Stabilized Higher-Order Influence Functions: Statistical Theory of a Class of Bilinear Forms

Higher-order influence functions, introduced in a series of articles (Robins et al., 2008, 2009a; van der Vaart, 2014; Robins et al., 2016, 2023; Liu et al., 2017), are a unified framework for constructing rate-optimal point estimates of a class of statistical functionals, under various complexity-reducing assumptions on the posited statistical model that generates the observed data. Although higher-order (influence functions) estimators are theoretically appealing, they have very limited practical uptake compared to their first-order counterparts. The original higher-order estimators proposed in Robins et al. (2008) and Robins et al. (2017) involve nonparametric density estimation of multi-dimensional covariates, a highly nontrivial statistical and computational problem on its own. The density estimator is, in turn, used in the evaluation of the inverse population Gram matrix $Ω$ of a set of $k$-dimensional basis transformations of covariates. There, $k$ is allowed to be as large as $o (n^2)$. To partially address this potential shortcoming, Liu et al. (2017) restrict $k$ to $o (n)$ and instead estimate $Ω$ directly using the inverse sample Gram matrix estimator, but computed from an independent sample often obtained by sample-splitting. Liu et al. (2017) refer to this alternative estimator as the empirical higher-order estimator. Although the empirical higher-order estimator bypasses density estimation, it suffers from numerical instability due to potentially inverting a large-dimensional sample Gram matrix. In this article, we propose a new stabilized higher-order estimator without sample splitting, which exhibits more stable finite-sample performance compared to the empirical higher-order estimator, and more importantly, we prove that this new class of higher-order estimators enjoys similar statistical guarantees.

JieHua Paintings Style Feature Extracting Model using Stable Diffusion with ControlNet

This study proposes a novel approach to extract stylistic features of Jiehua: the utilization of the Fine-tuned Stable Diffusion Model with ControlNet (FSDMC) to refine depiction techniques from artists' Jiehua. The training data for FSDMC is based on the opensource Jiehua artist's work collected from the Internet, which were subsequently manually constructed in the format of (Original Image, Canny Edge Features, Text Prompt). By employing the optimal hyperparameters identified in this paper, it was observed FSDMC outperforms CycleGAN, another mainstream style transfer model. FSDMC achieves FID of 3.27 on the dataset and also surpasses CycleGAN in terms of expert evaluation. This not only demonstrates the model's high effectiveness in extracting Jiehua's style features, but also preserves the original pre-trained semantic information. The findings of this study suggest that the application of FSDMC with appropriate hyperparameters can enhance the efficacy of the Stable Diffusion Model in the field of traditional art style migration tasks, particularly within the context of Jiehua.

A New Chinese Landscape Paintings Generation Model based on Stable Diffusion using DreamBooth

This study mainly introduces a method combining the Stable Diffusion Model (SDM) and Parameter-Efficient Fine-Tuning method for generating Chinese Landscape Paintings. This training process is accelerated by combining LoRA with pre-trained SDM and DreamBooth with pre-trained SDM, respectively. On the Chinese Landscape Paintings Internet dataset used in this paper, this study finds that SDM combined with DreamBooth exhibits superior performance, outperforming other models, including the generic pre-trained SDM and LoRA-based fine-tuning SDM. The SDM combined with DreamBooth achieves a FID of 12.75 on the dataset and outperforms all other models in terms of expert evaluation, highlighting the model's versatility in the field of Chinese Landscape Paintings given the unique identifier, high fidelity and high quality. This study illustrates the potential of specialised fine-tuning method to improve the performance of SDM on domain-specific tasks, particularly in the domain of Landscape Paintings.