Fully Bayesian Logistic Regression with Hyper-Lasso Priors for High-dimensional Feature Selection

High-dimensional feature selection arises in many areas of modern science. For example, in genomic research we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal) from tens of thousands of genes that are active (expressed) in certain tissue cells. To this end, we wish to fit regression and classification models with a large number of features (also called variables, predictors). In the past decade, penalized likelihood methods for fitting regression models based on hyper-LASSO penalization have received increasing attention in the literature. However, fully Bayesian methods that use Markov chain Monte Carlo (MCMC) are still in lack of development in the literature. In this paper we introduce an MCMC (fully Bayesian) method for learning severely multi-modal posteriors of logistic regression models based on hyper-LASSO priors (non-convex penalties). Our MCMC algorithm uses Hamiltonian Monte Carlo in a restricted Gibbs sampling framework; we call our method Bayesian logistic regression with hyper-LASSO (BLRHL) priors. We have used simulation studies and real data analysis to demonstrate the superior performance of hyper-LASSO priors, and to investigate the issues of choosing heaviness and scale of hyper-LASSO priors.Comment: 33 pages. arXiv admin note: substantial text overlap with arXiv:1308.469

TrojDiff: Trojan Attacks on Diffusion Models with Diverse Targets

Diffusion models have achieved great success in a range of tasks, such as image synthesis and molecule design. As such successes hinge on large-scale training data collected from diverse sources, the trustworthiness of these collected data is hard to control or audit. In this work, we aim to explore the vulnerabilities of diffusion models under potential training data manipulations and try to answer: How hard is it to perform Trojan attacks on well-trained diffusion models? What are the adversarial targets that such Trojan attacks can achieve? To answer these questions, we propose an effective Trojan attack against diffusion models, TrojDiff, which optimizes the Trojan diffusion and generative processes during training. In particular, we design novel transitions during the Trojan diffusion process to diffuse adversarial targets into a biased Gaussian distribution and propose a new parameterization of the Trojan generative process that leads to an effective training objective for the attack. In addition, we consider three types of adversarial targets: the Trojaned diffusion models will always output instances belonging to a certain class from the in-domain distribution (In-D2D attack), out-of-domain distribution (Out-D2D-attack), and one specific instance (D2I attack). We evaluate TrojDiff on CIFAR-10 and CelebA datasets against both DDPM and DDIM diffusion models. We show that TrojDiff always achieves high attack performance under different adversarial targets using different types of triggers, while the performance in benign environments is preserved. The code is available at https://github.com/chenweixin107/TrojDiff.Comment: CVPR202