Bin Nan

Ran Zou, Wanrong Zhu, Bin Nan

Conformal prediction provides distribution-free predictive intervals with finite-sample marginal coverage. However, achieving conditional validity and interval efficiency (in terms of short interval length) remains challenging, particularly in complex settings with heteroskedasticity, skewed responses, or estimation errors. We propose a conformal-style calibration method for responses obtained by the probability integral transform (PIT) of the conditional cumulative distribution function (CDF) estimated via neural networks to construct a finite-sample-adjusted percentile interval with the shortest length determined by the estimated conditional CDF. Calibrating in PIT space is effective because PIT values are asymptotically feature-independent when the CDF estimator is accurate, which mitigates feature-dependent miscoverage and improves conditional calibration. On the other hand, our percentile calibration adapts to the empirical PIT distribution, which is robust against a possibly imperfect estimation of the conditional CDF. We prove the finite-sample marginal coverage property of the proposed method and show its asymptotic conditional coverage under mild consistency conditions. Experiments on diverse synthetic and real-world benchmarks demonstrate better conditional calibration and substantially shorter intervals than existing methods.

Shaojie Zhang, Yinghui Wang, Bin Nan et al.

To address the issue of increased triangulation uncertainty caused by selecting views with small camera baselines in Structure from Motion (SFM) view selection, this paper proposes a robust error-resistant view selection method. The method utilizes a triangulation-based computation to obtain an error-resistant model, which is then used to construct an error-resistant matrix. The sorting results of each row in the error-resistant matrix determine the candidate view set for each view. By traversing the candidate view sets of all views and completing the missing views based on the error-resistant matrix, the integrity of 3D reconstruction is ensured. Experimental comparisons between this method and the exhaustive method with the highest accuracy in the COLMAP program are conducted in terms of average reprojection error and absolute trajectory error in the reconstruction results. The proposed method demonstrates an average reduction of 29.40% in reprojection error accuracy and 5.07% in absolute trajectory error on the TUM dataset and DTU dataset.

Shaojie Zhang, Yinghui Wang, Bin Nan et al.

To address the issue of feature descriptors being ineffective in representing grayscale feature information when images undergo high affine transformations, leading to a rapid decline in feature matching accuracy, this paper proposes a region feature descriptor based on simulating affine transformations using classification. The proposed method initially categorizes images with different affine degrees to simulate affine transformations and generate a new set of images. Subsequently, it calculates neighborhood information for feature points on this new image set. Finally, the descriptor is generated by combining the grayscale histogram of the maximum stable extremal region to which the feature point belongs and the normalized position relative to the grayscale centroid of the feature point's region. Experimental results, comparing feature matching metrics under affine transformation scenarios, demonstrate that the proposed descriptor exhibits higher precision and robustness compared to existing classical descriptors. Additionally, it shows robustness when integrated with other descriptors.

Hai Shu, Bin Nan

We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with longer memory than those considered in the current literature. We show that several commonly used methods for independent observations can be applied to the temporally dependent data. In particular, the rates of convergence are obtained for the generalized thresholding estimation of covariance and correlation matrices, and for the constrained $\ell_1$ minimization and the $\ell_1$ penalized likelihood estimation of precision matrix. Properties of sparsistency and sign-consistency are also established. A gap-block cross-validation method is proposed for the tuning parameter selection, which performs well in simulations. As a motivating example, we study the brain functional connectivity using resting-state fMRI time series data with long-range temporal dependence.

Hai Shu, Bin Nan, Robert Koeppe

Traditional voxel-level multiple testing procedures in neuroimaging, mostly $p$-value based, often ignore the spatial correlations among neighboring voxels and thus suffer from substantial loss of power. We extend the local-significance-index based procedure originally developed for the hidden Markov chain models, which aims to minimize the false nondiscovery rate subject to a constraint on the false discovery rate, to three-dimensional neuroimaging data using a hidden Markov random field model. A generalized expectation-maximization algorithm for maximizing the penalized likelihood is proposed for estimating the model parameters. Extensive simulations show that the proposed approach is more powerful than conventional false discovery rate procedures. We apply the method to the comparison between mild cognitive impairment, a disease status with increased risk of developing Alzheimer's or another dementia, and normal controls in the FDG-PET imaging study of the Alzheimer's Disease Neuroimaging Initiative.

Shengchun Kong, Bin Nan

We consider the finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz. We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulty caused by the lack of iid and Lipschitz property.