Gamma Mixture Model (GaMM) is a useful tool for representing complex distributions. However, estimating the parameters of GaMM faces challenges due to the lack of closed-form solution for the shape parameter. Existing parameter estimation methods face limitations stemming from their reliance on approximate computations, which degrade estimation accuracy, as well as the inherent complexity of numerical calculations, leading to computational inefficiency. To address these limitations and fully consider the multimodal nature of big data, this paper proposes a Mode-Partitioned GaMM (MP-GaMM) estimation method for large-scale multimodal data. The MP-GaMM method explores the spatial distribution characteristics of the data through clustering to partition the data into distinct modes, addresses mode overlap with a tune-up strategy, and employs closed-form estimator for parameter estimation of each mode in parallel. Experimental results demonstrate the rationality and effectiveness of the proposed MP-GaMM method, which outperforms existing methods in both accuracy and computational efficiency. Specifically, MP-GaMM exhibits lower error metrics, higher log-likelihood values and shorter runtime, indicating its capability to provide a more accurate estimation of the model parameters, and more precise characterization of the multimodal nature of large-scale data.

The existing methodologies for forecasting exchange rates exhibit significant accuracy, systematicity, and efficiency deficiencies. Traditional exchange rate forecasting methods are limited by siloed data acquisition, cumbersome data processing, subjective feature engineering, and low efficiency model forecasting. To address these limitations, this paper proposes an exchange rate forecasting paradigm based on multimodal big data. The paradigm effectively addresses the challenges of non-standardized feature selection inherent in traditional forecasting methods by introducing flexible algorithmic mechanisms and dynamic feature selection strategies. On this basis, this paper proposes the FX-Agents framework, which enables efficient data acquisition and processing through agent collaboration driven by large language models (LLMs). Its flexible multi-agent module design ensures efficient and stable forecasting performance. Experimental results demonstrate that FX-Agents outperform traditional methods in forecasting accuracy and processing efficiency. The source code of our work is publicly available at https://github.com/Kon-Kwok/FX-Agent.

The Thresholding Bandit (TB) problem is a popular sequential decision-making problem, which aims at identifying the systems whose means are greater than a threshold. Instead of working on the upper bound of a loss function, our approach stands out from conventional practices by directly minimizing the loss itself. Leveraging the large deviation theory, we firstly provide an asymptotically optimal allocation rule for the TB problem, and then propose a parameter-free Large Deviation (LD) algorithm to make the allocation rule implementable. Central limit theorem-based Large Deviation (CLD) algorithm is further proposed as a supplement to improve the computation efficiency using normal approximation. Extensive experiments are conducted to validate the superiority of our algorithms compared to existing methods, and demonstrate their broader applications to more general distributions and various kinds of loss functions.