In literature, scientists describe human mobility in a range of granularities by several different models. Using frameworks like MATSIM, VehiLux, or Sumo, they often derive individual human movement indicators in their most detail. However, such agent-based models tend to be difficult and require much information and computational power to correctly predict the commutation behavior of large mobility systems. Mobility information can be costly and researchers often cannot acquire it dynamically over large areas, which leads to a lack of adequate calibration parameters, rendering the easy and spontaneous prediction of mobility in additional areas impossible. This paper targets this problem and represents a concept that combines multiple substantial mobility theorems formulated in recent years to reduce the amount of required information compared to existing simulations. Our concept also targets computational expenses and aims to reduce them to enable a global prediction of mobility. Inspired by methods from other domains, the core idea of the conceptional innovation can be compared to weather models, which predict weather on a large scale, on an adequate level of regional information (airspeed, air pressure, etc.), but without the detailed movement information of each air atom and its particular simulation.
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This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics ingredients based on the Koopman operator theory. In the offline step of the proposed framework, DMD constructs a low-rank linear surrogate model for the high dimensional quantities of interest (QoIs) derived from the (nonlinear) complex high fidelity models (HFMs) of unknown forms. Then in the online step, the resulting local reduced order bases (ROBs) and parametric reduced order models (PROMs) at the training parameter sample points are interpolated to construct a new PROM with the corresponding ROB for a new set of target/test parameter values. The interpolations need to be done on the appropriate manifolds within consistent sets of generalized coordinates. The proposed framework is illustrated by numerical examples for both linear and nonlinear problems. In particular, its advantages in computational costs and accuracy are demonstrated by the comparisons with projection-based proper orthogonal decomposition (POD)-PROM and Kriging.
Appearance-based gaze estimation aims to predict the 3D eye gaze direction from a single image. While recent deep learning-based approaches have demonstrated excellent performance, they usually assume one calibrated face in each input image and cannot output multi-person gaze in real time. However, simultaneous gaze estimation for multiple people in the wild is necessary for real-world applications. In this paper, we propose the first one-stage end-to-end gaze estimation method, GazeOnce, which is capable of simultaneously predicting gaze directions for multiple faces (>10) in an image. In addition, we design a sophisticated data generation pipeline and propose a new dataset, MPSGaze, which contains full images of multiple people with 3D gaze ground truth. Experimental results demonstrate that our unified framework not only offers a faster speed, but also provides a lower gaze estimation error compared with state-of-the-art methods. This technique can be useful in real-time applications with multiple users.
Recent advances in deep learning and computer vision offer an excellent opportunity to investigate high-level visual analysis tasks such as human localization and human pose estimation. Although the performance of human localization and human pose estimation has significantly improved in recent reports, they are not perfect and erroneous localization and pose estimation can be expected among video frames. Studies on the integration of these techniques into a generic pipeline that is robust to noise introduced from those errors are still lacking. This paper fills the missing study. We explored and developed two working pipelines that suited the visual-based positioning and pose estimation tasks. Analyses of the proposed pipelines were conducted on a badminton game. We showed that the concept of tracking by detection could work well, and errors in position and pose could be effectively handled by a linear interpolation technique using information from nearby frames. The results showed that the Visual-based Positioning and Pose Estimation could deliver position and pose estimations with good spatial and temporal resolutions.
Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class of distribution-free regularized covariance estimation methods for high-dimensional matrix data under a separability condition and a bandable covariance structure. Under these conditions, the original covariance matrix is decomposed into a Kronecker product of two bandable small covariance matrices representing the variability over row and column directions. We formulate a unified framework for estimating bandable covariance, and introduce an efficient algorithm based on rank one unconstrained Kronecker product approximation. The convergence rates of the proposed estimators are established, and the derived minimax lower bound shows our proposed estimator is rate-optimal under certain divergence regimes of matrix size. We further introduce a class of robust covariance estimators and provide theoretical guarantees to deal with heavy-tailed data. We demonstrate the superior finite-sample performance of our methods using simulations and real applications from a gridded temperature anomalies dataset and a S&P 500 stock data analysis.
Many recent state-of-the-art (SOTA) optical flow models use finite-step recurrent update operations to emulate traditional algorithms by encouraging iterative refinements toward a stable flow estimation. However, these RNNs impose large computation and memory overheads, and are not directly trained to model such stable estimation. They can converge poorly and thereby suffer from performance degradation. To combat these drawbacks, we propose deep equilibrium (DEQ) flow estimators, an approach that directly solves for the flow as the infinite-level fixed point of an implicit layer (using any black-box solver), and differentiates through this fixed point analytically (thus requiring $O(1)$ training memory). This implicit-depth approach is not predicated on any specific model, and thus can be applied to a wide range of SOTA flow estimation model designs. The use of these DEQ flow estimators allows us to compute the flow faster using, e.g., fixed-point reuse and inexact gradients, consumes $4\sim6\times$ times less training memory than the recurrent counterpart, and achieves better results with the same computation budget. In addition, we propose a novel, sparse fixed-point correction scheme to stabilize our DEQ flow estimators, which addresses a longstanding challenge for DEQ models in general. We test our approach in various realistic settings and show that it improves SOTA methods on Sintel and KITTI datasets with substantially better computational and memory efficiency.
We propose in this paper a data driven state estimation scheme for generating nonlinear reduced models for parametric families of PDEs, directly providing data-to-state maps, represented in terms of Deep Neural Networks. A major constituent is a sensor-induced decomposition of a model-compliant Hilbert space warranting approximation in problem relevant metrics. It plays a similar role as in a Parametric Background Data Weak framework for state estimators based on Reduced Basis concepts. Extensive numerical tests shed light on several optimization strategies that are to improve robustness and performance of such estimators.
One of the most important problems in system identification and statistics is how to estimate the unknown parameters of a given model. Optimization methods and specialized procedures, such as Empirical Minimization (EM) can be used in case the likelihood function can be computed. For situations where one can only simulate from a parametric model, but the likelihood is difficult or impossible to evaluate, a technique known as the Two-Stage (TS) Approach can be applied to obtain reliable parametric estimates. Unfortunately, there is currently a lack of theoretical justification for TS. In this paper, we propose a statistical decision-theoretical derivation of TS, which leads to Bayesian and Minimax estimators. We also show how to apply the TS approach on models for independent and identically distributed samples, by computing quantiles of the data as a first step, and using a linear function as the second stage. The proposed method is illustrated via numerical simulations.
Imposing consistency through proxy tasks has been shown to enhance data-driven learning and enable self-supervision in various tasks. This paper introduces novel and effective consistency strategies for optical flow estimation, a problem where labels from real-world data are very challenging to derive. More specifically, we propose occlusion consistency and zero forcing in the forms of self-supervised learning and transformation consistency in the form of semi-supervised learning. We apply these consistency techniques in a way that the network model learns to describe pixel-level motions better while requiring no additional annotations. We demonstrate that our consistency strategies applied to a strong baseline network model using the original datasets and labels provide further improvements, attaining the state-of-the-art results on the KITTI-2015 scene flow benchmark in the non-stereo category. Our method achieves the best foreground accuracy (4.33% in Fl-all) over both the stereo and non-stereo categories, even though using only monocular image inputs.
A fundamental goal of scientific research is to learn about causal relationships. However, despite its critical role in the life and social sciences, causality has not had the same importance in Natural Language Processing (NLP), which has traditionally placed more emphasis on predictive tasks. This distinction is beginning to fade, with an emerging area of interdisciplinary research at the convergence of causal inference and language processing. Still, research on causality in NLP remains scattered across domains without unified definitions, benchmark datasets and clear articulations of the remaining challenges. In this survey, we consolidate research across academic areas and situate it in the broader NLP landscape. We introduce the statistical challenge of estimating causal effects, encompassing settings where text is used as an outcome, treatment, or as a means to address confounding. In addition, we explore potential uses of causal inference to improve the performance, robustness, fairness, and interpretability of NLP models. We thus provide a unified overview of causal inference for the computational linguistics community.
Image segmentation is still an open problem especially when intensities of the interested objects are overlapped due to the presence of intensity inhomogeneity (also known as bias field). To segment images with intensity inhomogeneities, a bias correction embedded level set model is proposed where Inhomogeneities are Estimated by Orthogonal Primary Functions (IEOPF). In the proposed model, the smoothly varying bias is estimated by a linear combination of a given set of orthogonal primary functions. An inhomogeneous intensity clustering energy is then defined and membership functions of the clusters described by the level set function are introduced to rewrite the energy as a data term of the proposed model. Similar to popular level set methods, a regularization term and an arc length term are also included to regularize and smooth the level set function, respectively. The proposed model is then extended to multichannel and multiphase patterns to segment colourful images and images with multiple objects, respectively. It has been extensively tested on both synthetic and real images that are widely used in the literature and public BrainWeb and IBSR datasets. Experimental results and comparison with state-of-the-art methods demonstrate that advantages of the proposed model in terms of bias correction and segmentation accuracy.
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