Deep generative models like VAEs and diffusion models have advanced various generation tasks by leveraging latent variables to learn data distributions and generate high-quality samples. Despite the field of explainable AI making strides in interpreting machine learning models, understanding latent variables in generative models remains challenging. This paper introduces LatentExplainer, a framework for automatically generating semantically meaningful explanations of latent variables in deep generative models. LatentExplainer tackles three main challenges: inferring the meaning of latent variables, aligning explanations with inductive biases, and handling varying degrees of explainability. By perturbing latent variables and interpreting changes in generated data, the framework provides a systematic approach to understanding and controlling the data generation process, enhancing the transparency and interpretability of deep generative models. We evaluate our proposed method on several real-world and synthetic datasets, and the results demonstrate superior performance in generating high-quality explanations of latent variables.

The bias of the sample means of the arms in multi-armed bandits is an important issue in adaptive data analysis that has recently received considerable attention in the literature. Existing results relate in precise ways the sign and magnitude of the bias to various sources of data adaptivity, but do not apply to the conditional inference setting in which the sample means are computed only if some specific conditions are satisfied. In this paper, we characterize the sign of the conditional bias of monotone functions of the rewards, including the sample mean. Our results hold for arbitrary conditioning events and leverage natural monotonicity properties of the data collection policy. We further demonstrate, through several examples from sequential testing and best arm identification, that the sign of the conditional and unconditional bias of the sample mean of an arm can be different, depending on the conditioning event. Our analysis offers new and interesting perspectives on the subtleties of assessing the bias in data adaptive settings.