Missing data may be disastrous for the identifiability of causal and statistical estimands. In graphical missing data models, colluders are dependence structures that have a special importance for identification considerations. It has been shown that the presence of a colluder makes the full law, i.e., the joint distribution of variables and response indicators, non-parametrically non-identifiable. However, with additional mild assumptions regarding the variables involved with the colluder structure, identifiability is regained. We present a necessary and sufficient condition for the identification of the full law in the presence of a colluder structure with arbitrary categorical variables.
相關內容
In compact settings, the convergence rate of the empirical optimal transport cost to its population value is well understood for a wide class of spaces and cost functions. In unbounded settings, however, hitherto available results require strong assumptions on the ground costs and the concentration of the involved measures. In this work, we pursue a decomposition-based approach to generalize the convergence rates found in compact spaces to unbounded settings under generic moment assumptions that are sharp up to an arbitrarily small $\epsilon > 0$. Hallmark properties of empirical optimal transport on compact spaces, like the recently established adaptation to lower complexity, are shown to carry over to the unbounded case.
With the rapidly increasing demand for oriented object detection (OOD), recent research involving weakly-supervised detectors for learning rotated box (RBox) from the horizontal box (HBox) has attracted more and more attention. In this paper, we explore a more challenging yet label-efficient setting, namely single point-supervised OOD, and present our approach called Point2RBox. Specifically, we propose to leverage two principles: 1) Synthetic pattern knowledge combination: By sampling around each labeled point on the image, we spread the object feature to synthetic visual patterns with known boxes to provide the knowledge for box regression. 2) Transform self-supervision: With a transformed input image (e.g. scaled/rotated), the output RBoxes are trained to follow the same transformation so that the network can perceive the relative size/rotation between objects. The detector is further enhanced by a few devised techniques to cope with peripheral issues, e.g. the anchor/layer assignment as the size of the object is not available in our point supervision setting. To our best knowledge, Point2RBox is the first end-to-end solution for point-supervised OOD. In particular, our method uses a lightweight paradigm, yet it achieves a competitive performance among point-supervised alternatives, 41.05%/27.62%/80.01% on DOTA/DIOR/HRSC datasets.
In addressing the challenge of analysing the large-scale Adolescent Brain Cognition Development (ABCD) fMRI dataset, involving over 5,000 subjects and extensive neuroimaging data, we propose a scalable Bayesian scalar-on-image regression model for computational feasibility and efficiency. Our model employs a relaxed-thresholded Gaussian process (RTGP), integrating piecewise-smooth, sparse, and continuous functions capable of both hard- and soft-thresholding. This approach introduces additional flexibility in feature selection in scalar-on-image regression and leads to scalable posterior computation by adopting a variational approximation and utilising the Karhunen-Lo\`eve expansion for Gaussian processes. This advancement substantially reduces the computational costs in vertex-wise analysis of cortical surface data in large-scale Bayesian spatial models. The model's parameter estimation and prediction accuracy and feature selection performance are validated through extensive simulation studies and an application to the ABCD study. Here, we perform regression analysis correlating intelligence scores with task-based functional MRI data, taking into account confounding factors including age, sex, and parental education level. This validation highlights our model's capability to handle large-scale neuroimaging data while maintaining computational feasibility and accuracy.
Additive spatial statistical models with weakly stationary process assumptions have become standard in spatial statistics. However, one disadvantage of such models is the computation time, which rapidly increases with the number of data points. The goal of this article is to apply an existing subsampling strategy to standard spatial additive models and to derive the spatial statistical properties. We call this strategy the ''spatial data subset model'' (SDSM) approach, which can be applied to big datasets in a computationally feasible way. Our approach has the advantage that one does not require any additional restrictive model assumptions. That is, computational gains increase as model assumptions are removed when using our model framework. This provides one solution to the computational bottlenecks that occur when applying methods such as Kriging to ''big data''. We provide several properties of this new spatial data subset model approach in terms of moments, sill, nugget, and range under several sampling designs. An advantage of our approach is that it subsamples without throwing away data, and can be implemented using datasets of any size that can be stored. We present the results of the spatial data subset model approach on simulated datasets, and on a large dataset consists of 150,000 observations of daytime land surface temperatures measured by the MODIS instrument onboard the Terra satellite.
Compositional data find broad application across diverse fields due to their efficacy in representing proportions or percentages of various components within a whole. Spatial dependencies often exist in compositional data, particularly when the data represents different land uses or ecological variables. Ignoring the spatial autocorrelations in modelling of compositional data may lead to incorrect estimates of parameters. Hence, it is essential to incorporate spatial information into the statistical analysis of compositional data to obtain accurate and reliable results. However, traditional statistical methods are not directly applicable to compositional data due to the correlation between its observations, which are constrained to lie on a simplex. To address this challenge, the Dirichlet distribution is commonly employed, as its support aligns with the nature of compositional vectors. Specifically, the R package DirichletReg provides a regression model, termed Dirichlet regression, tailored for compositional data. However, this model fails to account for spatial dependencies, thereby restricting its utility in spatial contexts. In this study, we introduce a novel spatial autoregressive Dirichlet regression model for compositional data, adeptly integrating spatial dependencies among observations. We construct a maximum likelihood estimator for a Dirichlet density function augmented with a spatial lag term. We compare this spatial autoregressive model with the same model without spatial lag, where we test both models on synthetic data as well as two real datasets, using different metrics. By considering the spatial relationships among observations, our model provides more accurate and reliable results for the analysis of compositional data. The model is further evaluated against a spatial multinomial regression model for compositional data, and their relative effectiveness is discussed.
Fatigue data arise in many research and applied areas and there have been statistical methods developed to model and analyze such data. The distributions of fatigue life and fatigue strength are often of interest to engineers designing products that might fail due to fatigue from cyclic-stress loading. Based on a specified statistical model and the maximum likelihood method, the cumulative distribution function (cdf) and quantile function (qf) can be estimated for the fatigue-life and fatigue-strength distributions. Likelihood-based confidence bands then can be obtained for the cdf and qf. This paper provides equivalence results for confidence bands for fatigue-life and fatigue-strength models. These results are useful for data analysis and computing implementation. We show (a) the equivalence of the confidence bands for the fatigue-life cdf and the fatigue-life qf, (b) the equivalence of confidence bands for the fatigue-strength cdf and the fatigue-strength qf, and (c) the equivalence of confidence bands for the fatigue-life qf and the fatigue-strength qf. Then we illustrate the usefulness of those equivalence results with two examples using experimental fatigue data.
To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve training efficiency and to enable control of the approximation error, the network mimics an adaptive finite element method (AFEM). It outputs a coarse grid solution and a series of corrections as produced in an AFEM, allowing a tracking of the error decay over successive layers of the network. The observed errors are measured by a reliable residual based a posteriori error estimator, enabling the reduction to only few parameters for the approximation in the output of the network. This leads to a problem adapted representation of the solution on locally refined grids. Furthermore, each solution of the AFEM is discretized in a hierarchical basis. For the architecture, convolutional neural networks (CNNs) are chosen. The hierarchical basis then allows to handle sparse images for finely discretized meshes. Additionally, as corrections on finer levels decrease in amplitude, i.e., importance for the overall approximation, the accuracy of the network approximation is allowed to decrease successively. This can either be incorporated in the number of generated high fidelity samples used for training or the size of the network components responsible for the fine grid outputs. The architecture is described and preliminary numerical examples are presented.
Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the samples these models generate? This work aims to provide an accessible entry point to understanding popular notions of statistical distances, requiring only foundational knowledge in mathematics and statistics. We focus on four commonly used notions of statistical distances representing different methodologies: Using low-dimensional projections (Sliced-Wasserstein; SW), obtaining a distance using classifiers (Classifier Two-Sample Tests; C2ST), using embeddings through kernels (Maximum Mean Discrepancy; MMD), or neural networks (Fr\'echet Inception Distance; FID). We highlight the intuition behind each distance and explain their merits, scalability, complexity, and pitfalls. To demonstrate how these distances are used in practice, we evaluate generative models from different scientific domains, namely a model of decision making and a model generating medical images. We showcase that distinct distances can give different results on similar data. Through this guide, we aim to help researchers to use, interpret, and evaluate statistical distances for generative models in science.
We prove that training neural networks on 1-D data is equivalent to solving a convex Lasso problem with a fixed, explicitly defined dictionary matrix of features. The specific dictionary depends on the activation and depth. We consider 2-layer networks with piecewise linear activations, deep narrow ReLU networks with up to 4 layers, and rectangular and tree networks with sign activation and arbitrary depth. Interestingly in ReLU networks, a fourth layer creates features that represent reflections of training data about themselves. The Lasso representation sheds insight to globally optimal networks and the solution landscape.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191