We investigate the decidability and computational complexity of conservative extensions and the related notions of inseparability and entailment in Horn description logics (DLs) with inverse roles. We consider both query conservative extensions, defined by requiring that the answers to all conjunctive queries are left unchanged, and deductive conservative extensions, which require that the entailed concept inclusions, role inclusions, and functionality assertions do not change. Upper bounds for query conservative extensions are particularly challenging because characterizations in terms of unbounded homomorphisms between universal models, which are the foundation of the standard approach to establishing decidability, fail in the presence of inverse roles. We resort to a characterization that carefully mixes unbounded and bounded homomorphisms and enables a decision procedure that combines tree automata and a mosaic technique. Our main results are that query conservative extensions are 2ExpTime-complete in all DLs between ELI and Horn-ALCHIF and between Horn-ALC and Horn-ALCHIF, and that deductive conservative extensions are 2ExpTime-complete in all DLs between ELI and ELHIF_bot. The same results hold for inseparability and entailment.

Researchers across the globe are seeking to rapidly repurpose existing drugs or discover new drugs to counter the the novel coronavirus disease (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). One promising approach is to train machine learning (ML) and artificial intelligence (AI) tools to screen large numbers of small molecules. As a contribution to that effort, we are aggregating numerous small molecules from a variety of sources, using high-performance computing (HPC) to computer diverse properties of those molecules, using the computed properties to train ML/AI models, and then using the resulting models for screening. In this first data release, we make available 23 datasets collected from community sources representing over 4.2 B molecules enriched with pre-computed: 1) molecular fingerprints to aid similarity searches, 2) 2D images of molecules to enable exploration and application of image-based deep learning methods, and 3) 2D and 3D molecular descriptors to speed development of machine learning models. This data release encompasses structural information on the 4.2 B molecules and 60 TB of pre-computed data. Future releases will expand the data to include more detailed molecular simulations, computed models, and other products.

Adversarially robust classification seeks a classifier that is insensitive to adversarial perturbations of test patterns. This problem is often formulated via a minimax objective, where the target loss is the worst-case value of the 0-1 loss subject to a bound on the size of perturbation. Recent work has proposed convex surrogates for the adversarial 0-1 loss, in an effort to make optimization more tractable. In this work, we consider the question of which surrogate losses are calibrated with respect to the adversarial 0-1 loss, meaning that minimization of the former implies minimization of the latter. We show that no convex surrogate loss is calibrated with respect to the adversarial 0-1 loss when restricted to the class of linear models. We further introduce a class of nonconvex losses and offer necessary and sufficient conditions for losses in this class to be calibrated.

Feature extraction for tensor data serves as an important step in many tasks such as anomaly detection, process monitoring, image classification, and quality control. Although many methods have been proposed for tensor feature extraction, there are still two challenges that need to be addressed: 1) how to reduce the computation cost for high dimensional and large volume tensor data; 2) how to interpret the output features and evaluate their significance. Although the most recent methods in deep learning, such as Convolutional Neural Network (CNN), have shown outstanding performance in analyzing tensor data, their wide adoption is still hindered by model complexity and lack of interpretability. To fill this research gap, we propose to use CP-decomposition to approximately compress the convolutional layer (CPAC-Conv layer) in deep learning. The contributions of our work could be summarized into three aspects: 1) we adapt CP-decomposition to compress convolutional kernels and derive the expressions of both forward and backward propagations for our proposed CPAC-Conv layer; 2) compared with the original convolutional layer, the proposed CPAC-Conv layer can reduce the number of parameters without decaying prediction performance. It can combine with other layers to build novel Neural Networks; 3) the value of decomposed kernels indicates the significance of the corresponding feature map, which increases model interpretability and provides us insights to guide feature selection.

Recent studies propose membership inference (MI) attacks on deep models. Despite the moderate accuracy of such MI attacks, we show that the way the attack accuracy is reported is often misleading and a simple blind attack which is highly unreliable and inefficient in reality can often represent similar accuracy. We show that the current MI attack models can only identify the membership of misclassified samples with mediocre accuracy at best, which only constitute a very small portion of training samples. We analyze several new features that have not been explored for membership inference before, including distance to the decision boundary and gradient norms, and conclude that deep models' responses are mostly indistinguishable among train and non-train samples. Moreover, in contrast with general intuition that deeper models have a capacity to memorize training samples, and, hence, they are more vulnerable to membership inference, we find no evidence to support that and in some cases deeper models are often harder to launch membership inference attack on. Furthermore, despite the common belief, we show that overfitting does not necessarily lead to higher degree of membership leakage. We conduct experiments on MNIST, CIFAR-10, CIFAR-100, and ImageNet, using various model architecture, including LeNet, ResNet, DenseNet, InceptionV3, and Xception.

Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte Carlo counterparts, OMC is used in a wide spectrum of challenging machine learning applications ranging from scalable kernel methods to predictive recurrent neural networks, generative models and reinforcement learning. However theoretical understanding of the method remains very limited. In this paper we shed new light on the theoretical principles behind OMC, applying theory of negatively dependent random variables to obtain several new concentration results. We also propose a novel extensions of the method leveraging number theory techniques and particle algorithms, called Near-Orthogonal Monte Carlo (NOMC). We show that NOMC is the first algorithm consistently outperforming OMC in applications ranging from kernel methods to approximating distances in probabilistic metric spaces.

We describe a necessary and sufficient condition for the convergence to minimum Bayes risk when training two-layer ReLU-networks by gradient descent in the mean field regime with omni-directional initial parameter distribution. This article extends recent results of Chizat and Bach to ReLU-activated networks and to the situation in which there are no parameters which exactly achieve MBR. The condition does not depend on the initalization of parameters and concerns only the weak convergence of the realization of the neural network, not its parameter distribution.

The vulnerability of deep networks to adversarial attacks is a central problem for deep learning from the perspective of both cognition and security. The current most successful defense method is to train a classifier using adversarial images created during learning. Another defense approach involves transformation or purification of the original input to remove adversarial signals before the image is classified. We focus on defending naturally-trained classifiers using Markov Chain Monte Carlo (MCMC) sampling with an Energy-Based Model (EBM) for adversarial purification. In contrast to adversarial training, our approach is intended to secure pre-existing and highly vulnerable classifiers. The memoryless behavior of long-run MCMC sampling will eventually remove adversarial signals, while metastable behavior preserves consistent appearance of MCMC samples after many steps to allow accurate long-run prediction. Balancing these factors can lead to effective purification and robust classification. We evaluate adversarial defense with an EBM using the strongest known attacks against purification. Our contributions are 1) an improved method for training EBM's with realistic long-run MCMC samples, 2) an Expectation-Over-Transformation (EOT) defense that resolves theoretical ambiguities for stochastic defenses and from which the EOT attack naturally follows, and 3) state-of-the-art adversarial defense for naturally-trained classifiers and competitive defense compared to adversarially-trained classifiers on Cifar-10, SVHN, and Cifar-100. Code and pre-trained models are available at https://github.com/point0bar1/ebm-defense.

Kernel methods have proven to be powerful techniques for pattern analysis and machine learning (ML) in a variety of domains. However, many of their original or advanced implementations remain in Matlab. With the incredible rise and adoption of Python in the ML and data science world, there is a clear need for a well-defined library that enables not only the use of popular kernels, but also allows easy definition of customized kernels to fine-tune them for diverse applications. The kernelmethods library fills that important void in the python ML ecosystem in a domain-agnostic fashion, allowing the sample data type to be anything from numerical, categorical, graphs or a combination of them. In addition, this library provides a number of well-defined classes to make various kernel-based operations efficient (for large scale datasets), modular (for ease of domain adaptation), and inter-operable (across different ecosystems). The library is available at https://github.com/raamana/kernelmethods.

The reliable estimation of forecast uncertainties is crucial for risk-sensitive optimal decision making. In this paper, we propose implicit generative ensemble post-processing, a novel framework for multivariate probabilistic electricity price forecasting. We use a likelihood-free implicit generative model based on an ensemble of point forecasting models to generate multivariate electricity price scenarios with a coherent dependency structure as a representation of the joint predictive distribution. Our ensemble post-processing method outperforms well-established model combination benchmarks. This is demonstrated on a data set from the German day-ahead market. As our method works on top of an ensemble of domain-specific expert models, it can readily be deployed to other forecasting tasks.