Liuhua Peng

Yinjie Min, Liuhua Peng, Changliang Zou

Existing evaluations of conformal prediction, such as prediction efficiency and test-conditional coverage, are defined in expectation over the calibration data. In practice, when only one calibration set of limited size is available, prediction sets often exhibit high variability in size, especially for methods with localization. We formalize this concern as set stability, defined as the variance of the conditional expectation of the set size given the calibration data. To improve stability without requiring additional target-task labels, we propose Stable Conformal Prediction (StCP), a transfer learning approach that utilizes labeled source-task data and unlabeled target data. Theoretically, we characterize the marginal coverage and stability of StCP; empirically, it delivers more stable prediction sets than standard conformal prediction methods, especially for those with localization, when calibration data are limited.

Xiaoning Wang, Yuyang Huo, Liuhua Peng et al.

$U$-statistics play a central role in statistical inference. In many modern applications, however, acquiring the labels required for $U$-statistics is costly. Motivated by recent advances in active inference, we develop an active inference framework for $U$-statistics that selectively queries informative labels to improve estimation efficiency under a fixed labeling budget, while preserving valid statistical inference. Our approach is built on the augmented inverse probability weighting $U$-statistic, which is designed to incorporate the sampling rule and machine learning predictions. We characterize the optimal sampling rule that minimizes its variance and design practical sampling strategies. We further extend the framework to $U$-statistic-based empirical risk minimization. Experiments on real datasets demonstrate substantial gains in estimation efficiency over baseline methods, while maintaining target coverage.

Zhijian Zhou, Liuhua Peng, Xunye Tian et al.

The relative similarity testing aims to determine which of the distributions, P or Q, is closer to an anchor distribution U. Existing kernel-based approaches often test the relative similarity with a fixed kernel in a manually specified alternative hypothesis, e.g., Q is closer to U than P. Although kernel selection is known to be important to kernel-based testing methods, the manually specified hypothesis poses a significant challenge for kernel selection in relative similarity testing: Once the hypothesis is specified first, we can always find a kernel such that the hypothesis is rejected. This challenge makes relative similarity testing ill-defined when we want to select a good kernel after the hypothesis is specified. In this paper, we cope with this challenge via learning a proper hypothesis and a kernel simultaneously, instead of learning a kernel after manually specifying the hypothesis. We propose an anchor-based maximum discrepancy (AMD), which defines the relative similarity as the maximum discrepancy between the distances of (U, P) and (U, Q) in a space of deep kernels. Based on AMD, our testing incorporates two phases. In Phase I, we estimate the AMD over the deep kernel space and infer the potential hypothesis. In Phase II, we assess the statistical significance of the potential hypothesis, where we propose a unified testing framework to derive thresholds for tests over different possible hypotheses from Phase I. Lastly, we validate our method theoretically and demonstrate its effectiveness via extensive experiments on benchmark datasets. Codes are publicly available at: https://github.com/zhijianzhouml/AMD.

Zhekai Du, Yinjie Min, Jingjing Li et al.

Low-rank adaptation (LoRA) has become a prevalent method for adapting pre-trained large language models to downstream tasks. However, the simple low-rank decomposition form may constrain the hypothesis space. To address this limitation, we introduce Location-aware Cosine Adaptation (LoCA), a novel frequency-domain parameter-efficient fine-tuning method based on inverse Discrete Cosine Transform (iDCT) with selective locations of learnable components. We begin with a comprehensive theoretical comparison between frequency-domain and low-rank decompositions for fine-tuning pre-trained large models. Our analysis reveals that frequency-domain decomposition with carefully selected frequency components can surpass the expressivity of traditional low-rank-based methods. Furthermore, we demonstrate that iDCT offers a more efficient implementation compared to inverse Discrete Fourier Transform (iDFT), allowing for better selection and tuning of frequency components while maintaining equivalent expressivity to the optimal iDFT-based adaptation. By employing finite-difference approximation to estimate gradients for discrete locations of learnable coefficients on the DCT spectrum, LoCA dynamically selects the most informative frequency components during training. Experiments on diverse language and vision fine-tuning tasks demonstrate that LoCA offers enhanced parameter efficiency while maintains computational feasibility comparable to low-rank-based methods.

Xunye Tian, Liuhua Peng, Zhijian Zhou et al.

Learning effective data representations has been crucial in non-parametric two-sample testing. Common approaches will first split data into training and test sets and then learn data representations purely on the training set. However, recent theoretical studies have shown that, as long as the sample indexes are not used during the learning process, the whole data can be used to learn data representations, meanwhile ensuring control of Type-I errors. The above fact motivates us to use the test set (but without sample indexes) to facilitate the data representation learning in the testing. To this end, we propose a representation-learning two-sample testing (RL-TST) framework. RL-TST first performs purely self-supervised representation learning on the entire dataset to capture inherent representations (IRs) that reflect the underlying data manifold. A discriminative model is then trained on these IRs to learn discriminative representations (DRs), enabling the framework to leverage both the rich structural information from IRs and the discriminative power of DRs. Extensive experiments demonstrate that RL-TST outperforms representative approaches by simultaneously using data manifold information in the test set and enhancing test power via finding the DRs with the training set.

Zhijian Zhou, Liuhua Peng, Xunye Tian et al.

The distribution closeness testing (DCT) assesses whether the distance between a distribution pair is at least $ε$-far. Existing DCT methods mainly measure discrepancies between a distribution pair defined on discrete one-dimensional spaces (e.g., using total variation), which limits their applications to complex data (e.g., images). To extend DCT to more types of data, a natural idea is to introduce maximum mean discrepancy (MMD), a powerful measurement of the distributional discrepancy between two complex distributions, into DCT scenarios. However, we find that MMD's value can be the same for many pairs of distributions that have different norms in the same reproducing kernel Hilbert space (RKHS), making MMD less informative when assessing the closeness levels for multiple distribution pairs. To mitigate the issue, we design a new measurement of distributional discrepancy, norm-adaptive MMD (NAMMD), which scales MMD's value using the RKHS norms of distributions. Based on the asymptotic distribution of NAMMD, we finally propose the NAMMD-based DCT to assess the closeness levels of a distribution pair. Theoretically, we prove that NAMMD-based DCT has higher test power compared to MMD-based DCT, with bounded type-I error, which is also validated by extensive experiments on many types of data (e.g., synthetic noise, real images). Furthermore, we also apply the proposed NAMMD for addressing the two-sample testing problem and find NAMMD-based two-sample test has higher test power than the MMD-based two-sample test in both theory and experiments.

Yuchen Luo, Xinyu Li, Liuhua Peng et al.

In multivariate time series forecasting (MTSF), accurately modeling the intricate dependencies among multiple variables remains a significant challenge due to the inherent limitations of traditional approaches. Most existing models adopt either \textbf{channel-independent} (CI) or \textbf{channel-dependent} (CD) strategies, each presenting distinct drawbacks. CI methods fail to leverage the potential insights from inter-channel interactions, resulting in models that may not fully exploit the underlying statistical dependencies present in the data. Conversely, CD approaches often incorporate too much extraneous information, risking model overfitting and predictive inefficiency. To address these issues, we introduce the Adaptive Forecasting Transformer (\textbf{Adapformer}), an advanced Transformer-based framework that merges the benefits of CI and CD methodologies through effective channel management. The core of Adapformer lies in its dual-stage encoder-decoder architecture, which includes the \textbf{A}daptive \textbf{C}hannel \textbf{E}nhancer (\textbf{ACE}) for enriching embedding processes and the \textbf{A}daptive \textbf{C}hannel \textbf{F}orecaster (\textbf{ACF}) for refining the predictions. ACE enhances token representations by selectively incorporating essential dependencies, while ACF streamlines the decoding process by focusing on the most relevant covariates, substantially reducing noise and redundancy. Our rigorous testing on diverse datasets shows that Adapformer achieves superior performance over existing models, enhancing both predictive accuracy and computational efficiency, thus making it state-of-the-art in MTSF.

Zhijian Zhou, Xunye Tian, Liuhua Peng et al.

To adapt kernel two-sample and independence testing to complex structured data, aggregation of multiple kernels is frequently employed to boost testing power compared to single-kernel tests. However, we observe a phenomenon that directly maximizing multiple kernel-based statistics may result in highly similar kernels that capture highly overlapping information, limiting the effectiveness of aggregation. To address this, we propose an aggregated statistic that explicitly incorporates kernel diversity based on the covariance between different kernels. Moreover, we identify a fundamental challenge: a trade-off between the diversity among kernels and the test power of individual kernels, i.e., the selected kernels should be both effective and diverse. This motivates a testing framework with selection inference, which leverages information from the training phase to select kernels with strong individual performance from the learned diverse kernel pool. We provide rigorous theoretical statements and proofs to show the consistency on the test power and control of Type-I error, along with asymptotic analysis of the proposed statistics. Lastly, we conducted extensive empirical experiments demonstrating the superior performance of our proposed approach across various benchmarks for both two-sample and independence testing.

Xiaojun Mao, Liuhua Peng, Zhonglei Wang

Random forests are a widely used machine learning algorithm, but their computational efficiency is undermined when applied to large-scale datasets with numerous instances and useless features. Herein, we propose a nonparametric feature selection algorithm that incorporates random forests and deep neural networks, and its theoretical properties are also investigated under regularity conditions. Using different synthetic models and a real-world example, we demonstrate the advantage of the proposed algorithm over other alternatives in terms of identifying useful features, avoiding useless ones, and the computation efficiency. Although the algorithm is proposed using standard random forests, it can be widely adapted to other machine learning algorithms, as long as features can be sorted accordingly.