Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects

Testing independence or conditional independence is fundamental to statistical inference, yet existing methods for non-Euclidean random objects often face a difficult trade-off between geometric flexibility and theoretical tractability. We introduce the Distance Profile Embedding (DPE), a novel representation that maps random objects from general metric spaces into a Hilbert space of square-integrable functions. We prove that this mapping is injective and preserves full distributional information without requiring isometric Hilbert embeddings or one-to-one correspondence conditions. Leveraging the DPE, we develop a unified framework for marginal and conditional independence testing of random objects that enjoys a rigorous asymptotic theory for both size and power. Notably, our framework is the first in the literature to accommodate object-valued conditioning variables when testing conditional independence, overcoming the Euclidean or Hilbertian constraints of existing methodologies. We facilitate the calculation of analytic $p$-values using closed-form asymptotic null distributions, which avoids the computational burden of permutation tests common in existing metric-based methods. The numerical properties of our methods are demonstrated through both simulations and two real-world applications involving gut microbiome compositions and global human mortality distributions, respectively.

Infor-Coef: Information Bottleneck-based Dynamic Token Downsampling for Compact and Efficient language model

The prevalence of Transformer-based pre-trained language models (PLMs) has led to their wide adoption for various natural language processing tasks. However, their excessive overhead leads to large latency and computational costs. The statically compression methods allocate fixed computation to different samples, resulting in redundant computation. The dynamic token pruning method selectively shortens the sequences but are unable to change the model size and hardly achieve the speedups as static pruning. In this paper, we propose a model accelaration approaches for large language models that incorporates dynamic token downsampling and static pruning, optimized by the information bottleneck loss. Our model, Infor-Coef, achieves an 18x FLOPs speedup with an accuracy degradation of less than 8\% compared to BERT. This work provides a promising approach to compress and accelerate transformer-based models for NLP tasks.