Data depth has emerged as an invaluable nonparametric measure for the ranking of multivariate samples. The main contribution of depth-based two-sample comparisons is the introduction of the Q statistic (Liu and Singh, 1993), a quality index. Unlike traditional methods, data depth does not require the assumption of normal distributions and adheres to four fundamental properties. Many existing two-sample homogeneity tests, which assess mean and/or scale changes in distributions often suffer from low statistical power or indeterminate asymptotic distributions. To overcome these challenges, we introduced a DEEPEAST (depth-explored same-attraction sample-to-sample central-outward ranking) technique for improving statistical power in two-sample tests via the same-attraction function. We proposed two novel and powerful depth-based test statistics: the sum test statistic and the product test statistic, which are rooted in Q statistics, share a "common attractor" and are applicable across all depth functions. We further proved the asymptotic distribution of these statistics for various depth functions. To assess the performance of power gain, we apply three depth functions: Mahalanobis depth (Liu and Singh, 1993), Spatial depth (Brown, 1958; Gower, 1974), and Projection depth (Liu, 1992). Through two-sample simulations, we have demonstrated that our sum and product statistics exhibit superior power performance, utilizing a strategic block permutation algorithm and compare favourably with popular methods in literature. Our tests are further validated through analysis on Raman spectral data, acquired from cellular and tissue samples, highlighting the effectiveness of the proposed tests highlighting the effective discrimination between health and cancerous samples.
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Despite that the segment anything model (SAM) achieved impressive results on general-purpose semantic segmentation with strong generalization ability on daily images, its demonstrated performance on medical image segmentation is less precise and not stable, especially when dealing with tumor segmentation tasks that involve objects of small sizes, irregular shapes, and low contrast. Notably, the original SAM architecture is designed for 2D natural images, therefore would not be able to extract the 3D spatial information from volumetric medical data effectively. In this paper, we propose a novel adaptation method for transferring SAM from 2D to 3D for promptable medical image segmentation. Through a holistically designed scheme for architecture modification, we transfer the SAM to support volumetric inputs while retaining the majority of its pre-trained parameters for reuse. The fine-tuning process is conducted in a parameter-efficient manner, wherein most of the pre-trained parameters remain frozen, and only a few lightweight spatial adapters are introduced and tuned. Regardless of the domain gap between natural and medical data and the disparity in the spatial arrangement between 2D and 3D, the transformer trained on natural images can effectively capture the spatial patterns present in volumetric medical images with only lightweight adaptations. We conduct experiments on four open-source tumor segmentation datasets, and with a single click prompt, our model can outperform domain state-of-the-art medical image segmentation models on 3 out of 4 tasks, specifically by 8.25%, 29.87%, and 10.11% for kidney tumor, pancreas tumor, colon cancer segmentation, and achieve similar performance for liver tumor segmentation. We also compare our adaptation method with existing popular adapters, and observed significant performance improvement on most datasets.
The various limitations of Generative AI, such as hallucinations and model failures, have made it crucial to understand the role of different modalities in Visual Language Model (VLM) predictions. Our work investigates how the integration of information from image and text modalities influences the performance and behavior of VLMs in visual question answering (VQA) and reasoning tasks. We measure this effect through answer accuracy, reasoning quality, model uncertainty, and modality relevance. We study the interplay between text and image modalities in different configurations where visual content is essential for solving the VQA task. Our contributions include (1) the Semantic Interventions (SI)-VQA dataset, (2) a benchmark study of various VLM architectures under different modality configurations, and (3) the Interactive Semantic Interventions (ISI) tool. The SI-VQA dataset serves as the foundation for the benchmark, while the ISI tool provides an interface to test and apply semantic interventions in image and text inputs, enabling more fine-grained analysis. Our results show that complementary information between modalities improves answer and reasoning quality, while contradictory information harms model performance and confidence. Image text annotations have minimal impact on accuracy and uncertainty, slightly increasing image relevance. Attention analysis confirms the dominant role of image inputs over text in VQA tasks. In this study, we evaluate state-of-the-art VLMs that allow us to extract attention coefficients for each modality. A key finding is PaliGemma's harmful overconfidence, which poses a higher risk of silent failures compared to the LLaVA models. This work sets the foundation for rigorous analysis of modality integration, supported by datasets specifically designed for this purpose.
We propose a fast scheme for approximating the Mittag-Leffler function by an efficient sum-of-exponentials (SOE), and apply the scheme to the viscoelastic model of wave propagation with mixed finite element methods for the spatial discretization and the Newmark-beta scheme for the second-order temporal derivative. Compared with traditional L1 scheme for fractional derivative, our fast scheme reduces the memory complexity from $\mathcal O(N_sN) $ to $\mathcal O(N_sN_{exp})$ and the computation complexity from $\mathcal O(N_sN^2)$ to $\mathcal O(N_sN_{exp}N)$, where $N$ denotes the total number of temporal grid points, $N_{exp}$ is the number of exponentials in SOE, and $N_s$ represents the complexity of memory and computation related to the spatial discretization. Numerical experiments are provided to verify the theoretical results.
In the analysis of spatially resolved transcriptomics data, detecting spatially variable genes (SVGs) is crucial. Numerous computational methods exist, but varying SVG definitions and methodologies lead to incomparable results. We review \rv{33} state-of-the-art methods, categorizing SVGs into three types: overall, cell-type-specific, and spatial-domain-marker SVGs. Our review explains the intuitions underlying these methods, summarizes their applications, and categorizes the hypothesis tests they use in the trade-off between generality and specificity for SVG detection. We discuss challenges in SVG detection and propose future directions for improvement. Our review offers insights for method developers and users, advocating for category-specific benchmarking.
Randomized matrix algorithms have become workhorse tools in scientific computing and machine learning. To use these algorithms safely in applications, they should be coupled with posterior error estimates to assess the quality of the output. To meet this need, this paper proposes two diagnostics: a leave-one-out error estimator for randomized low-rank approximations and a jackknife resampling method to estimate the variance of the output of a randomized matrix computation. Both of these diagnostics are rapid to compute for randomized low-rank approximation algorithms such as the randomized SVD and randomized Nystr\"om approximation, and they provide useful information that can be used to assess the quality of the computed output and guide algorithmic parameter choices.
We discuss the second-order differential uniformity of vectorial Boolean functions. The closely related notion of second-order zero differential uniformity has recently been studied in connection to resistance to the boomerang attack. We prove that monomial functions with univariate form $x^d$ where $d=2^{2k}+2^k+1$ and $\gcd(k,n)=1$ have optimal second-order differential uniformity. Computational results suggest that, up to affine equivalence, these might be the only optimal cubic power functions. We begin work towards generalising such conditions to all monomial functions of algebraic degree 3. We also discuss further questions arising from computational results.
Finding vertex-to-vertex correspondences in real-world graphs is a challenging task with applications in a wide variety of domains. Structural matching based on graphs connectivities has attracted considerable attention, while the integration of all the other information stemming from vertices and edges attributes has been mostly left aside. Here we present the Graph Attributes and Structure Matching (GASM) algorithm, which provides high-quality solutions by integrating all the available information in a unified framework. Parameters quantifying the reliability of the attributes can tune how much the solutions should rely on the structure or on the attributes. We further show that even without attributes GASM consistently finds as-good-as or better solutions than state-of-the-art algorithms, with similar processing times.
Treatment effect estimation under unconfoundedness is a fundamental task in causal inference. In response to the challenge of analyzing high-dimensional datasets collected in substantive fields such as epidemiology, genetics, economics, and social sciences, various methods for treatment effect estimation with high-dimensional nuisance parameters (the outcome regression and the propensity score) have been developed in recent years. However, it is still unclear what is the necessary and sufficient sparsity condition on the nuisance parameters such that we can estimate the treatment effect at $1 / \sqrt{n}$-rate. In this paper, we propose a new Double-Calibration strategy that corrects the estimation bias of the nuisance parameter estimates computed by regularized high-dimensional techniques and demonstrate that the corresponding Doubly-Calibrated estimator achieves $1 / \sqrt{n}$-rate as long as one of the nuisance parameters is sparse with sparsity below $\sqrt{n} / \log p$, where $p$ denotes the ambient dimension of the covariates, whereas the other nuisance parameter can be arbitrarily complex and completely misspecified. The Double-Calibration strategy can also be applied to settings other than treatment effect estimation, e.g. regression coefficient estimation in the presence of a diverging number of controls in a semiparametric partially linear model, and local average treatment effect estimation with instrumental variables.
To avoid ineffective collisions between the equilibrium states, the hybrid method with deviational particles (HDP) has been proposed to integrate the Fokker-Planck-Landau system, while leaving a new issue in sampling deviational particles from the high-dimensional source term. In this paper, we present an adaptive sampling (AS) strategy that first adaptively reconstructs a piecewise constant approximation of the source term based on sequential clustering via discrepancy estimation, and then samples deviational particles directly from the resulting adaptive piecewise constant function without rejection. The mixture discrepancy, which can be easily calculated thanks to its explicit analytical expression, is employed as a measure of uniformity instead of the star discrepancy the calculation of which is NP-hard. The resulting method, dubbed the HDP-AS method, runs approximately ten times faster than the HDP method while keeping the same accuracy in the Landau damping, two stream instability, bump on tail and Rosenbluth's test problem.
The preservation of stochastic orders by distortion functions has become a topic of increasing interest in the reliability analysis of coherent systems. The reason of this interest is that the reliability function of a coherent system with identically distributed components can be represented as a distortion function of the common reliability function of the components. In this framework, we study the preservation of the excess wealth order, the total time on test transform order, the decreasing mean residual live order, and the quantile mean inactivity time order by distortion functions. The results are applied to study the preservation of these stochastic orders under the formation of coherent systems with exchangeable components.
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