Bivariate causal discovery is challenging when unmeasured confounders exist. To adjust for the bias, previous methods employed the proxy variable (i.e., negative control outcome (NCO)) to test the treatment-outcome relationship through integral equations – and assumed that violation of this equation indicates the causal relationship. Upon this, they could establish asymptotic properties for causal hypothesis testing. However, these methods either relied on parametric assumptions or required discretizing continuous variables, which may lead to information loss. Moreover, it is unclear when this underlying integral-related assumption holds, making it difficult to justify the utility in practice. To address these problems, we first consider the scenario where only NCO is available. We propose a novel non-parametric procedure, which enjoys asymptotic properties and preserves more information. Moreover, we find that when NCO affects the outcome, the above integral-related assumption may not hold, rendering the causal relation unidentifiable. Informed by this, we further consider the scenario when the negative control exposure (NCE) is also available. In this scenario, we construct another integral restriction aided by this proxy, which can discover causation when NCO affects the outcome. We demonstrate these findings and the effectiveness of our proposals through comprehensive numerical studies.

Proximal causal learning is a powerful framework for identifying the causal effect under the existence of unmeasured confounders. Within this framework, the doubly robust (DR) estimator was derived and has shown its effectiveness in estimation, especially when the model assumption is violated. However, the current form of the DR estimator is restricted to binary treatments, while the treatments can be continuous in many real-world applications. The primary obstacle to continuous treatments resides in the delta function present in the original DR estimator, making it infeasible in causal effect estimation and introducing a heavy computational burden in nuisance function estimation. To address these challenges, we propose a kernel-based DR estimator that can well handle continuous treatments for proximal causal learning. Equipped with its smoothness, we show that its oracle form is a consistent approximation of the influence function. Further, we propose a new approach to efficiently solve the nuisance functions. We then provide a comprehensive convergence analysis in terms of the mean square error. We demonstrate the utility of our estimator on synthetic datasets and real-world applications.

This study aimed to improve the accuracy and robustness of a real-time assistive human machine interface system by classifying between the controlled movements related tongue-movement ear pressure (TMEP) signals and the interfering signals. The controlled movement TMEP signals were collected during left, right, up, down, flicking and pushing tongue motions. The TMEP signals were processed and classified using detection, segmentation, feature extraction and classification. The segmented signals were decomposed into the time-scale domain using a wavelet packet transform. The variance of the wavelet packet coefficients and its ratio between low-to-high scales were defined as features and the intended tongue movement commands and interfering signals were classified using both a Bayesian and support vector machine (SVM) classifiers for comparison. The average classification accuracy for discriminating between the controlled movements and the interfering signals achieved 97.8% (Bayesian) and 98.5% (SVM). The classifiers were robust remaining at a similar performance level when generalised interferences from all subjects were used. It was shown that the Bayesian classifier performed better than the SVM in a real-time environment. The approach of combining the Bayesian classifier and the wavelet packet transform provides a robust and efficient method for a real-time assistive human machine interface based on tongue-movement ear pressure signals.

Real-time implementation of an assistive human-machine interface system based around tongue-movement ear pressure (TMEP) signals is presented, alongside results from a series of simulated control tasks. The implementation of this system into an online setting involves short-term energy calculation, detection, segmentation and subsequent signal classification, all of which had to be reformulated based on previous off-line testing. This has included the formulation of a new classification and feature extraction method. This scheme utilises the discrete cosine transform to extract the frequency features from the time domain information, a univariate Gaussian maximum likelihood classifier and a two phase cross-validation procedure for feature selection and extraction. The performance of this classifier is presented alongside a real-time implementation of the decision fusion classification algorithm, with each achieving 96.28% and 93.12% respectively. The system testing takes into consideration potential segmentation of false positive signals. A simulation mapping commands to a planar wheelchair demonstrates the capacity of the system for assistive robotic control. These are the first real-time results published for a tongue-based human-machine interface that does not require a transducer to be placed within the vicinity of the oral cavity.