arXiv subjects

Ikjun Choi

Publications and source records attributed to Ikjun Choi.

3 recordsLinked to original sources

arXiv2026

On Statistical-Computational Gaps in Graph Combinatorial Testing Problems

We study high-dimensional graph combinatorial hypothesis testing problems in which a signal is supported on the edge set of an unknown subgraph drawn from a class invariant under vertex relabeling. For Gaussian observations, we characterize sharp statistical and computational thresholds (at polynomial order) for the signal magnitude required for strong detection across various combinatorial graph alternatives. Our analysis is based on bounding the second moments of the full and low-degree likelihood ratios in terms of the overlap of two independent latent structures and comparing the resulting lower bounds with scan, average, and coordinatewise maximum tests. Under an appropriate low-degree conjecture for computational hardness, we obtain planted-clique thresholds matching those known for Gaussian submatrix detection and identify new statistical-computational gaps for multiple planted cliques and hypercliques, thick cycles and thick paths. We also establish a novel transfer principle across natural exponential family observation models: matching the one-coordinate chi-square divergence preserves full likelihood-ratio second moments exactly and makes low-degree second moments equivalent up to constant factors under a degree condition. Under local regularity, we obtain corresponding testing upper bounds in terms of an effective signal strength. When these upper and lower bounds match, they yield universal threshold scales in the local alternative regime. As a consequence, statistical-computational gaps for planted-clique detection in Erdős--Rényi settings can be deduced from the Gaussian model.

math.ST↗

arXiv2026

InstantMimic: A High Performance System for Learning Physics-based Skills in Seconds

Physics-based character control is a long-standing challenge in computer graphics and robotics, requiring policies that satisfy complex dynamics while producing realistic motion. Recent Deep RL approaches, particularly imitation learning methods such as DeepMimic, have had broad impact beyond animation, influencing robotics by enabling agile and expressive behaviors. While these approaches achieve impressive results, they remain computationally inefficient to train in practice. Despite GPU-accelerated simulation, we find that end-to-end pipelines often underutilize hardware due to overheads outside the physics solver, caused by fragmented GPU kernels and CPU memory access in the critical path. We present InstantMimic, a system that addresses these inefficiencies by making the entire training loop GPU-native. Built on a GPU-native physics backend, our unified pipeline integrates simulation, environment computation, policy inference, and policy updates within a single execution flow. As a result, InstantMimic reduces training time for diverse physics-based skills to a few seconds and makes LLM-agent-driven hyperparameter search practical.

cs.GR↗

arXiv2026

Computational-Statistical Trade-off in Kernel Two-Sample Testing with Random Fourier Features

Recent years have seen a surge in methods for two-sample testing, among which the Maximum Mean Discrepancy (MMD) test has emerged as an effective tool for handling complex and high-dimensional data. Despite its success and widespread adoption, the primary limitation of the MMD test has been its quadratic-time complexity, which poses challenges for large-scale analysis. While various approaches have been proposed to expedite the procedure, it has been unclear whether it is possible to attain the same power guarantee as the MMD test at sub-quadratic time cost. To fill this gap, we revisit the approximated MMD test using random Fourier features, and investigate its computational-statistical trade-off. We start by revealing that the approximated MMD test is pointwise consistent in power only when the number of random features approaches infinity. We then consider the uniform power of the test and study the time-power trade-off under the minimax testing framework. Our result shows that, by carefully choosing the number of random features, it is possible to attain the same minimax separation rates as the MMD test within sub-quadratic time. We demonstrate this point under different distributional assumptions such as densities in a Sobolev ball. Our theoretical findings are corroborated by simulation studies.

stat.ML↗