Recently there have been increasing interests in learning and inference with implicit distributions (i.e., distributions without tractable densities). To this end, we develop a gradient estimator for implicit distributions based on Stein's identity and a spectral decomposition of kernel operators, where the eigenfunctions are approximated by the Nystr\"om method. Unlike the previous works that only provide estimates at the sample points, our approach directly estimates the gradient function, thus allows for a simple and principled out-of-sample extension. We provide theoretical results on the error bound of the estimator and discuss the bias-variance tradeoff in practice. The effectiveness of our method is demonstrated by applications to gradient-free Hamiltonian Monte Carlo and variational inference with implicit distributions. Finally, we discuss the intuition behind the estimator by drawing connections between the Nystr\"om method and kernel PCA, which indicates that the estimator can automatically adapt to the geometry of the underlying distribution.

We present a novel cost function for semi-supervised learning of neural networks that encourages compact clustering of the latent space to facilitate separation. The key idea is to dynamically create a graph over embeddings of labeled and unlabeled samples of a training batch to capture underlying structure in feature space, and use label propagation to estimate its high and low density regions. We then devise a cost function based on Markov chains on the graph that regularizes the latent space to form a single compact cluster per class, while avoiding to disturb existing clusters during optimization. We evaluate our approach on three benchmarks and compare to state-of-the art with promising results. Our approach combines the benefits of graph-based regularization with efficient, inductive inference, does not require modifications to a network architecture, and can thus be easily applied to existing networks to enable an effective use of unlabeled data.

Software Defined Internet of Things (SD-IoT) Networks profits from centralized management and interactive resource sharing which enhances the efficiency and scalability of IoT applications. But with the rapid growth in services and applications, it is vulnerable to possible attacks and faces severe security challenges. Intrusion detection has been widely used to ensure network security, but classical detection means are usually signature-based or explicit-behavior-based and fail to detect unknown attacks intelligently, which are hard to satisfy the requirements of SD-IoT Networks. In this paper, we propose an AI-based two-stage intrusion detection empowered by software defined technology. It flexibly captures network flows with a globle view and detects attacks intelligently through applying AI algorithms. We firstly leverage Bat algorithm with swarm division and Differential Mutation to select typical features. Then, we exploit Random forest through adaptively altering the weights of samples using weighted voting mechanism to classify flows. Evaluation results prove that the modified intelligent algorithms select more important features and achieve superior performance in flow classification. It is also verified that intelligent intrusion detection shows better accuracy with lower overhead comparied with existing solutions.

This problem is faced in many applications such as link prediction, community detection, node classification, and network visualization, among others. Now, it has been shown that the standard shortest path distance and the resistance distance (Klein & Randić, 1993) suffer from important drawbacks in some situations, which sometimes hinders their use as distance measures between nodes in some applications. More precisely, the shortest path distance does not integrate the concept of high connectivity between the two nodes (it only considers the shortest paths, see, e.g., (Fouss et al., 2016)), while the resistance distance provides useless results when dealing with large graphs (the so-called "lost-in-space effect" (von Luxburg, Radl, & Hein, 2010, 2014)). Another drawback of the shortest path distance is that it provides lots of ties when comparing distances, especially on unweighted undirected graphs. In order to avoid the drawbacks of the shortest path and resistance distances, new families of distance measures, interpolating between these two extremes, were recently suggested based on a bag-of-paths (BoP) framework (Françoisse et al., 2017; Kivimäki, Shimbo, & Saerens, 2014; Mantrach et al., 2010). This framework defines a Gibbs-Boltzmann probability distribution over paths on a graph, which focuses on the shortest paths, but spreads also on longer paths and random walks.

Stochastic gradient descent is the workhorse behind the recent deep learning revolution. This simple and ageold algorithm has been supplemented with a variety of enhancements to improve its practical performance, and sometimes its theoretical guarantees. Amongst the acceleration methods there are three main categories: momentum, adaptive regularization, and variance reduction. Momentum (in its various incarnations, like heavy-ball or Nesterov acceleration) is the oldest enhancement. It has a well-developed theory, and is known to improve practical convergence in a variety of tasks, small and large. It is also easy to implement.

Variance reduction has been commonly used in stochastic optimization. It relies crucially on the assumption that the data set is finite. However, when the data are imputed with random noise as in data augmentation, the perturbed data set be- comes essentially infinite. Recently, the stochastic MISO (S-MISO) algorithm is introduced to address this expected risk minimization problem. Though it converges faster than SGD, a significant amount of memory is required. In this pa- per, we propose two SGD-like algorithms for expected risk minimization with random perturbation, namely, stochastic sample average gradient (SSAG) and stochastic SAGA (S-SAGA). The memory cost of SSAG does not depend on the sample size, while that of S-SAGA is the same as those of variance reduction methods on un- perturbed data. Theoretical analysis and experimental results on logistic regression and AUC maximization show that SSAG has faster convergence rate than SGD with comparable space requirement, while S-SAGA outperforms S-MISO in terms of both iteration complexity and storage.

Dimensionality reduction is one of the key issues in the design of effective machine learning methods for automatic induction. In this work, we introduce recursive maxima hunting (RMH) for variable selection in classification problems with functional data. In this context, variable selection techniques are especially attractive because they reduce the dimensionality, facilitate the interpretation and can improve the accuracy of the predictive models. The method, which is a recursive extension of maxima hunting (MH), performs variable selection by identifying the maxima of a relevance function, which measures the strength of the correlation of the predictor functional variable with the class label. At each stage, the information associated with the selected variable is removed by subtracting the conditional expectation of the process. The results of an extensive empirical evaluation are used to illustrate that, in the problems investigated, RMH has comparable or higher predictive accuracy than the standard dimensionality reduction techniques, such as PCA and PLS, and state-of-the-art feature selection methods for functional data, such as maxima hunting.

We propose a novel method for imputing missing data by adapting the well-known Generative Adversarial Nets (GAN) framework. Accordingly, we call our method Generative Adversarial Imputation Nets (GAIN). The generator (G) observes some components of a real data vector, imputes the missing components conditioned on what is actually observed, and outputs a completed vector. The discriminator (D) then takes a completed vector and attempts to determine which components were actually observed and which were imputed. To ensure that D forces G to learn the desired distribution, we provide D with some additional information in the form of a hint vector. The hint reveals to D partial information about the missingness of the original sample, which is used by D to focus its attention on the imputation quality of particular components. This hint ensures that G does in fact learn to generate according to the true data distribution. We tested our method on various datasets and found that GAIN significantly outperforms state-of-the-art imputation methods.

Batch Normalization (BN) is essential to effectively train state-of-the-art deep Convolutional Neural Networks (CNN). It normalizes inputs to the layers during training using the statistics of each mini-batch. In this work, we study BN from the viewpoint of Fisher kernels. We show that assuming samples within a mini-batch are from the same probability density function, then BN is identical to the Fisher vector of a Gaussian distribution. That means BN can be explained in terms of kernels that naturally emerge from the probability density function of the underlying data distribution. However, given the rectifying non-linearities employed in CNN architectures, distribution of inputs to the layers show heavy tail and asymmetric characteristics. Therefore, we propose approximating underlying data distribution not with one, but a mixture of Gaussian densities. Deriving Fisher vector for a Gaussian Mixture Model (GMM), reveals that BN can be improved by independently normalizing with respect to the statistics of disentangled sub-populations. We refer to our proposed soft piecewise version of BN as Mixture Normalization (MN). Through extensive set of experiments on CIFAR-10 and CIFAR-100, we show that MN not only effectively accelerates training image classification and Generative Adversarial networks, but also reaches higher quality models.

Machine learning approaches have been effective in predicting adverse outcomes in different clinical settings. These models are often developed and evaluated on datasets with heterogeneous patient populations. However, good predictive performance on the aggregate population does not imply good performance for specific groups. In this work, we present a two-step framework to 1) learn relevant patient subgroups, and 2) predict an outcome for separate patient populations in a multi-task framework, where each population is a separate task. We demonstrate how to discover relevant groups in an unsupervised way with a sequence-to-sequence autoencoder. We show that using these groups in a multi-task framework leads to better predictive performance of in-hospital mortality both across groups and overall. We also highlight the need for more granular evaluation of performance when dealing with heterogeneous populations.