We present a general numerical approach for constructing governing equations for unknown dynamical systems when only data on a subset of the state variables are available. The unknown equations for these observed variables are thus a reduced system of the complete set of state variables. Reduced systems possess memory integrals, based on the well known Mori-Zwanzig (MZ) formulism. Our numerical strategy to recover the reduced system starts by formulating a discrete approximation of the memory integral in the MZ formulation. The resulting unknown approximate MZ equations are of finite dimensional, in the sense that a finite number of past history data are involved. We then present a deep neural network structure that directly incorporates the history terms to produce memory in the network. The approach is suitable for any practical systems with finite memory length. We then use a set of numerical examples to demonstrate the effectiveness of our method.

High-fidelity complex engineering simulations are highly predictive, but also computationally expensive and often require substantial computational efforts. The mitigation of computational burden is usually enabled through parallelism in high-performance cluster (HPC) architecture. In this paper, an asynchronous constrained batch-parallel Bayesian optimization method is proposed to efficiently solve the computationally-expensive simulation-based optimization problems on the HPC platform, with a budgeted computational resource, where the maximum number of simulations is a constant. The advantages of this method are three-fold. First, the efficiency of the Bayesian optimization is improved, where multiple input locations are evaluated massively parallel in an asynchronous manner to accelerate the optimization convergence with respect to physical runtime. This efficiency feature is further improved so that when each of the inputs is finished, another input is queried without waiting for the whole batch to complete. Second, the method can handle both known and unknown constraints. Third, the proposed method considers several acquisition functions at the same time and sample based on an evolving probability mass distribution function using GP-Hedge scheme, where parameters are corresponding to the performance of each acquisition function. The proposed framework is termed aphBO-2GP-3B, which corresponds to asynchronous parallel hedge Bayesian optimization with two Gaussian processes and three batches. The aphBO-2GP-3B framework is demonstrated using two high-fidelity expensive industrial applications, where the first one is based on finite element analysis (FEA) and the second one is based on computational fluid dynamics (CFD) simulations.

This study presents early phase detection of Coronavirus (COVID-19), which is named by World Health Organization (WHO), by machine learning methods. The detection process was implemented on abdominal Computed Tomography (CT) images. The expert radiologists detected from CT images that COVID-19 shows different behaviours from other viral pneumonia. Therefore, the clinical experts specify that COV\.ID-19 virus needs to be diagnosed in early phase. For detection of the COVID-19, four different datasets were formed by taking patches sized as 16x16, 32x32, 48x48, 64x64 from 150 CT images. The feature extraction process was applied to patches to increase the classification performance. Grey Level Co-occurrence Matrix (GLCM), Local Directional Pattern (LDP), Grey Level Run Length Matrix (GLRLM), Grey-Level Size Zone Matrix (GLSZM), and Discrete Wavelet Transform (DWT) algorithms were used as feature extraction methods. Support Vector Machines (SVM) classified the extracted features. 2-fold, 5-fold and 10-fold cross-validations were implemented during the classification process. Sensitivity, specificity, accuracy, precision, and F-score metrics were used to evaluate the classification performance. The best classification accuracy was obtained as 99.68% with 10-fold cross-validation and GLSZM feature extraction method.

In many real world applications, reinforcement learning agents have to optimize multiple objectives while following certain rules or satisfying a list of constraints. Classical methods based on reward shaping, i.e. a weighted combination of different objectives in the reward signal, or Lagrangian methods, including constraints in the loss function, have no guarantees that the agent satisfies the constraints at all points in time and lack in interpretability. When a discrete policy is extracted from an action-value function, safe actions can be ensured by restricting the action space at maximization, but can lead to sub-optimal solutions among feasible alternatives. In this work, we propose Multi Time-scale Constrained DQN, a novel algorithm restricting the action space directly in the Q-update to learn the optimal Q-function for the constrained MDP and the corresponding safe policy. In addition to single-step constraints referring only to the next action, we introduce a formulation for approximate multi-step constraints under the current target policy based on truncated value-functions to enhance interpretability. We compare our algorithm to reward shaping and Lagrangian methods in the application of high-level decision making in autonomous driving, considering constraints for safety, keeping right and comfort. We train our agent in the open-source simulator SUMO and on the real HighD data set.

Bayesian experimental design (BED) is a framework that uses statistical models and decision making under uncertainty to optimise the cost and performance of a scientific experiment. Sequential BED, as opposed to static BED, considers the scenario where we can sequentially update our beliefs about the model parameters through data gathered in the experiment. A class of models of particular interest for the natural and medical sciences are implicit models, where the data generating distribution is intractable, but sampling from it is possible. Even though there has been a lot of work on static BED for implicit models in the past few years, the notoriously difficult problem of sequential BED for implicit models has barely been touched upon. We address this gap in the literature by devising a novel sequential design framework for parameter estimation that uses the Mutual Information (MI) between model parameters and simulated data as a utility function to find optimal experimental designs, which has not been done before for implicit models. Our approach uses likelihood-free inference by ratio estimation to simultaneously estimate posterior distributions and the MI. During the sequential BED procedure we utilise Bayesian optimisation to help us optimise the MI utility. We find that our framework is efficient for the various implicit models tested, yielding accurate parameter estimates after only a few iterations.

Despite vast research in adversarial examples, the root causes of model susceptibility are not well understood. Instead of looking at attack-specific robustness, we propose a notion that evaluates the sensitivity of individual neurons in terms of how robust the model's output is to direct perturbations of that neuron's output. Analyzing models from this perspective reveals distinctive characteristics of standard as well as adversarially-trained robust models, and leads to several curious results. In our experiments on CIFAR-10 and ImageNet, we find that attacks using a loss function that targets just a single sensitive neuron find adversarial examples nearly as effectively as ones that target the full model. We analyze the properties of these sensitive neurons to propose a regularization term that can help a model achieve robustness to a variety of different perturbation constraints while maintaining accuracy on natural data distributions. Code for all our experiments is available at https://github.com/iamgroot42/sauron .

One of the most natural tasks in graph theory is community detection, i.e., the identification of similarity groups on a given network. Practically, for an unweighted and undirected graph G(V, E) with V n nodes and E edges, community detection consists in finding a non-overlapping partition of the nodes that identifies underlying communities in a completely unsupervised manner. There is no unique definition of a community, but a general criterion is to impose that nodes in the same community have more interconnections than nodes in different communities, as a consequence of the stronger affinity among members of the same community [17]. There exist many ways of formalizing this intuition, some of them under the form of a cost function to minimize, such as the MinCut, RatioCut, and NormalizedCut costs [53]. The resulting optimizations are however NPhard problems and, as a consequence, many algorithms consist in retrieving relaxed continuous solutions of the problem.

Canonical correlation analysis (CCA for short) describes the relationship between two sets of variables by finding some linear combinations of these variables that maximizing the correlation coefficient. However, in high-dimensional settings where the number of variables exceeds sample size, or in the case of that the variables are highly correlated, the traditional CCA is no longer appropriate. In this paper, an adaptive sparse version of CCA (ASCCA for short) is proposed by using the trace Lasso regularization. The proposed ASCCA reduces the instability of the estimator when the covariates are highly correlated, and thus improves its interpretation. The ASCCA is further reformulated to an optimization problem on Riemannian manifolds, and an manifold inexact augmented Lagrangian method is then proposed for the resulting optimization problem. The performance of the ASCCA is compared with the other sparse CCA techniques in different simulation settings, which illustrates that the ASCCA is feasible and efficient.

In the VC framework[42], both for binary and multi-category classification tasks, when minimal assumption on the predictive model is made, the (optimal) way one controls the uniform convergence of the empirical performance to the generalization one depends on the loss function used based on which these performances are defined. The choice of the loss function leads to an upper bound involving one of capacity measures, the quantity characterizing the rate of the uniform convergence. The seminal work dealt with the standard indicator loss function [43] leading to bounds involving the VC-dimension as a capacity measure. This was improved in [12] via the Rademacher complexity since the mentioned capacity measure is upper bounded by the VC-dimension. Classifiers implementing real-valued functions offer a richer setting to the assessment of their classification performance since the latter can be defined based on a family of margin loss functions which can be distinguished into two classes: margin indicator loss function and those that are Lipschitz continuous [27].

One task that is often discussed in a computer vision is the mapping of an image from one domain to a corresponding image in another domain known as image-to-image translation. Currently there are several approaches solving this task. In this paper, we present an enhancement of the UNIT framework that aids in removing its main drawbacks. More specifically, we introduce an additional adversarial discriminator on the latent representation used instead of VAE, which enforces the latent space distributions of both domains to be similar. On MNIST and USPS domain adaptation tasks, this approach greatly outperforms competing approaches.