Different from general assembly datasets, we treat assemblable features, such as holes, stud and USB female, as objects, to enable finer-grained assembly knowledge understanding.

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.