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.

Learning Implicit Generative Models with Theoretical Guarantees

We propose a \textbf{uni}fied \textbf{f}ramework for \textbf{i}mplicit \textbf{ge}nerative \textbf{m}odeling (UnifiGem) with theoretical guarantees by integrating approaches from optimal transport, numerical ODE, density-ratio (density-difference) estimation and deep neural networks. First, the problem of implicit generative learning is formulated as that of finding the optimal transport map between the reference distribution and the target distribution, which is characterized by a totally nonlinear Monge-Amp\`{e}re equation. Interpreting the infinitesimal linearization of the Monge-Amp\`{e}re equation from the perspective of gradient flows in measure spaces leads to the continuity equation or the McKean-Vlasov equation. We then solve the McKean-Vlasov equation numerically using the forward Euler iteration, where the forward Euler map depends on the density ratio (density difference) between the distribution at current iteration and the underlying target distribution. We further estimate the density ratio (density difference) via deep density-ratio (density-difference) fitting and derive explicit upper bounds on the estimation error. Experimental results on both synthetic datasets and real benchmark datasets support our theoretical findings and demonstrate the effectiveness of UnifiGem.

On Newton Screening

Screening and working set techniques are important approaches to reducing the size of an optimization problem. They have been widely used in accelerating first-order methods for solving large-scale sparse learning problems. In this paper, we develop a new screening method called Newton screening (NS) which is a generalized Newton method with a built-in screening mechanism. We derive an equivalent KKT system for the Lasso and utilize a generalized Newton method to solve the KKT equations. Based on this KKT system, a built-in working set with a relatively small size is first determined using the sum of primal and dual variables generated from the previous iteration, then the primal variable is updated by solving a least-squares problem on the working set and the dual variable updated based on a closed-form expression. Moreover, we consider a sequential version of Newton screening (SNS) with a warm-start strategy. We show that NS possesses an optimal convergence property in the sense that it achieves one-step local convergence. Under certain regularity conditions on the feature matrix, we show that SNS hits a solution with the same signs as the underlying true target and achieves a sharp estimation error bound with high probability. Simulation studies and real data analysis support our theoretical results and demonstrate that SNS is faster and more accurate than several state-of-the-art methods in our comparative studies.

A Support Detection and Root Finding Approach for Learning High-dimensional Generalized Linear Models

Feature selection is important for modeling high-dimensional data, where the number of variables can be much larger than the sample size. In this paper, we develop a support detection and root finding procedure to learn the high dimensional sparse generalized linear models and denote this method by GSDAR. Based on the KKT condition for $\ell_0$-penalized maximum likelihood estimations, GSDAR generates a sequence of estimators iteratively. Under some restricted invertibility conditions on the maximum likelihood function and sparsity assumption on the target coefficients, the errors of the proposed estimate decays exponentially to the optimal order. Moreover, the oracle estimator can be recovered if the target signal is stronger than the detectable level. We conduct simulations and real data analysis to illustrate the advantages of our proposed method over several existing methods, including Lasso and MCP.

Supervised Discriminative Sparse PCA with Adaptive Neighbors for Dimensionality Reduction

Dimensionality reduction is an important operation in information visualization, feature extraction, clustering, regression, and classification, especially for processing noisy high dimensional data. However, most existing approaches preserve either the global or the local structure of the data, but not both. Approaches that preserve only the global data structure, such as principal component analysis (PCA), are usually sensitive to outliers. Approaches that preserve only the local data structure, such as locality preserving projections, are usually unsupervised (and hence cannot use label information) and uses a fixed similarity graph. We propose a novel linear dimensionality reduction approach, supervised discriminative sparse PCA with adaptive neighbors (SDSPCAAN), to integrate neighborhood-free supervised discriminative sparse PCA and projected clustering with adaptive neighbors. As a result, both global and local data structures, as well as the label information, are used for better dimensionality reduction. Classification experiments on nine high-dimensional datasets validated the effectiveness and robustness of our proposed SDSPCAAN.