Relative Entropy Gradient Sampler for Unnormalized Distributions

We propose a relative entropy gradient sampler (REGS) for sampling from unnormalized distributions. REGS is a particle method that seeks a sequence of simple nonlinear transforms iteratively pushing the initial samples from a reference distribution into the samples from an unnormalized target distribution. To determine the nonlinear transforms at each iteration, we consider the Wasserstein gradient flow of relative entropy. This gradient flow determines a path of probability distributions that interpolates the reference distribution and the target distribution. It is characterized by an ODE system with velocity fields depending on the density ratios of the density of evolving particles and the unnormalized target density. To sample with REGS, we need to estimate the density ratios and simulate the ODE system with particle evolution. We propose a novel nonparametric approach to estimating the logarithmic density ratio using neural networks. Extensive simulation studies on challenging multimodal 1D and 2D mixture distributions and Bayesian logistic regression on real datasets demonstrate that the REGS outperforms the state-of-the-art sampling methods included in the comparison.

An error analysis of generative adversarial networks for learning distributions

This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined through H\"older classes, including the Wasserstein distance as a special case. We also show that GANs are able to adaptively learn data distributions with low-dimensional structures or have H\"older densities, when the network architectures are chosen properly. In particular, for distributions concentrated around a low-dimensional set, we show that the learning rates of GANs do not depend on the high ambient dimension, but on the lower intrinsic dimension. Our analysis is based on a new oracle inequality decomposing the estimation error into the generator and discriminator approximation error and the statistical error, which may be of independent interest.

Non-asymptotic Excess Risk Bounds for Classification with Deep Convolutional Neural Networks

In this paper, we consider the problem of binary classification with a class of general deep convolutional neural networks, which includes fully-connected neural networks and fully convolutional neural networks as special cases. We establish non-asymptotic excess risk bounds for a class of convex surrogate losses and target functions with different modulus of continuity. An important feature of our results is that we clearly define the prefactors of the risk bounds in terms of the input data dimension and other model parameters and show that they depend polynomially on the dimensionality in some important models. We also show that the classification methods with CNNs can circumvent the curse of dimensionality if the input data is supported on an approximate low-dimensional manifold. To establish these results, we derive an upper bound for the covering number for the class of general convolutional neural networks with a bias term in each convolutional layer, and derive new results on the approximation power of CNNs for any uniformly-continuous target functions. These results provide further insights into the complexity and the approximation power of general convolutional neural networks, which are of independent interest and may have other applications. Finally, we apply our general results to analyze the non-asymptotic excess risk bounds for four widely used methods with different loss functions using CNNs, including the least squares, the logistic, the exponential and the SVM hinge losses.

Natural grasp intention recognition based on gaze fixation in human-robot interaction

Eye movement is closely related to limb actions, so it can be used to infer movement intentions. More importantly, in some cases, eye movement is the only way for paralyzed and impaired patients with severe movement disorders to communicate and interact with the environment. Despite this, eye-tracking technology still has very limited application scenarios as an intention recognition method. The goal of this paper is to achieve a natural fixation-based grasping intention recognition method, with which a user with hand movement disorders can intuitively express what tasks he/she wants to do by directly looking at the object of interest. Toward this goal, we design experiments to study the relationships of fixations in different tasks. We propose some quantitative features from these relationships and analyze them statistically. Then we design a natural method for grasping intention recognition. The experimental results prove that the accuracy of the proposed method for the grasping intention recognition exceeds 89\% on the training objects. When this method is extendedly applied to objects not included in the training set, the average accuracy exceeds 85\%. The grasping experiment in the actual environment verifies the effectiveness of the proposed method.

Generative Learning With Euler Particle Transport

We propose an Euler particle transport (EPT) approach for generative learning. The proposed approach is motivated by the problem of finding an optimal transport map from a reference distribution to a target distribution characterized by the Monge-Ampere equation. Interpreting the infinitesimal linearization of the Monge-Ampere equation from the perspective of gradient flows in measure spaces leads to a stochastic McKean-Vlasov equation. We use the forward Euler method to solve this equation. The resulting forward Euler map pushes forward a reference distribution to the target. This map is the composition of a sequence of simple residual maps, which are computationally stable and easy to train. The key task in training is the estimation of the density ratios or differences that determine the residual maps. We estimate the density ratios (differences) based on the Bregman divergence with a gradient penalty using deep density-ratio (difference) fitting. We show that the proposed density-ratio (difference) estimators do not suffer from the "curse of dimensionality" if data is supported on a lower-dimensional manifold. Numerical experiments with multi-mode synthetic datasets and comparisons with the existing methods on real benchmark datasets support our theoretical results and demonstrate the effectiveness of the proposed method.

EEG-Based Brain-Computer Interfaces Are Vulnerable to Backdoor Attacks

Research and development of electroencephalogram (EEG) based brain-computer interfaces (BCIs) have advanced rapidly, partly due to the wide adoption of sophisticated machine learning approaches for decoding the EEG signals. However, recent studies have shown that machine learning algorithms are vulnerable to adversarial attacks, e.g., the attacker can add tiny adversarial perturbations to a test sample to fool the model, or poison the training data to insert a secret backdoor. Previous research has shown that adversarial attacks are also possible for EEG-based BCIs. However, only adversarial perturbations have been considered, and the approaches are theoretically sound but very difficult to implement in practice. This article proposes to use narrow period pulse for poisoning attack of EEG-based BCIs, which is more feasible in practice and has never been considered before. One can create dangerous backdoors in the machine learning model by injecting poisoning samples into the training set. Test samples with the backdoor key will then be classified into the target class specified by the attacker. What most distinguishes our approach from previous ones is that the backdoor key does not need to be synchronized with the EEG trials, making it very easy to implement. The effectiveness and robustness of the backdoor attack approach is demonstrated, highlighting a critical security concern for EEG-based BCIs.

Transfer Learning for Brain-Computer Interfaces: A Complete Pipeline

Transfer learning (TL) has been widely used in electroencephalogram (EEG) based brain-computer interfaces (BCIs) to reduce the calibration effort for a new subject, and demonstrated promising performance. After EEG signal acquisition, a closed-loop EEG-based BCI system also includes signal processing, feature engineering, and classification/regression blocks before sending out the control signal, whereas previous approaches only considered TL in one or two such components. This paper proposes that TL could be considered in all three components (signal processing, feature engineering, and classification/regression). Furthermore, it is also very important to specifically add a data alignment component before signal processing to make the data from different subjects more consistent, and hence to facilitate subsequential TL. Offline calibration experiments on two MI datasets verified our proposal. Especially, integrating data alignment and sophisticated TL approaches can significantly improve the classification performance, and hence greatly reduce the calibration effort.

Deep Dimension Reduction for Supervised Representation Learning

The success of deep supervised learning depends on its automatic data representation abilities. Among all the characteristics of an ideal representation for high-dimensional complex data, information preservation, low dimensionality and disentanglement are the most essential ones. In this work, we propose a deep dimension reduction (DDR) approach to achieving a good data representation with these characteristics for supervised learning. At the population level, we formulate the ideal representation learning task as finding a nonlinear dimension reduction map that minimizes the sum of losses characterizing conditional independence and disentanglement. We estimate the target map at the sample level nonparametrically with deep neural networks. We derive a bound on the excess risk of the deep nonparametric estimator. The proposed method is validated via comprehensive numerical experiments and real data analysis in the context of regression and classification.

Efficient Use of heuristics for accelerating XCS-based Policy Learning in Markov Games

In Markov games, playing against non-stationary opponents with learning ability is still challenging for reinforcement learning (RL) agents, because the opponents can evolve their policies concurrently. This increases the complexity of the learning task and slows down the learning speed of the RL agents. This paper proposes efficient use of rough heuristics to speed up policy learning when playing against concurrent learners. Specifically, we propose an algorithm that can efficiently learn explainable and generalized action selection rules by taking advantages of the representation of quantitative heuristics and an opponent model with an eXtended classifier system (XCS) in zero-sum Markov games. A neural network is used to model the opponent from their behaviors and the corresponding policy is inferred for action selection and rule evolution. In cases of multiple heuristic policies, we introduce the concept of Pareto optimality for action selection. Besides, taking advantages of the condition representation and matching mechanism of XCS, the heuristic policies and the opponent model can provide guidance for situations with similar feature representation. Furthermore, we introduce an accuracy-based eligibility trace mechanism to speed up rule evolution, i.e., classifiers that can match the historical traces are reinforced according to their accuracy. We demonstrate the advantages of the proposed algorithm over several benchmark algorithms in a soccer and a thief-and-hunter scenarios.

BoostTree and BoostForest for Ensemble Learning

Bootstrap aggregation (Bagging) and boosting are two popular ensemble learning approaches, which combine multiple base learners to generate a composite learner. This article proposes BoostForest, which is an ensemble learning approach using BoostTree as base learners and can be used for both classification and regression. BoostTree constructs a tree by gradient boosting, which trains a linear or nonlinear model at each node. When a new sample comes in, BoostTree first sorts it down to a leaf, then computes the final prediction by summing up the outputs of all models along the path from the root node to that leaf. BoostTree achieves high randomness (diversity) by sampling its parameters randomly from a parameter pool, and selecting a subset of features randomly at node splitting. BoostForest further increases the randomness by bootstrapping the training data in constructing different BoostTrees. BoostForest is compared with four classical ensemble learning approaches on 30 classification and regression datasets, demonstrating that it can generate more accurate and more robust composite learners.