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Exact null distributions of goodness-of-fit test statistics are generally challenging to obtain in tractable forms. Practitioners are therefore usually obliged to rely on asymptotic null distributions or Monte Carlo methods, either in the form of a lookup table or carried out on demand, to apply a goodness-of-fit test. Stephens (1970) provided remarkable simple and useful transformations of several classic goodness-of-fit test statistics that stabilized their exact-$n$ critical values for varying sample sizes $n$. However, detail on the accuracy of these and subsequent transformations in yielding exact $p$-values, or even deep understanding on the derivation of several transformations, is still scarce nowadays. We illuminate and automatize, using modern tools, the latter stabilization approach to (i) expand its scope of applicability and (ii) yield semi-continuous exact $p$-values, as opposed to exact critical values for fixed significance levels. We show improvements on the stabilization accuracy of the exact null distributions of the Kolmogorov-Smirnov, Cram\'er-von Mises, Anderson-Darling, Kuiper, and Watson test statistics. In addition, we provide a parameter-dependent exact-$n$ stabilization for several novel statistics for testing uniformity on the hypersphere of arbitrary dimension. A data application in astronomy illustrates the benefits of the advocated stabilization for quickly analyzing small-to-moderate sequentially-measured samples.

Estimating the mask-wearing ratio in public places is important as it enables health authorities to promptly analyze and implement policies. Methods for estimating the mask-wearing ratio on the basis of image analysis have been reported. However, there is still a lack of comprehensive research on both methodologies and datasets. Most recent reports straightforwardly propose estimating the ratio by applying conventional object detection and classification methods. It is feasible to use regression-based approaches to estimate the number of people wearing masks, especially for congested scenes with tiny and occluded faces, but this has not been well studied. A large-scale and well-annotated dataset is still in demand. In this paper, we present two methods for ratio estimation that leverage either a detection-based or regression-based approach. For the detection-based approach, we improved the state-of-the-art face detector, RetinaFace, used to estimate the ratio. For the regression-based approach, we fine-tuned the baseline network, CSRNet, used to estimate the density maps for masked and unmasked faces. We also present the first large-scale dataset, the ``NFM dataset,'' which contains 581,108 face annotations extracted from 18,088 video frames in 17 street-view videos. Experiments demonstrated that the RetinaFace-based method has higher accuracy under various situations and that the CSRNet-based method has a shorter operation time thanks to its compactness.

We investigate several rank-based change-point procedures for the covariance operator in a sequence of observed functions, called FKWC change-point procedures. Our methods allow the user to test for one change-point, to test for an epidemic period, or to detect an unknown amount of change-points in the data. Our methodology combines functional data depth values with the traditional Kruskal Wallis test statistic. By taking this approach we have no need to estimate the covariance operator, which makes our methods computationally cheap. For example, our procedure can identify multiple change-points in $O(n\log n)$ time. Our procedure is fully non-parametric and is robust to outliers through the use of data depth ranks. We show that when $n$ is large, our methods have simple behaviour under the null hypothesis.We also show that the FKWC change-point procedures are $n^{-1/2}$-consistent. In addition to asymptotic results, we provide a finite sample accuracy result for our at-most-one change-point estimator. In simulation, we compare our methods against several others. We also present an application of our methods to intraday asset returns and f-MRI scans.

A matrix formalism for the determination of the best estimator in certain simulation-based parameter estimation problems will be presented and discussed. The equations, termed as the Linear Template Fit, combine a linear regression with a least square method and its optimization. The Linear Template Fit employs only predictions that are calculated beforehand and which are provided for a few values of the parameter of interest. Therefore, the Linear Template Fit is particularly suited for parameter estimation with computationally intensive simulations that are otherwise often limited in their usability for statistical inference, or for performance critical applications. Equations for error propagation are discussed, and the analytic form provides comprehensive insights into the parameter estimation problem. Furthermore, the quickly-converging algorithm of the Quadratic Template Fit will be presented, which is suitable for a non-linear dependence on the parameters. As an example application, a determination of the strong coupling constant, $\alpha_s(m_Z)$, from inclusive jet cross section data at the CERN Large Hadron Collider is studied and compared with previously published results.

One of the central problems in machine learning is domain adaptation. Unlike past theoretical work, we consider a new model for subpopulation shift in the input or representation space. In this work, we propose a provably effective framework for domain adaptation based on label propagation. In our analysis, we use a simple but realistic ``expansion'' assumption, proposed in \citet{wei2021theoretical}. Using a teacher classifier trained on the source domain, our algorithm not only propagates to the target domain but also improves upon the teacher. By leveraging existing generalization bounds, we also obtain end-to-end finite-sample guarantees on the entire algorithm. In addition, we extend our theoretical framework to a more general setting of source-to-target transfer based on a third unlabeled dataset, which can be easily applied in various learning scenarios.

Modern neural network training relies heavily on data augmentation for improved generalization. After the initial success of label-preserving augmentations, there has been a recent surge of interest in label-perturbing approaches, which combine features and labels across training samples to smooth the learned decision surface. In this paper, we propose a new augmentation method that leverages the first and second moments extracted and re-injected by feature normalization. We replace the moments of the learned features of one training image by those of another, and also interpolate the target labels. As our approach is fast, operates entirely in feature space, and mixes different signals than prior methods, one can effectively combine it with existing augmentation methods. We demonstrate its efficacy across benchmark data sets in computer vision, speech, and natural language processing, where it consistently improves the generalization performance of highly competitive baseline networks.

The main contribution of this paper is a new submap joining based approach for solving large-scale Simultaneous Localization and Mapping (SLAM) problems. Each local submap is independently built using the local information through solving a small-scale SLAM; the joining of submaps mainly involves solving linear least squares and performing nonlinear coordinate transformations. Through approximating the local submap information as the state estimate and its corresponding information matrix, judiciously selecting the submap coordinate frames, and approximating the joining of a large number of submaps by joining only two maps at a time, either sequentially or in a more efficient Divide and Conquer manner, the nonlinear optimization process involved in most of the existing submap joining approaches is avoided. Thus the proposed submap joining algorithm does not require initial guess or iterations since linear least squares problems have closed-form solutions. The proposed Linear SLAM technique is applicable to feature-based SLAM, pose graph SLAM and D-SLAM, in both two and three dimensions, and does not require any assumption on the character of the covariance matrices. Simulations and experiments are performed to evaluate the proposed Linear SLAM algorithm. Results using publicly available datasets in 2D and 3D show that Linear SLAM produces results that are very close to the best solutions that can be obtained using full nonlinear optimization algorithm started from an accurate initial guess. The C/C++ and MATLAB source codes of Linear SLAM are available on OpenSLAM.

Tumor detection in biomedical imaging is a time-consuming process for medical professionals and is not without errors. Thus in recent decades, researchers have developed algorithmic techniques for image processing using a wide variety of mathematical methods, such as statistical modeling, variational techniques, and machine learning. In this paper, we propose a semi-automatic method for liver segmentation of 2D CT scans into three labels denoting healthy, vessel, or tumor tissue based on graph cuts. First, we create a feature vector for each pixel in a novel way that consists of the 59 intensity values in the time series data and propose a simplified perimeter cost term in the energy functional. We normalize the data and perimeter terms in the functional to expedite the graph cut without having to optimize the scaling parameter $\lambda$. In place of a training process, predetermined tissue means are computed based on sample regions identified by expert radiologists. The proposed method also has the advantage of being relatively simple to implement computationally. It was evaluated against the ground truth on a clinical CT dataset of 10 tumors and yielded segmentations with a mean Dice similarity coefficient (DSC) of .77 and mean volume overlap error (VOE) of 36.7%. The average processing time was 1.25 minutes per slice.

Data augmentation has been widely used for training deep learning systems for medical image segmentation and plays an important role in obtaining robust and transformation-invariant predictions. However, it has seldom been used at test time for segmentation and not been formulated in a consistent mathematical framework. In this paper, we first propose a theoretical formulation of test-time augmentation for deep learning in image recognition, where the prediction is obtained through estimating its expectation by Monte Carlo simulation with prior distributions of parameters in an image acquisition model that involves image transformations and noise. We then propose a novel uncertainty estimation method based on the formulated test-time augmentation. Experiments with segmentation of fetal brains and brain tumors from 2D and 3D Magnetic Resonance Images (MRI) showed that 1) our test-time augmentation outperforms a single-prediction baseline and dropout-based multiple predictions, and 2) it provides a better uncertainty estimation than calculating the model-based uncertainty alone and helps to reduce overconfident incorrect predictions.

The Normalized Cut (NCut) objective function, widely used in data clustering and image segmentation, quantifies the cost of graph partitioning in a way that biases clusters or segments that are balanced towards having lower values than unbalanced partitionings. However, this bias is so strong that it avoids any singleton partitions, even when vertices are very weakly connected to the rest of the graph. Motivated by the B\"uhler-Hein family of balanced cut costs, we propose the family of Compassionately Conservative Balanced (CCB) Cut costs, which are indexed by a parameter that can be used to strike a compromise between the desire to avoid too many singleton partitions and the notion that all partitions should be balanced. We show that CCB-Cut minimization can be relaxed into an orthogonally constrained $\ell_{\tau}$-minimization problem that coincides with the problem of computing Piecewise Flat Embeddings (PFE) for one particular index value, and we present an algorithm for solving the relaxed problem by iteratively minimizing a sequence of reweighted Rayleigh quotients (IRRQ). Using images from the BSDS500 database, we show that image segmentation based on CCB-Cut minimization provides better accuracy with respect to ground truth and greater variability in region size than NCut-based image segmentation.