High-dimensional mediation analysis is often associated with a multiple testing problem for detecting significant mediators. Assessing the uncertainty of this detecting process via false discovery rate (FDR) has garnered great interest. To control the FDR in multiple testing, two essential steps are involved: ranking and selection. Existing approaches either construct p-values without calibration or disregard the joint information across tests, leading to conservation in FDR control or non-optimal ranking rules for multiple hypotheses. In this paper, we develop an adaptive mediation detection procedure (referred to as "AMDP") to identify relevant mediators while asymptotically controlling the FDR in high-dimensional mediation analysis. AMDP produces the optimal rule for ranking hypotheses and proposes a data-driven strategy to determine the threshold for mediator selection. This novel method captures information from the proportions of composite null hypotheses and the distribution of p-values, which turns the high dimensionality into an advantage instead of a limitation. The numerical studies on synthetic and real data sets illustrate the performances of AMDP compared with existing approaches.

We introduce a suite of new particle-based algorithms for sampling in constrained domains which are entirely learning rate free. Our approach leverages coin betting ideas from convex optimisation, and the viewpoint of constrained sampling as a mirrored optimisation problem on the space of probability measures. Based on this viewpoint, we also introduce a unifying framework for several existing constrained sampling algorithms, including mirrored Langevin dynamics and mirrored Stein variational gradient descent. We demonstrate the performance of our algorithms on a range of numerical examples, including sampling from targets on the simplex, sampling with fairness constraints, and constrained sampling problems in postselection inference. Our results indicate that our algorithms achieve competitive performance with existing constrained sampling methods, without the need to tune any hyperparameters.

Large language models (LLMs) can learn to perform a wide range of natural language tasks from just a handful of in-context examples. However, for generating strings from highly structured languages (e.g., semantic parsing to complex domainspecific languages), it is challenging for the LLM to generalize from just a few exemplars. We propose grammar prompting, a simple approach to enable LLMs to use external knowledge and domain-specific constraints, expressed through a grammar in Backus-Naur Form (BNF), during in-context learning. Grammar prompting augments each demonstration example with a specialized grammar that is minimally sufficient for generating the particular output example, where the specialized grammar is a subset of the full DSL grammar. For inference, the LLM first predicts a BNF grammar given a test input, and then generates the output according to the rules of the grammar. Experiments demonstrate that grammar prompting can enable LLMs to perform competitively on a diverse set of DSL generation tasks, including semantic parsing (SMCalFlow, Overnight, GeoQuery), PDDL planning, and SMILES-based molecule generation.

While numerous works have focused on devising efficient algorithms for reinforcement learning (RL) with uniformly bounded rewards, it remains an open question whether sample or time-efficient algorithms for RL with large state-action space exist when the rewards are heavy-tailed, i.e., with only finite (1+ϵ)-th moments for some ϵ (0,1]. In this work, we address the challenge of such rewards in RL with linear function approximation.

The advent of high-capacity pre-trained models has revolutionized problem-solving in computer vision, shifting the focus from training task-specific models to adapting pre-trained models. Consequently, effectively adapting large pre-trained models to downstream tasks in an efficient manner has become a prominent research area. Existing solutions primarily concentrate on designing lightweight adapters and their interaction with pre-trained models, with the goal of minimizing the number of parameters requiring updates. In this study, we propose a novel Adapter ReComposing (ARC) strategy that addresses efficient pre-trained model adaptation from a fresh perspective. Our approach considers the reusability of adaptation parameters and introduces a parameter-sharing scheme. Specifically, we leverage symmetric down-/up-projections to construct bottleneck operations, which are shared across layers.

Consider the problem of improving the estimation of conditional average treatment effects (CATE) for a target domain of interest by leveraging related information from a source domain with a different feature space. This heterogeneous transfer learning problem for CATE estimation is ubiquitous in areas such as healthcare where we may wish to evaluate the effectiveness of a treatment for a new patient population for which different clinical covariates and limited data are available. In this paper, we address this problem by introducing several building blocks that use representation learning to handle the heterogeneous feature spaces and a flexible multi-task architecture with shared and private layers to transfer information between potential outcome functions across domains. Then, we show how these building blocks can be used to recover transfer learning equivalents of the standard CATE learners. On a new semi-synthetic data simulation benchmark for heterogeneous transfer learning we not only demonstrate performance improvements of our heterogeneous transfer causal effect learners across datasets, but also provide insights into the differences between these learners from a transfer perspective.

Having defined and validated the pairwise feedback simulator and evaluations in AlpacaFarm, we569 now turn our attention to studying methods that learn from pairwise feedback on AlpacaFarm.570 Unfortunately, the lack of existing benchmarks for learning from pairwise feedback for instruction571 following means that there has not been any open study of these methods in the instruction-following572 setting. In the remainder of this section, we will introduce our reference methods, which fall into two575 categories based on whether they fit a surrogate reward model as part of the learning process.576 FeedME is a method proposed by OpenAI [45] that incorporates human feedback578 with supervised fine-tuning on model generations that are rated 7/7 by human labelers. We adapt579 this approach to the pairwise feedback setting and call this baseline binary FeedME. This approach580 fine-tunes the SFT model on the chosen response in each preference pair with supervised learning.581 Motivated by controllable generation through conditioning [27, 34,582 29, 21], we propose binary reward conditioning, a baseline method that fine-tunes the SFT model583 with the feedback data Dpairwise by conditioning instances with either a positive or negative control584 token. Specifically, for each instance (x,y0,y1,z) 2D pairwise, the string concatenation of instruction585 x and response yz denoted as [x,yz] is prepended with the positive token and used in supervised586 fine-tuning (similarly [x,y1 z]is prepended with the negative token). This process creates a modified587 demonstration dataset that is double the size of Dpairwise. At test time, we draw samples from the588 fine-tuned model conditioned on the positive token.589 A.2 Methods that optimize a surrogate reward function590 We now describe methods that incorporate feedback by first building a surrogate reward model with591 pairwise feedback data. To start, we describe the step of training the surrogate reward model.592 While this can be a powerful approach,596 we will see that it can also lead to over-optimization [19] where models learn to exploit the reward597 model rather than achieve high true reward. We now describe 4 methods that leverage the surrogate598 reward model.599