary classifiers from the representations. Both our basic network MIML-FCN and WSSDN achieve better performance than VeryDeep.
More importantly, Table 2 demonstrates the effectiveness of using privileged information. Note that since captions are only available in MS COCO dataset, MIML-FCN+CP is only applied on COCO. From the table, we can see that MIML-FCN+BB achieves around performance gain over MIML-FCN on all three datasets, confirming the effectiveness our privileged bag idea. Although MIML-FCN+CP is not as effective as MIML-FCN+BB, it still outperforms MIML-FCN. Comparing MIML-FCN+BB with the state-of-the-art multi-view multi-instance (MVMI) framework , both methods make use of bounding boxes, where our framework utilizes BB as PI while their framework implicitly uses BB as label view in the multi-view setup. Note that the results shown for  in Table 2 is a fusion of their system and VeryDeep, but our MIML-FCN+BB still achieves better performance.
In addition, comparing the results between MIML-FCN+BB and G-MIML-FCN+BB and between MIML-FCN+CP and G-MIML-FCN+CP, we can see that by further exploiting inter-instance correlations, our framework can perform even better.
In this paper, we have proposed a two-stream fully convolutional network, named MIML-FCN+, for multi-instance multi-label learning with privileged bags. Compared with existing works on PI, we explored privileged bags instead of privileged instances. We also proposed a novel PI loss, which is similar to the high level idea of SVM+, but is SGD-compatible and can be integrated into deep learning networks. We have also explored the benefits of making use of structured correlations among instances by simple modifications to the network architecture. We demonstrated the effectiveness of our system by a practical example of multi-object recognition. We achieved significantly better performance in all the three benchmark datasets containing millions of instances. For future directions, we intend to explore more possible applications as well as other kinds of privileged information. We could also study the theoretical differences between the proposed PI loss and SVM+ loss.
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