In this work, we propose Mutual Reinforcing Data Synthesis (MRDS) within LLMs to improve few-shot dialogue summarization task. Unlike prior methods that require external knowledge, we mutually reinforce the LLM\'s dialogue synthesis and summarization capabilities, allowing them to complement each other during training and enhance overall performances. The dialogue synthesis capability is enhanced by directed preference optimization with preference scoring from summarization capability. The summarization capability is enhanced by the additional high quality dialogue-summary paired data produced by the dialogue synthesis capability. By leveraging the proposed MRDS mechanism, we elicit the internal knowledge of LLM in the format of synthetic data, and use it to augment the few-shot real training dataset. Empirical results demonstrate that our method improves dialogue summarization, achieving a 1.5% increase in ROUGE scores and a 0.3% improvement in BERT scores in few-shot settings. Furthermore, our method attains the highest average scores in human evaluations, surpassing both the pre-trained models and the baselines fine-tuned solely for summarization tasks.

The integration of uncertainty sets has diverse applications but also presents challenges, particularly when only initial sets and their control levels are available, along with potential dependencies. Examples include merging confidence sets from different distributed sites with communication constraints, as well as combining conformal prediction sets generated by different learning algorithms or data splits. In this article, we introduce an efficient and flexible Synthetic, Aggregation, and Test inversion (SAT) approach to merge various potentially dependent uncertainty sets into a single set. The proposed method constructs a novel class of synthetic test statistics, aggregates them, and then derives merged sets through test inversion. Our approach leverages the duality between set estimation and hypothesis testing, ensuring reliable coverage in dependent scenarios. The procedure is data-light, meaning it relies solely on initial sets and control levels without requiring raw data, and it adapts to any user-specified initial uncertainty sets, accommodating potentially varying coverage levels. Theoretical analyses and numerical experiments confirm that SAT provides finite-sample coverage guarantees and achieves small set sizes.

Tensor-valued data arise frequently from a wide variety of scientific applications, and many among them can be translated into an alteration detection problem of tensor dependence structures. In this article, we formulate the problem under the popularly adopted tensor-normal distributions and aim at two-sample correlation/partial correlation comparisons of tensor-valued observations. Through decorrelation and centralization, a separable covariance structure is employed to pool sample information from different tensor modes to enhance the power of the test. Additionally, we propose a novel Sparsity-Exploited Reranking Algorithm (SERA) to further improve the multiple testing efficiency. The algorithm is approached through reranking of the p-values derived from the primary test statistics, by incorporating a carefully constructed auxiliary tensor sequence. Besides the tensor framework, SERA is also generally applicable to a wide range of two-sample large-scale inference problems with sparsity structures, and is of independent interest. The asymptotic properties of the proposed test are derived and the algorithm is shown to control the false discovery at the pre-specified level. We demonstrate the efficacy of the proposed method through intensive simulations and two scientific applications.

Linkage analysis has provided valuable insights to the GWAS studies, particularly in revealing that SNPs in linkage disequilibrium (LD) can jointly influence disease phenotypes. However, the potential of LD network data has often been overlooked or underutilized in the literature. In this paper, we propose a locally adaptive structure learning algorithm (LASLA) that provides a principled and generic framework for incorporating network data or multiple samples of auxiliary data from related source domains; possibly in different dimensions/structures and from diverse populations. LASLA employs a $p$-value weighting approach, utilizing structural insights to assign data-driven weights to individual test points. Theoretical analysis shows that LASLA can asymptotically control FDR with independent or weakly dependent primary statistics, and achieve higher power when the network data is informative. Efficiency again of LASLA is illustrated through various synthetic experiments and an application to T2D-associated SNP identification.

Generative adversarial networks (GANs) are powerful tools for learning generative models. In practice, the training may suffer from lack of convergence. GANs are commonly viewed as a two-player zero-sum game between two neural networks. Here, we leverage this game theoretic view to study the convergence behavior of the training process. Inspired by the fictitious play learning process, a novel training method, referred to as Fictitious GAN, is introduced. Fictitious GAN trains the deep neural networks using a mixture of historical models. Specifically, the discriminator (resp. generator) is updated according to the best-response to the mixture outputs from a sequence of previously trained generators (resp. discriminators). It is shown that Fictitious GAN can effectively resolve some convergence issues that cannot be resolved by the standard training approach. It is proved that asymptotically the average of the generator outputs has the same distribution as the data samples.