Model uncertainty quantification involves measuring and evaluating the uncertainty linked to a model’s predictions, helping assess their reliability and confidence. Noise injection is a technique used to enhance the robustness of neural networks by introducing randomness. In this paper, we establish a connection between noise injection and uncertainty quantification from a Bayesian standpoint. We theoretically demonstrate that injecting noise into the weights of a neural network is equivalent to Bayesian inference on a deep Gaussian process. Consequently, we introduce a Monte Carlo Noise Injection (MCNI) method, which involves injecting noise into the parameters during training and performing multiple forward propagations during inference to estimate the uncertainty of the prediction. Through simulation and experiments on regression and classification tasks, our method demonstrates superior performance compared to the baseline model.

Explicit noise-level conditioning is widely regarded as essential for the effective operation of Graph Diffusion Models (GDMs). In this work, we challenge this assumption by investigating whether denoisers can implicitly infer noise levels directly from corrupted graph structures, potentially eliminating the need for explicit noise conditioning. To this end, we develop a theoretical framework centered on Bernoulli edge-flip corruptions and extend it to encompass more complex scenarios involving coupled structure-attribute noise. Extensive empirical evaluations on both synthetic and real-world graph datasets, using models such as GDSS and DiGress, provide strong support for our theoretical findings. Notably, unconditional GDMs achieve performance comparable or superior to their conditioned counterparts, while also offering reductions in parameters (4-6%) and computation time (8-10%). Our results suggest that the high-dimensional nature of graph data itself often encodes sufficient information for the denoising process, opening avenues for simpler, more efficient GDM architectures.

The current volume of data in the field of securities investment is increasing dramatically. Simultaneously, the linkage of data from multiple parties makes investment reasoning decisions more challenging than ever. In response to this problem, the financial field's knowledge graph can improve the efficiency, depth, and breadth of financial practitioners' information analysis. Some existing financial knowledge graphs analyze the shareholding relationship between companies. Still, because they are limited to observing data from the company's perspective, users without professional industry background cannot quickly find the industry factors of stock market changes. This paper proposes a financial knowledge graph from the industry chain's perspective. This paper builds upstream and downstream relationships between industries through Transformer-based bidirectional encoder to mine potential industry chain associations from text data and completes the long industry chain of the stock market. This paper also builds a visualization system to display and explore the connection between listed companies and industries. Users can inspect the industry chain's composition and each company's revenue status and stock market conditions in the industry chain. The experiment shows that when the market price fluctuation is detected, the stock price fluctuation can be traced back to its origin in the knowledge graph.

Recent detection method based on machine learning demonstrates significant advantages against varieties of network attacks, and has been widely deployed in cloud applications. However, novel attacks such as Advanced Persistent Threats (APTs) could evade detection of the intrusion detection system, which may lead to serious data leakage in cloud. Existing methods studied the countermeasures to defend against evasion attacks. However, a cloud service provider (CSP) also have to balance between its expect revenue and the security risk of system with limited resources. In this paper, we present the CSP's optimal strategy for effective and safety operation, in which the CSP decides the size of users that the cloud service will provide and whether enhanced countermeasures will be conducted for discovering the possible evasion attacks. While the CSP tries to optimize its profit by carefully making a two-step decision of the defense plan and service scale, the attacker considers its expected revenue to launch evasion attacks or not. To obtain insights of such a highly coupled system, we consider a system with one CSP and one attacker with two attack choices of whether to launch an evasion attack. We propose a two-stage Stackelberg game, in which the CSP acts as the leader who decides the defense plan and service scale in Stage I, and the attacker acts as the follower that determines whether to make evasion attacks in Stage II. We derive the Nash Equilibrium by analyzing the attacker's choices under different scenarios that the CSP selects. Then, we provide the CSP's optimal strategies to maximize its revenue. The simulation results help to better understand the CSP's optimal solutions under different situations.

If the local area of a three-dimensional object surface can be considered as a plane, the deformation between its two images captured from different camera placements is modelled by a homography. By tuning the parameters in a homographic mapping, all possible deformations caused by the change of camera placement can be simulated for the local feature matching method. Since aliasing may happen when resampling the original image to the geometry of the simulated image, an antialiasing convolution must be applied before resampling. However, the antialiasing convolution itself must also be homography-adaptive. In the scale invariant feature transform (SIFT) or affine-SIFT (ASIFT) method, the similitude or affine rectification scheme of the convolution is applied to solve this problem under similitude or affine mapping. However, these schemes will not work under homographic or perspective mapping. Although the perspective invariant matching method (perspective-SIFT or PSIFT) has been proposed in some references, the antialiasing scheme with perspective-adaption has not been proposed. This paper will show that the standard convolution is not adaptive to the change of planar mapping, and the simulated images under the same simulated camera placement will not be identical if they are resampled from different original images captured from different camera placements. To solve this issue, a natural extension of the standard convolution, the mapping-adaptive convolution (MA-convolution), is proposed, and its mapping-adaption is proved mathematically in this paper. Based on this novel convolution, the homography invariant simulation scheme can be modelled. We have applied the MA-convolution to the antialiasing scheme in the PSIFT method, and the effectiveness of the MA-convolution has been verified experimentally.