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### A Lipschitz-constrained anomaly discriminator framework

Anomaly detection is a problem of great interest in medicine, finance, and other fields where error and fraud need to be detected and corrected. Most deep anomaly detection methods rely on autoencoder reconstruction error. However, we show that this approach has limited value. First, this approach starts to perform poorly when either noise or anomalies contaminate training data, even to a small extent. Second, this approach cannot detect anomalous but simple to reconstruct points. This can be seen even in relatively simple examples, such as feeding a black image to detectors trained on MNIST digits. Here, we introduce a new discriminator-based unsupervised Lipschitz anomaly detector (LAD). We train a Wasserstein discriminator, similar to the ones used in GANs, to detect the difference between the training data and corruptions of the training data. We show that this procedure successfully detects unseen anomalies with guarantees on those that have a certain Wasserstein distance from the data or corrupted training set. Finally, we show results of this system in an electronic medical record dataset of HIV-positive veterans from the veterans aging cohort study (VACS) to establish usability in a medical setting.

### Spatio-Temporal Adversarial Learning for Detecting Unseen Falls

Fall detection is an important problem from both the health and machine learning perspective. A fall can lead to severe injuries, long term impairments or even death in some cases. In terms of machine learning, it presents a severely class imbalance problem with very few or no training data for falls owing to the fact that falls occur rarely. In this paper, we take an alternate philosophy to detect falls in the absence of their training data, by training the classifier on only the normal activities (that are available in abundance) and identifying a fall as an anomaly. To realize such a classifier, we use an adversarial learning framework, which comprises of a spatio-temporal autoencoder for reconstructing input video frames and a spatio-temporal convolution network to discriminate them against original video frames. 3D convolutions are used to learn spatial and temporal features from the input video frames. The adversarial learning of the spatio-temporal autoencoder will enable reconstructing the normal activities of daily living efficiently; thus, rendering detecting unseen falls plausible within this framework. We tested the performance of the proposed framework on camera sensing modalities that may preserve an individual's privacy (fully or partially), such as thermal and depth camera. Our results on three publicly available datasets show that the proposed spatio-temporal adversarial framework performed better than other frame based (or spatial) adversarial learning methods.

### Anomaly Detection with Generative Adversarial Networks for Multivariate Time Series

Today's Cyber-Physical Systems (CPSs) are large, complex, and affixed with networked sensors and actuators that are targets for cyber-attacks. Conventional detection techniques are unable to deal with the increasingly dynamic and complex nature of the CPSs. On the other hand, the networked sensors and actuators generate large amounts of data streams that can be continuously monitored for intrusion events. Unsupervised machine learning techniques can be used to model the system behaviour and classify deviant behaviours as possible attacks. In this work, we proposed a novel Generative Adversarial Networks-based Anomaly Detection (GAN-AD) method for such complex networked CPSs. We used LSTM-RNN in our GAN to capture the distribution of the multivariate time series of the sensors and actuators under normal working conditions of a CPS. Instead of treating each sensor's and actuator's time series independently, we model the time series of multiple sensors and actuators in the CPS concurrently to take into account of potential latent interactions between them. To exploit both the generator and the discriminator of our GAN, we deployed the GAN-trained discriminator together with the residuals between generator-reconstructed data and the actual samples to detect possible anomalies in the complex CPS. We used our GAN-AD to distinguish abnormal attacked situations from normal working conditions for a complex six-stage Secure Water Treatment (SWaT) system. Experimental results showed that the proposed strategy is effective in identifying anomalies caused by various attacks with high detection rate and low false positive rate as compared to existing methods.

### Anomaly Detection via Minimum Likelihood Generative Adversarial Networks

Anomaly detection aims to detect abnormal events by a model of normality. It plays an important role in many domains such as network intrusion detection, criminal activity identity and so on. With the rapidly growing size of accessible training data and high computation capacities, deep learning based anomaly detection has become more and more popular. In this paper, a new domain-based anomaly detection method based on generative adversarial networks (GAN) is proposed. Minimum likelihood regularization is proposed to make the generator produce more anomalies and prevent it from converging to normal data distribution. Proper ensemble of anomaly scores is shown to improve the stability of discriminator effectively. The proposed method has achieved significant improvement than other anomaly detection methods on Cifar10 and UCI datasets.

### Bayesian Conditional Generative Adverserial Networks

Traditional GANs use a deterministic generator function (typically a neural network) to transform a random noise input $z$ to a sample $\mathbf{x}$ that the discriminator seeks to distinguish. We propose a new GAN called Bayesian Conditional Generative Adversarial Networks (BC-GANs) that use a random generator function to transform a deterministic input $y'$ to a sample $\mathbf{x}$. Our BC-GANs extend traditional GANs to a Bayesian framework, and naturally handle unsupervised learning, supervised learning, and semi-supervised learning problems. Experiments show that the proposed BC-GANs outperforms the state-of-the-arts.