Objective. To develop and implement a novel approach which combines the technique of scout EEG source imaging (ESI) with convolutional neural network (CNN) for the classification of motor imagery (MI) tasks. Approach. The technique of ESI uses a boundary element method (BEM) and weighted minimum norm estimation (WMNE) to solve the EEG forward and inverse problems, respectively. Ten scouts are then created within the motor cortex to select the region of interest (ROI). We extract features from the time series of scouts using a Morlet wavelet approach. Lastly, CNN is employed for classifying MI tasks. Main results. The overall mean accuracy on the Physionet database reaches 94.5% and the individual accuracy of each task reaches 95.3%, 93.3%, 93.6%, 96% for the left fist, right fist, both fists and both feet, correspondingly, validated using ten-fold cross validation. We report an increase of up to 14.4% for overall classification compared with the competitive results from the state-of-the-art MI classification methods. Then, we add four new subjects to verify the validity of the method and the overall mean accuracy is 92.5%. Furthermore, the global classifier was adapted to single subjects improving the overall mean accuracy to 94.54%. Significance. The combination of scout ESI and CNN enhances BCI performance of decoding EEG four-class MI tasks.

We propose a framework of boosting for learning and control in environments that maintain a state. Leveraging methods for online learning with memory and for online boosting, we design an efficient online algorithm that can provably improve the accuracy of weak-learners in stateful environments. As a consequence, we give efficient boosting algorithms for both prediction and the control of dynamical systems. Empirical evaluation on simulated and real data for both control and prediction supports our theoretical findings.

It is well-known that standard neural networks, even with a high classification accuracy, are vulnerable to small ∞ -norm bounded adversarial perturbations. Although many attempts have been made, most previous works either can only provide empirical verification of the defense to a particular attack method, or can only develop a certified guarantee of the model robustness in limited scenarios. In this paper, we seek for a new approach to develop a theoretically principled neural network that inherently resists ∞ perturbations. In particular, we design a novel neuron that uses ∞ -distance as its basic operation (which we call ∞ -dist neuron), and show that any neural network constructed with ∞ -dist neurons (called ∞ -dist net) is naturally a 1-Lipschitz function with respect to ∞ -norm. This directly provides a rigorous guarantee of the certified robustness based on the margin of prediction outputs. We also prove that such networks have enough expressive power to approximate any 1-Lipschitz function with robust generalization guarantee. Our experimental results show that the proposed network is promising. Using ∞ -dist nets as the basic building blocks, we consistently achieve state-ofthe-art performance on commonly used datasets: 93.09% certified accuracy on MNIST ( = 0.3), 79.23% on Fashion MNIST ( = 0.1) and 35.10% on CIFAR-10 ( = 8/255).∞ perturbation. In particular, we propose a novel neuron called ∞ -dist neuron. Unlike the standard neuron design that uses a linear transformation followed by a non-linear activation, the ∞ -dist neuron is purely based on computing