Model Reduction and Neural Networks for Parametric PDEs

We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with ideas from model reduction. This combination results in a neural network approximation which, in principle, is defined on infinite-dimensional spaces and, in practice, is robust to the dimension of finite-dimensional approximations of these spaces required for computation. For a class of input-output maps, and suitably chosen probability measures on the inputs, we prove convergence of the proposed approximation methodology. Numerically we demonstrate the effectiveness of the method on a class of parametric elliptic PDE problems, showing convergence and robustness of the approximation scheme with respect to the size of the discretization, and compare our method with existing algorithms from the literature

Towards Efficient Maximum Likelihood Estimation of LPV-SS Models

How to efficiently identify multiple-input multiple-output (MIMO) linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable still remains an open question, as identification methods proposed in the literature suffer heavily from the curse of dimensionality and/or depend on over-restrictive approximations of the measured signal behaviors. However, obtaining an SS model of the targeted system is crucial for many LPV control synthesis methods, as these synthesis tools are almost exclusively formulated for the aforementioned representation of the system dynamics. Therefore, in this paper, we tackle the problem by combining state-of-the-art LPV input-output (IO) identification methods with an LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step. The resulting modular LPV-SS identification approach achieves statical efficiency with a relatively low computational load. The method contains the following three steps: 1) estimation of the Markov coefficient sequence of the underlying system using correlation analysis or Bayesian impulse response estimation, then 2) LPV-SS realization of the estimated coefficients by using a basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate from a maximum-likelihood point of view by a gradient-based or an expectation-maximization optimization methodology. The effectiveness of the full identification scheme is demonstrated by a Monte Carlo study where our proposed method is compared to existing schemes for identifying a MIMO LPV system

Learning Latent Representations of Bank Customers With The Variational Autoencoder

Learning data representations that reflect the customers' creditworthiness can improve marketing campaigns, customer relationship management, data and process management or the credit risk assessment in retail banks. In this research, we adopt the Variational Autoencoder (VAE), which has the ability to learn latent representations that contain useful information. We show that it is possible to steer the latent representations in the latent space of the VAE using the Weight of Evidence and forming a specific grouping of the data that reflects the customers' creditworthiness. Our proposed method learns a latent representation of the data, which shows a well-defied clustering structure capturing the customers' creditworthiness. These clusters are well suited for the aforementioned banks' activities. Further, our methodology generalizes to new customers, captures high-dimensional and complex financial data, and scales to large data sets.Comment: arXiv admin note: substantial text overlap with arXiv:1806.0253

ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models

Deep neural networks (DNNs) are one of the most prominent technologies of our time, as they achieve state-of-the-art performance in many machine learning tasks, including but not limited to image classification, text mining, and speech processing. However, recent research on DNNs has indicated ever-increasing concern on the robustness to adversarial examples, especially for security-critical tasks such as traffic sign identification for autonomous driving. Studies have unveiled the vulnerability of a well-trained DNN by demonstrating the ability of generating barely noticeable (to both human and machines) adversarial images that lead to misclassification. Furthermore, researchers have shown that these adversarial images are highly transferable by simply training and attacking a substitute model built upon the target model, known as a black-box attack to DNNs. Similar to the setting of training substitute models, in this paper we propose an effective black-box attack that also only has access to the input (images) and the output (confidence scores) of a targeted DNN. However, different from leveraging attack transferability from substitute models, we propose zeroth order optimization (ZOO) based attacks to directly estimate the gradients of the targeted DNN for generating adversarial examples. We use zeroth order stochastic coordinate descent along with dimension reduction, hierarchical attack and importance sampling techniques to efficiently attack black-box models. By exploiting zeroth order optimization, improved attacks to the targeted DNN can be accomplished, sparing the need for training substitute models and avoiding the loss in attack transferability. Experimental results on MNIST, CIFAR10 and ImageNet show that the proposed ZOO attack is as effective as the state-of-the-art white-box attack and significantly outperforms existing black-box attacks via substitute models.Comment: Accepted by 10th ACM Workshop on Artificial Intelligence and Security (AISEC) with the 24th ACM Conference on Computer and Communications Security (CCS