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Title: Classifier-to-Generator Attack: Estimation of Training Data Distribution from Classifier

Paper content:
Suppose a deep classification model is trained with samples that need to be kept private for privacy or confidentiality reasons.
In this setting, can an adversary obtain the private samples if the classification model is given to the adversary?
We call this reverse engineering against the classification model the Classifier-to-Generator (C2G) Attack.
This situation arises when the classification model is embedded into mobile devices for offline prediction (e.g., object recognition for the automatic driving car and face recognition for mobile phone authentication).
For C2G attack, we introduce a novel GAN, PreImageGAN.
In PreImageGAN, the generator is designed to estimate the the sample distribution conditioned by the preimage of classification model $f$, $P(X|f(X)=y)$, where $X$ is the random variable on the sample space and $y$ is the probability vector representing the target label arbitrary specified by the adversary.
In experiments, we demonstrate PreImageGAN works successfully with hand-written character recognition and face recognition.
In character recognition, we show that, given a recognition model of hand-written digits, PreImageGAN allows the adversary to extract alphabet letter images without knowing that the model is built for alphabet letter images.
In face recognition, we show that, when an adversary obtains a face recognition model for a set of individuals, PreImageGAN allows the adversary to extract face images of specific individuals contained in the set, even when the adversary has no knowledge of the face of the individuals.
Recent rapid advances in deep learning technologies are expected to promote the application of deep learning to online services with recognition of complex objects.
Let us consider the face recognition task as an example.
The probabilistic classification model f takes a face image x and the model predicts the probability of which the given face image is associated with an individual t, f (x) ≃ Pr[T = t|X = x].The
following three scenarios pose situations that probabilistic classification models need to revealed in public for online services in real applications:Prediction with cloud environment: Suppose an enterprise provides an online prediction service with a cloud environment, in which the service takes input from a user and returns predictions to the user in an online manner. The
enterprise needs to deploy the model f into the cloud to achieve this.Prediction with private information: Suppose an enterprise develops a prediction model f (e.g., disease risk prediction) and a user wishes to have a prediction of the model with private input (e.g., personal genetic information). The
most straightforward way to preserve the user's privacy entirely is to let the user download the entire model and perform prediction on the user side locally.Offline prediction: Automatic driving cars or laptops with face authentication contain face/object recognition systems in the device. Since
these devices are for mobile use and need to work standalone, the full model f needs to be embedded in the device.In such situations that classification model f is revealed, we consider a reverse-engineering problem of models with deep architectures. Let D
tr and d X,T be a set of training samples and its underlying distribution, respectively. Let f
be a model trained with D tr . In this
situation, is it possible for an adversary to obtain the training samples D tr (or its underlying distribution d X,T ) if the classification model is given to the adversary?. If this
is possible, this can cause serious problems, particularly when D tr or d X,T is private or confidential information.Privacy violation by releasing face authentication: Let us consider the face authentication task as an example again. Suppose an adversary is given the classification model f . The adversary aims to estimate the data (face) distribution of a target individual t * , d X|T =t * . If this kind of reverseengineering works successfully, serious privacy violation arises because individual faces are private information. Furthermore, once d X|T =t * is revealed, the adversary can draw samples from d X|T =t * , which would cause another privacy violation (say, the adversary can draw an arbitrary number of the target's face images).Confidential information leakage by releasing object recognizer: Let us consider an object recognition system for automatic driving cars. Suppose a model f takes as input images from car-mounted cameras and detect various objects such as traffic signs or traffic lights. Given f , the reverse engineering reveals the sample distribution of the training samples, which might help adversaries having malicious intentions. For example, generation of adversarial examples that make the recognition system confuse without being detected would be possible. Also, this kind of attack allows exposure of hidden functionalities for privileged users or unexpected vulnerabilities of the system.If this kind of attack is possible, it indicates that careful treatment is needed before releasing model f in public considering that publication of f might cause serious problems as listed above. We name this type of reverse engineering classifier-to-generator (C2G) attack . In principle, estimation of labeled sample distributions from a classification/recognition model of complex objects (e.g., face images) is a difficult task because of the following two reasons. First, estimation of generative models of complex objects is believed to be a challenging problem itself. Second, model f often does not contain sufficient information to estimate the generative model of samples. In supervised classification, the label space is always much more abstract than the sample space. The classification model thus makes use of only a limited amount of information in the sample space that is sufficient to classify objects into the abstract label space. In this sense, it is difficult to estimate the sample distribution given only classification model f .To resolve the first difficulty, we employ Generative Adversarial Networks (GANs). GANs are a neural network architecture for generative models which has developed dramatically in the field of deep learning. Also, we exploit one remarkable property of GANs, the ability to interpolate latent variables of inputs. With this interpolation, GANs can generate samples (say, images) that are not included in the training samples, but realistic samples 1 .Even with this powerful generation ability of GANs, it is difficult to resolve the second difficulty. To overcome this for the C2G attack, we assume that the adversary can make use of unlabeled auxiliary samples D aux as background knowledge. Suppose f be a face recognition model that recognizes Alice and Bob, and the adversary tries to extract Alice's face image from f . It is natural to suppose that the adversary can use public face image samples that do not contain Alice's and Bob's face images as D aux . PreImageGAN exploits unlabeled auxiliary samples to complement knowledge extracted from the model f .
As described in this paper, we formulated the Classifier-to-Generator (C2G) Attack, which estimates the training sample distribution ρ t * from given classification model f and auxiliary dataset D tr .
As an algorithm for C2G attack, we proposed PreImageGAN which is based on ACGAN and WGAN.
Fig.
7 represents the results of the C2G attack when the auxiliary data consists of noisy images which are drawn from the uniform distribution.
All generated images look like noise images, not numeric letters.
This result reveals that the C2G attack fails when the auxiliary dataset is not sufficiently informative.
More specifically, we can consider the C2G attack fails when the attacker does not have appropriate background knowledge of the training data distribution.(a
) t * = 0 DISPLAYFORM0 Figure 7: Images generated by the C2G attack when the target label is set as t * = 0, 1, 2 and uniformly generated noise images are used as the auxiliary dataset. We
used an alphanumeric letter classifier (label num:62) described in Sec. 5.2 as f for this experiment.

assistant: text: Estimation of training data distribution from trained classifier using GAN.