Nonparametric density estimation has been extensively used in various application scenarios and theoretical models. However, the modeling of these powerful methods is inseparable from the sample data and comes at the cost of repeated and intensive kernel calculations, which makes their efficiency greatly affected by the sample scale, data dimension, and evaluation scale. Inspired by the knowledge distillation method, a student-teacher paradigm model named density convolutional neural network (DCNN) is proposed in this article. The method extracts the density knowledge of the samples based on the density convolution rule and transfers it to a compact and small deep neural network, in order to separate the sample data from the modeling and avoid the cumbersome kernel calculations. Experimental results show the superiority of the proposed method to various nonparametric estimation methods in terms of accuracy, stability, processing efficiency, and low-storage advantage. Especially, for the estimation speed, a univariate density estimation on 1.0E + 08 evaluation points using GPU only takes 1.57 s, and a 10-D multivariate density estimation on 1.0E + 08 evaluation points only takes 10.50 s, which makes our method very suitable for real-time and large-scale repetitive density estimation tasks.

Optical coherence tomography (OCT) is one of the most significant advances in medical images, and OCT segmentation is an important task in medical-assisted diagnostics. However, existing 3D processing methods require large computational resources. To alleviate this problem, we present an improved image projection network (I2PN), which is an end-to-end OCT image segmentation model. Our key insight is to build a simple projection module (SPM) that uses several group convolutions to conduct effective feature extraction and dimension reduction concurrently. By stacking multiple SPMs, the proposed network can process 3D OCTA data into a high-level semantic feature map. Afterward, the Down-Up modules (DUM) that contain down-sampling and up-sampling are applied to align the SPM features to the OCT image segmentation target. Finally, with a category-dependent segmentation head (CDS), which can balance region selection among hierarchical feature maps, the I2PN model can handle the OCTA image segmentation tasks simultaneously, such as retinal vessel and FAZ segmentation. I2PN provides a succinct idea for the quantification of retinal indicators. Extensive experiments on the OCTA-500 dataset validate the effectiveness of the proposed method I2PN.

Random variate generation has been widely used in various engineering applications and model frameworks. The introduction of the proposal distribution makes this kind of methods can deal with more general sampling problems with complex probability density representation. However, the design of proposal distribution is usually difficult, especially when the target distribution is so complex that it contains asymmetric, multimodal and skewed, or even unsmooth, heavy tailed and illegal density, the sampling performance and efficiency will be greatly affected. In this paper, a novel parameter optimization method with efficient self-tuning strategy is proposed in order to automatically construct the optimal proposal distribution for any complex target density, which treats the design of proposal distribution as a parameter search process and search the optimal solution in an infeasible region by evaluating the loss of solution. The significant advantage of the proposed method is that the search based on infeasible region can converge to a good solution with only a few iterations, making our method far superior to other existing methods in efficiency, which is very suitable for the complex target distribution model with time-consuming density calculation process. Experimental results show the advantages of the proposed method in terms of search strategy, optimal solution performance, search efficiency and robustness.