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A completely randomized experiment allows us to estimate the causal effect by the difference in the averages of the outcome under the treatment and control. But, difference-in-means type estimators behave poorly if the potential outcomes have a heavy-tail, or contain a few extreme observations or outliers. We study an alternative estimator by Rosenbaum that estimates the causal effect by inverting a randomization test using ranks. We study the asymptotic properties of this estimator and develop a framework to compare the efficiencies of different estimators of the treatment effect in the setting of randomized experiments. In particular, we show that the Rosenbaum estimator has variance that is asymptotically, in the worst case, at most about 1.16 times the variance of the difference-in-means estimator, and can be much smaller when the potential outcomes are not light-tailed. We further derive a consistent estimator of the asymptotic standard error for the Rosenbaum estimator which immediately yields a readily computable confidence interval for the treatment effect, thereby alleviating the expensive numerical calculations needed to implement the original proposal of Rosenbaum. Further, we propose a regression adjusted version of the Rosenbaum estimator to incorporate additional covariate information in randomization inference. We prove gain in efficiency by this regression adjustment method under a linear regression model. Finally, we illustrate through simulations that, unlike the difference-in-means based estimators, either unadjusted or regression adjusted, these rank-based estimators are efficient and robust against heavy-tailed distributions, contamination, and various model misspecifications.

This paper addresses the problem of 3D human body shape and pose estimation from RGB images. Some recent approaches to this task predict probability distributions over human body model parameters conditioned on the input images. This is motivated by the ill-posed nature of the problem wherein multiple 3D reconstructions may match the image evidence, particularly when some parts of the body are locally occluded. However, body shape parameters in widely-used body models (e.g. SMPL) control global deformations over the whole body surface. Distributions over these global shape parameters are unable to meaningfully capture uncertainty in shape estimates associated with locally-occluded body parts. In contrast, we present a method that (i) predicts distributions over local body shape in the form of semantic body measurements and (ii) uses a linear mapping to transform a local distribution over body measurements to a global distribution over SMPL shape parameters. We show that our method outperforms the current state-of-the-art in terms of identity-dependent body shape estimation accuracy on the SSP-3D dataset, and a private dataset of tape-measured humans, by probabilistically-combining local body measurement distributions predicted from multiple images of a subject.

With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of spatially referenced data collected over time, motivated by environmental studies utilizing remotely sensed satellite data. In particular, we specify a semiparametric autoregressive model without the usual Gaussian assumption and devise a computationally scalable procedure that enables the regression analysis of large datasets. We estimate the model parameters by quasi maximum likelihood and show that the computational complexity can be reduced from cubic to linear of the sample size. Asymptotic properties under suitable regularity conditions are further established that inform the computational procedure to be efficient and scalable. A simulation study is conducted to evaluate the finite-sample properties of the parameter estimation and statistical inference. We illustrate our methodology by a dataset with over 2.96 million observations of annual land surface temperature and the comparison with an existing state-of-the-art approach highlights the advantages of our method.

We present an approach to learn dense, continuous 2D-3D correspondence distributions over the surface of objects from data with no prior knowledge of visual ambiguities like symmetry. We also present a new method for 6D pose estimation of rigid objects using the learnt distributions to sample, score and refine pose hypotheses. The correspondence distributions are learnt with a contrastive loss, represented in object-specific latent spaces by an encoder-decoder query model and a small fully connected key model. Our method is unsupervised with respect to visual ambiguities, yet we show that the query- and key models learn to represent accurate multi-modal surface distributions. Our pose estimation method improves the state-of-the-art significantly on the comprehensive BOP Challenge, trained purely on synthetic data, even compared with methods trained on real data. The project site is at //surfemb.github.io/ .

We study the problem of density estimation for a random vector ${\boldsymbol X}$ in $\mathbb R^d$ with probability density $f(\boldsymbol x)$. For a spanning tree $T$ defined on the vertex set $\{1,\dots ,d\}$, the tree density $f_{T}$ is a product of bivariate conditional densities. The optimal spanning tree $T^*$ is the spanning tree $T$, for which the Kullback-Leibler divergence of $f$ and $f_{T}$ is the smallest. From i.i.d. data we identify the optimal tree $T^*$ and computationally efficiently construct a tree density estimate $f_n$ such that, without any regularity conditions on the density $f$, one has that $\lim_{n\to \infty} \int |f_n(\boldsymbol x)-f_{T^*}(\boldsymbol x)|d\boldsymbol x=0$ a.s. For Lipschitz continuous $f$ with bounded support, $\mathbb E\{ \int |f_n(\boldsymbol x)-f_{T^*}(\boldsymbol x)|d\boldsymbol x\}=O(n^{-1/4})$.

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.

In this paper, we consider a boundary value problem (BVP) for a fourth order nonlinear functional integro-differential equation. We establish the existence and uniqueness of solution and construct a numerical method for solving it. We prove that the method is of second order accuracy and obtain an estimate for the total error. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the numerical method.

We introduce HuMoR: a 3D Human Motion Model for Robust Estimation of temporal pose and shape. Though substantial progress has been made in estimating 3D human motion and shape from dynamic observations, recovering plausible pose sequences in the presence of noise and occlusions remains a challenge. For this purpose, we propose an expressive generative model in the form of a conditional variational autoencoder, which learns a distribution of the change in pose at each step of a motion sequence. Furthermore, we introduce a flexible optimization-based approach that leverages HuMoR as a motion prior to robustly estimate plausible pose and shape from ambiguous observations. Through extensive evaluations, we demonstrate that our model generalizes to diverse motions and body shapes after training on a large motion capture dataset, and enables motion reconstruction from multiple input modalities including 3D keypoints and RGB(-D) videos.

Human pose estimation - the process of recognizing human keypoints in a given image - is one of the most important tasks in computer vision and has a wide range of applications including movement diagnostics, surveillance, or self-driving vehicle. The accuracy of human keypoint prediction is increasingly improved thanks to the burgeoning development of deep learning. Most existing methods solved human pose estimation by generating heatmaps in which the ith heatmap indicates the location confidence of the ith keypoint. In this paper, we introduce novel network structures referred to as multiresolution representation learning for human keypoint prediction. At different resolutions in the learning process, our networks branch off and use extra layers to learn heatmap generation. We firstly consider the architectures for generating the multiresolution heatmaps after obtaining the lowest-resolution feature maps. Our second approach allows learning during the process of feature extraction in which the heatmaps are generated at each resolution of the feature extractor. The first and second approaches are referred to as multi-resolution heatmap learning and multi-resolution feature map learning respectively. Our architectures are simple yet effective, achieving good performance. We conducted experiments on two common benchmarks for human pose estimation: MS-COCO and MPII dataset.

This study considers the 3D human pose estimation problem in a single RGB image by proposing a conditional random field (CRF) model over 2D poses, in which the 3D pose is obtained as a byproduct of the inference process. The unary term of the proposed CRF model is defined based on a powerful heat-map regression network, which has been proposed for 2D human pose estimation. This study also presents a regression network for lifting the 2D pose to 3D pose and proposes the prior term based on the consistency between the estimated 3D pose and the 2D pose. To obtain the approximate solution of the proposed CRF model, the N-best strategy is adopted. The proposed inference algorithm can be viewed as sequential processes of bottom-up generation of 2D and 3D pose proposals from the input 2D image based on deep networks and top-down verification of such proposals by checking their consistencies. To evaluate the proposed method, we use two large-scale datasets: Human3.6M and HumanEva. Experimental results show that the proposed method achieves the state-of-the-art 3D human pose estimation performance.