Time series classification (TSC) is a critical area with broad applications. In the field of evidence theory, quantum evidence theory (QET) offers a promising framework for onedimensional TSC tasks, leveraging the capabilities of quantum basic probability amplitude (QBPA) to capture two-dimensional uncertainty. However, as the first step for the application of QET to TSC, how to construct QBPA still remains an open issue. In this paper, a novel approach to generate QBPA is devised. Specifically, we first apply the discrete Fourier transform (DFT) to the original data, extracting two-dimensional features embedded in the magnitude and phase from the frequency domain based on the front-few multi-frequency components, achieved by setting a threshold frequency index (TFI) to limit the frequencies considered. Next, we introduce the complex dual gaussian fuzzy number (CDGFN) as a carrier for QBPA, effectively representing two-dimensional uncertainty in the data. A CDGFN-based multisource information fusion (CDGFN-MSIF) algorithm for decision-making is proposed to combine information from different frequency components. Finally, the decisionmaking algorithm is validated on multiple time series datasets. Experimental results highlight the superior performance of the proposed approach over other state-of-the-art models, demonstrating its effectiveness and enhanced classification accuracy.

Off-policy evaluation (OPE) is a crucial problem in reinforcement learning (RL), where the goal is to estimate the long-term cumulative reward of a target policy using historical data generated by a potentially different behaviour policy. In many real-world applications, such as precision medicine and recommendation systems, unobserved confounders may influence the action, reward, and state transition dynamics, which leads to biased estimates if not properly addressed. While existing methods for handling unobserved confounders in OPE focus on single-action settings, they are less effective in multi-action scenarios commonly found in practical applications, where an agent can take multiple actions simultaneously. In this paper, we propose a novel auxiliary variable-aided method for OPE in multi-action settings with unobserved confounders. Our approach overcomes the limitations of traditional auxiliary variable methods for multi-action scenarios by requiring only a single auxiliary variable, relaxing the need for as many auxiliary variables as the actions. Through theoretical analysis, we prove that our method provides an unbiased estimation of the target policy value. Empirical evaluations demonstrate that our estimator achieves better performance compared to existing baseline methods, highlighting its effectiveness and reliability in addressing unobserved confounders in multi-action OPE settings.

Few-Shot Class-Incremental Learning (FSCIL)presents an extension of the Class Incremental Learning (CIL)problem where a model is faced with the problem of data scarcity while addressing the Catastrophic Forgetting (CF)problem. This problem remains an open problem because all recent works are built upon the Convolutional Neural Networks (CNNs)performing sub-optimally compared to the transformer approaches. Our paper presents Robust Transformer Approach (ROBUSTA)built upon the Compact Convolutional Transformer (CCT). The issue of overfitting due to few samples is overcome with the notion of the stochastic classifier, where the classifier's weights are sampled from a distribution with mean and variance vectors, thus increasing the likelihood of correct classifications, and the batch-norm layer to stabilize the training process. The issue of CFis dealt with the idea of delta parameters, small task-specific trainable parameters while keeping the backbone networks frozen. A non-parametric approach is developed to infer the delta parameters for the model's predictions. The prototype rectification approach is applied to avoid biased prototype calculations due to the issue of data scarcity. The advantage of ROBUSTAis demonstrated through a series of experiments in the benchmark problems where it is capable of outperforming prior arts with big margins without any data augmentation protocols.

Multisource information fusion is a comprehensive and interdisciplinary subject. Dempster-Shafer (D-S) evidence theory copes with uncertain information effectively. Pattern classification is the core research content of pattern recognition, and multisource information fusion based on D-S evidence theory can be effectively applied to pattern classification problems. However, in D-S evidence theory, highly-conflicting evidence may cause counterintuitive fusion results. Belief divergence theory is one of the theories that are proposed to address problems of highly-conflicting evidence. Although belief divergence can deal with conflict between evidence, none of the existing belief divergence methods has considered how to effectively measure the discrepancy between two pieces of evidence with time evolutionary. In this study, a novel fractal belief Rényi (FBR) divergence is proposed to handle this problem. We assume that it is the first divergence that extends the concept of fractal to R/'enyi divergence. The advantage is measuring the discrepancy between two pieces of evidence with time evolution, which satisfies several properties and is flexible and practical in various circumstances. Furthermore, a novel algorithm for multisource information fusion based on FBR divergence, namely FBReD-based weighted multisource information fusion, is developed. Ultimately, the proposed multisource information fusion algorithm is applied to a series of experiments for pattern classification based on real datasets, where our proposed algorithm achieved superior performance.

Complex evidence theory (CET) is an effective method for uncertainty reasoning in knowledge-based systems with good interpretability that has recently attracted much attention. However, approaches to improve the performance of uncertainty reasoning in CET-based expert systems remains an open issue. One key to performance improvement is the adequate management of conflict from multisource information. In this paper, a generalized correlation coefficient, namely, the complex evidential correlation coefficient (CECC), is proposed for the complex mass functions or complex basic belief assignments (CBBAs) in CET. On this basis, a complex conflict coefficient is proposed to measure the conflict between CBBAs; when CBBAs turn into classic BBAs, the complex correlation and conflict coefficients will degrade into traditional coefficients. The complex conflict coefficient satisfies nonnegativity, symmetry, boundedness, extreme consistency, and insensitivity to refinement properties, which are desirable for conflict measurement. Several numerical examples validate through comparisons the superiority of the complex conflict coefficient. In this context, a weighted discounting multisource information fusion algorithm, which is called the CECC-WDMSIF, is designed based on the CECC to improve the performance of CET-based expert systems. By applying the CECC-WDMSIF method to the pattern classification of diverse real-world datasets, it is demonstrated that the proposed CECC-WDMSIF outperforms well-known related approaches with higher classification accuracy and robustness.