Imputation methods play a critical role in enhancing the quality of practical time-series data, which often suffer from pervasive missing values. Recently, diffusion-based generative imputation methods have demonstrated remarkable success compared to autoregressive and conventional statistical approaches. Despite their empirical success, the theoretical understanding of how well diffusion-based models capture complex spatial and temporal dependencies between the missing values and observed ones remains limited. Our work addresses this gap by investigating the statistical efficiency of conditional diffusion transformers for imputation and quantifying the uncertainty in missing values. Specifically, we derive statistical sample complexity bounds based on a novel approximation theory for conditional score functions using transformers, and, through this, construct tight confidence regions for missing values. Our findings also reveal that the efficiency and accuracy of imputation are significantly influenced by the missing patterns. Furthermore, we validate these theoretical insights through simulation and propose a mixed-masking training strategy to enhance the imputation performance.

Predicting cognitive load is a crucial issue in the emerging field of human-computer interaction and holds significant practical value, particularly in flight scenarios. Although previous studies have realized efficient cognitive load classification, new research is still needed to adapt the current state-of-the-art multimodal fusion methods. Here, we proposed a feature selection framework based on multiview learning to address the challenges of information redundancy and reveal the common physiological mechanisms underlying cognitive load. Specifically, the multimodal signal features [electroencephalogram (EEG), electrodermal activity (EDA), electrocardiogram (ECG), electrooculogram (EOG), & eye movements] at three cognitive load levels were estimated during multiattribute task battery (MATB) tasks performed by 22 healthy participants and fed into a feature selection-multiview classification with cohesion and diversity (FS-MCCD) framework. The optimized feature set was extracted from the original feature set by integrating the weight of each view and the feature weights to formulate the ranking criteria. The cognitive load prediction model, evaluated using real-time classification results, achieved an average accuracy of 81.08% and an average F1-score of 80.94% for three-class classification among 22 participants. Furthermore, the weights of the physiological signal features revealed the physiological mechanisms related to cognitive load. Specifically, heightened cognitive load was linked to amplified $\delta$ and $\theta$ power in the frontal lobe, reduced $\alpha$ power in the parietal lobe, and an increase in pupil diameter. Thus, the proposed multimodal feature fusion framework emphasizes the effectiveness and efficiency of using these features to predict cognitive load.

We study the dynamic pricing problem where the demand function is nonparametric and Hölder smooth, and we focus on adaptivity to the unknown Hölder smoothness parameter $\beta$ of the demand function. Traditionally the optimal dynamic pricing algorithm heavily relies on the knowledge of $\beta$ to achieve a minimax optimal regret of $\widetilde{O}(T^{\frac{\beta+1}{2\beta+1}})$. However, we highlight the challenge of adaptivity in this dynamic pricing problem by proving that no pricing policy can adaptively achieve this minimax optimal regret without knowledge of $\beta$. Motivated by the impossibility result, we propose a self-similarity condition to enable adaptivity. Importantly, we show that the self-similarity condition does not compromise the problem’s inherent complexity since it preserves the regret lower bound $\Omega(T^{\frac{\beta+1}{2\beta+1}})$. Furthermore, we develop a smoothness-adaptive dynamic pricing algorithm and theoretically prove that the algorithm achieves this minimax optimal regret bound without the prior knowledge $\beta$.

Data-driven decision-making processes increasingly utilize end-to-end learnable deep neural networks to render final decisions. Sometimes, the output of the forward functions in certain layers is determined by the solutions to mathematical optimization problems, leading to the emergence of differentiable optimization layers that permit gradient back-propagation. However, real-world scenarios often involve large-scale datasets and numerous constraints, presenting significant challenges. Current methods for differentiating optimization problems typically rely on implicit differentiation, which necessitates costly computations on the Jacobian matrices, resulting in low efficiency. In this paper, we introduce BPQP, a differentiable convex optimization framework designed for efficient end-to-end learning. To enhance efficiency, we reformulate the backward pass as a simplified and decoupled quadratic programming problem by leveraging the structural properties of the Karush–Kuhn–Tucker (KKT) matrix. This reformulation enables the use of first-order optimization algorithms in calculating the backward pass gradients, allowing our framework to potentially utilize any state-of-the-art solver. As solver technologies evolve, BPQP can continuously adapt and improve its efficiency. Extensive experiments on both simulated and real-world datasets demonstrate that BPQP achieves a significant improvement in efficiency—typically an order of magnitude faster in overall execution time compared to other differentiable optimization layers. Our results not only highlight the efficiency gains of BPQP but also underscore its superiority over differential optimization layer baselines.

Previous studies have made great efforts to expand the instruction set in steady-state visual evoked potential (SSVEP)-based brain-computer interfaces. However, most systems are limited to single persons and expand the instruction set by increasing the flicker stimulation frequency range or via multiple frequencies sequential coding or joint frequency/phase coding. In this article, we propose a multibrain coding SSVEP paradigm that encodes the SSVEP instructions generated byNindependent subjects withMflicker stimuli, thus increasing the instruction set toMNinstructions. A total of 40 subjects participated in online experiments in this article. The results show that there is no significant difference in accuracy (p> 0.05, paired t test) between the multibrain and single-brain coding systems, while the information transfer rate (ITR) increases significantly (pN= 3 andM= 5. In summary, the proposed multibrain coding paradigm exponentially increases the number of instructions without increasing the output instruction time, which is of great significance to the application and promotion of BCIs.

Cognitive load prediction is one of the most important issues in the nascent field of neuroergonomics, and it has significant value in real-world applications. Most of the previous studies of cognitive load prediction only utilized electroencephalography (EEG)-based spectral signatures or interchannel connectivity, ignoring abundant temporal microstate features, which may represent the transient topologies of EEG signals. Furthermore, previous studies have mostly focused on the binary-level classification of cognitive load for single-type cognitive tasks. To date, there are few studies on the multilevel prediction of cognitive load during mixed cognitive tasks. Here, we first designed a new paradigm termed the “finding fault game,” mixing multiple tasks of memory, counting, and visual search, and then developed a multidimensional analysis framework to improve cognitive load prediction using a fusion of spatial, temporal, and spectral EEG features. Specifically, EEG-based functional connectivity, microstates and power spectral densities (PSD) were calculated for three cognitive load levels. Twelve adult subjects participated in the study. The experimental results show that increased cognitive load was associated with elevated theta and degraded alpha power and significant changes in interchannel connectivity and microstates, and that fusing the three types of EEG features improved the performance of three-level cognitive load prediction, achieving the accuracies of greater than 80% in the cross-validation, real-time, and over-time prediction. The findings suggest that all three types of EEG features can serve as signatures of cognitive load and that their fusion can improve multilevel prediction.