In this paper, we present an efficient scenario reduction method for optimization problems whose objective function is the higher moment coherent risk (HMCR) measures. Compared with existing approaches, our method places greater emphasis on the characteristics of optimization problems. Because the value of HMCR measures only depends on a small subset of scenarios that correspond to high cost or loss, our approach is based mostly on the concept of ineffective scenarios previously proposed in the literature, which entails identifying the scenarios whose removal from the problem results in no change of the optimal value. We test our method on a simple portfolio optimization problem with only nine risky assets and a realistic one with 50 risky assets and cardinality constraints. Results show that our scenario reduction method can yield a more accurate optimal solution and optimal value, along with a smaller reduced-scenario set. Even at the same reduction level, our method continues to outperform the existing scenario reduction methods. Interestingly, the portfolio produced by our method is also more diversified than others. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the National Natural Science Foundation of China [Grants 71720107002 and U1901223]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0375 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0375 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Abstract Recently, a robust steganographic algorithm that achieves errorless robustness against JPEG recompression has been proposed. The method employs a lattice embedding scheme and utilizes the syndrome-trellis code (STC) for practical embedding. However, we have noticed that errorless robust embedding with STC may encounter failures due to modifications on wet coefficients, especially when a high quality factor is used by the compression channel. To solve this problem, we have discovered that using steganographic polar code (SPC) for embedding has better performance in avoiding modifications on wet coefficients. In this paper, we conduct theoretical analysis to prove the better performance of SPC in wet paper embedding. We establish the condition of avoiding modifications on wet coefficients, followed by presenting a recursive calculation method for determining the distribution of columns in the generator matrix of SPC. The findings reveal that SPC can avoid modifications on wet coefficients under a larger number of wet coefficients compared with STC, and therefore we propose a better errorless robust embedding method employing SPC. The experimental results demonstrate that under close security performance, the proposed method achieves a higher success rate compared with embedding with STC. Specifically, when the quality factor of the compressor is 95 and the payload size is 0.4 bpnzac, our method achieves a success rate of 99.85%, surpassing the 91.95% success rate of the embedding with STC.

Abstract Because the JPEG recompression in social networks changes the DCT coefficients of uploaded images, applying image steganography in popular image-sharing social networks requires robustness. Currently, most robust steganography algorithms rely on the resistance of embedding to the general JPEG recompression process. The operations in a specific compression channel are usually ignored, which reduces the robustness performance. Besides, to acquire the robust cover image, the state-of-the-art robust steganography needs to upload the cover image to social networks several times, which may be insecure regarding behavior security. In this paper, a robust steganography method based on the softmax outputs of a trained classifier and protocol message embedding is proposed. In the proposed method, a deep learning-based robustness classifier is trained to model the specific process of the JPEG recompression channel. The prediction result of the classifier is used to select the robust DCT blocks to form the embedding domain. The selection information is embedded as the protocol messages into the middle-frequency coefficients of DCT blocks. To further improve the recovery possibility of the protocol message, a robustness enhancement method is proposed. It decreases the predicted non-robust possibility of the robustness classifier by modifying low-frequency coefficients of DCT blocks. The experimental results show that the proposed method has better robustness performance compared with state-of-the-art robust steganography and does not have the disadvantage regarding behavior security. The method is universal and can be implemented in different JPEG compression channels after fine-tuning the classifier. Moreover, it has better security performance compared with the state-of-the-art method when embedding large-sized secret messages.

Scenario reduction is an effective method to ease the computational burden of stochastic programming problems, which aims at choosing a subset of scenarios that can better represent a large number of possible scenarios. Higher-order moments are critical in the scenario reduction process, especially for stochastic programming problems that are greatly affected by the moments. From this idea, we construct a mixed integer linear programming model to improve the reduction accuracy of traditional methods by minimizing the moments’ information loss between the original and reduced scenarios. An improved Benders decomposition algorithm is then designed to find an optimal solution for the model. Finally, the resulting scenarios are examined on an international portfolio selection problem. Empirical and comparative studies are also carried out to reveal the superiority of our proposed scenario reduction method over other existing approaches or models, together with the superior performance of the algorithm. Summary of Contribution: To effectively solve stochastic programming problems, the scenario reduction method has become an active research area to strike a balance between the fine representation of random variables and computational complexity. Thus, how to design a reasonable optimal scenario reduction model and effectively solve this complex model is very important and meaningful. On the other hand, for some stochastic programming problems, especially the portfolio selection problems, statistical properties of risky assets returns may play a more important role in the scenario reduction process. However, the traditional scenario reduction methods have ignored this point. Thus, in this paper, we propose a mixed integer linear programming model to improve the reduction accuracy by minimizing the higher-order moments’ information loss between the original and reduced scenarios. Furthermore, an accelerated Benders decomposition algorithm is also designed to solve the proposed model. Hence, the aim of this paper is to extend the existing scenario reduction method in substantial and meaningful ways.

Due to a large number of user-uploaded images, social networks have become secure channels for covert communication. However, the JPEG recompression of social networks changes the DCT coefficients of stego images, resulting in the failure of adaptive steganography. To achieve steganography in lossy channels, robust steganography has been proposed. In this letter, the ability against JPEG recompression of robust steganography is further improved by introducing a robustness cost function. For calculating the robustness cost, a robustness model based on the spatial domain calculated from DCT coefficients is firstly proposed. Then the robustness cost is acquired by measuring the distance between the spatial pixels calculated from modified DCT coefficients and the robustness model adjusted spatial pixels. Combining the distortion function and the robustness cost function, the method proposed has considerable robustness performance while maintaining satisfying security performance. Experimental results show that with the maximum reduction of 4.04% on security performance, the algorithm proposed has a significant improvement on robustness performance compared with state-of-the-art robust steganography.

To cope with the abuse of steganography using H.264 videos, i.e., the dominant video format, as the carrier, this paper presents a steganalytic method which works well even in the scenario where both the training data and the prior knowledge of the test data are limited. As a key feature of H.264, intra prediction is incorporated to remove redundancies within one single frame by predicting the current block using previously coded blocks. Unlike in JPEG domain, the quantized discrete cosine transform (QDCT) coefficients in H.264 videos come from the prediction error (residual) blocks (PEBs) instead of the original pixel block, hence we suggest shifting the focal point from the spatial domain to the prediction error domain, i.e., the PEB domain. According to the traits of video coding, 3 types of subtractive PEB (SPEB) are defined to capture the inconsistency between correlated PEBs, and the differences between correlated SPEBs are modeled by first-order Markov chain. Then the so-called SUPERB (SUbtractive Prediction ERror Block) features are engineered by subsets of sample transition probability matrices for a steganalyzer. What's more, the features derived from IPM (Intra Prediction Mode) transition probabilities are also merged into SUPERB to improve detection ability. Extensive experiments are carried out from different aspects. Performance results demonstrate the effectiveness of SUPERB, particularly its essence of general applicability when the training and test data are of quite different attributes, which is more favorable for real-world applications.