Gaussian Conditional Random Fields Research Articles

Structured prediction of sparse dependent variables for traffic state estimation in large-scale networks

Currently, one of the biggest challenges in modern traffic engineering is related to traffic state estimation (TSE). Although many machine learning and domain models can be used for TSE, they do not consider the sparsity and spatial dependence of traffic state variables. In this paper, we propose a hybrid soft computing model of two Gaussian conditional random field (GCRF) models for the inference of traffic speed, which is a relevant variable for TSE and travel information systems. The proposed model can infer the traffic state variables in large-scale networks whose nodes are geographically dispersed. Moreover, by combining a Gaussian conditional random field binary classification model (GCRFBC), which classifies traffic regimes as free-flow or potentially congested, and a regression GCRF model for the prediction of traffic speed in potentially congested traffic regimes, the model addresses two specifics of the problem: sparsity in traffic data, and the fact that observations are not independent. The proposed model was tested on two large-scale real-world networks in Serbia, namely an arterial E70-E75 335 km long highway stretch and the major ski resort Kopaonik with 55 km of ski slopes. In addition, the proposed model showed better prediction performance than several other unstructured and structured models.

Gaussian conditional random fields for classification

Gaussian conditional random fields (GCRF) are a well-known structured model for continuous outputs that uses multiple unstructured predictors to form its features and at the same time exploits dependence structure among outputs, which is provided by a similarity measure. In this paper, a Gaussian conditional random field model for structured binary classification (GCRFBC) is proposed. The model is applicable to classification problems with undirected graphs, intractable for standard classification CRFs. The model representation of GCRFBC is extended by latent variables which yield some appealing properties. Thanks to the GCRF latent structure, the model becomes tractable, efficient and open to improvements previously applied to GCRF regression models. In addition, the model allows for reduction of noise, that might appear if structures were defined directly between discrete outputs. Two different forms of the algorithm are presented: GCRFBCb (GCRGBC — Bayesian) and GCRFBCnb (GCRFBC — non-Bayesian). The extended method of local variational approximation of sigmoid function is used for solving empirical Bayes in Bayesian GCRFBCb variant, whereas MAP value of latent variables is the basis for learning and inference in the GCRFBCnb variant. The inference in GCRFBCb is solved by Newton–Cotes formulas for one-dimensional integration. Both models are evaluated on synthetic data and real-world data. We show that both models achieve better prediction performance than unstructured predictors. Furthermore, computational and memory complexity is evaluated. Advantages and disadvantages of the proposed GCRFBCb and GCRFBCnb are discussed in detail.

Bayesian Estimation of Gaussian Conditional Random Fields

Bayesian Estimation of Gaussian Conditional Random Fields

Complementary Convolution Residual Networks for Semantic Segmentation in Street Scenes with Deep Gaussian CRF

To understand surrounding scenes accurately, the semantic segmentation of images is vital in autonomous driving tasks, such as navigation, and route planning. Currently, convolutional neural networks (CNN) are widely employed in semantic segmentation to perform precise prediction in the dense pixel level. A recent trend in network design is the stacking of small convolution kernels. In this work, small convolution kernels (3 × 3) are decomposed into complementary convolution kernels (1 × 3 + 3 × 1, 3 × 1 + 1 × 3), the complementary small convolution kernels perform better in the classification and location tasks of semantic segmentation. Subsequently, a complementary convolution residual network (CCRN) is proposed to improve the speed and accuracy of semantic segmentation. To further locate the edge of objects precisely, A coupled Gaussian conditional random field (G-CRF) is utilized for CCRN post-processing. Proposal approach achieved 81.8% and 73.1% mean Intersection-over-Union (mIoU) on PASCAL VOC-2012 test set and Cityscapes test set, respectively.

SWIFT: A non-emergency response prediction system using sparse Gaussian Conditional Random Fields

Cities have limited resources that must be used efficiently to maintain their smooth operation. To facilitate efficient resource allocation and management in cities, in this paper, we study one such important problem: how long does it take to resolve non-emergency 311 service requests? We present SWIFT, a Non-emergency Response prediction system based on a recently developed structured regression model, sparse Gaussian Conditional Random Fields (GCRFs), that successfully captures the dependencies between historical and future response times. Through extensive experimentation on 311 service requests from New York City (NYC), Kansas City and Baltimore over a three and a half year period between January 2015 to June 2018, we demonstrate that our trained system is able to accurately predict future response times one week in advance using just the previous two weeks data at test time. SWIFT achieves superior prediction performance across all agencies, complaint types, and locations for all the three cities when compared to linear regression, ARIMA and Seasonal ARIMA baselines (up to a factor of 2X). The trained SWIFT system requires low computational resources and data at test time, thus making it an attractive system that can be readily deployed in practice.

Short-Term Demand Forecasting for on-Demand Mobility Service

To improve the mymargin efficiency of urban on-demand mobility services (OMS) (e.g., taxi and for-hire vehicles such as Uber, Lyft, and Didi), it is important to frame proactive operation strategies before the actual demand is revealed. The task is challenging since the effectiveness depends on the knowledge of passenger demand distribution in immediate future and is prone to prediction errors. In this study, we develop the boosting Gaussian conditional random field (boosting-GCRF) model to accurately forecast the distribution of short-term future OMS demand using historical OMS demand data. Comprehensive numerical experiments are conducted to evaluate the performance of boosting-GCRF as compared to four other benchmark algorithms. The results suggest that the boosting-GCRF is superior with the best mean absolute percentage error being 14%. In addition, the model is found to be robust under demand anomalies, and the density functions generated by the boosting-GCRF model are found to well capture the actual distribution of the short-term taxi demand.

Desert Seismic Data Denoising Based on Gaussian Conditional Random Field With Sparsity Measurement

Desert seismic data have the characteristics of low signal-to-noise ratio (SNR) and low-frequency, which pose a major challenge to noise attenuation. In this letter, we propose a denoising method for desert seismic data that combines the Gaussian conditional random field (GCRF) and the sparsity measurement. The sparsity measurement method is designed to replace the noise sampling method in the posterior frame. To calculate the block sparsity, first the seismic data blocks are divided into three groups: high sparsity blocks, medium sparsity blocks, and low sparsity blocks. Then different denoising parameters are determined according to the sparsity of seismic signal and the nonsparsity of desert low-frequency noise. Consequently, this targeted parameter setting achieves a more thorough suppression of noise and less attenuation of seismic signals. Both the synthetic and real data experiments prove the effectiveness of the method in this letter.

Pavement defect detection with fully convolutional network and an uncertainty framework

AbstractImage segmentation has been implemented for pavement defect detection, from which types, locations, and geometric information can be obtained. In this study, an integration of a fully convolutional network with a Gaussian‐conditional random field (G‐CRF), an uncertainty framework, and probability‐based rejection is proposed for detecting pavement defects. First, a fully convolutional network is designed to generate preliminary segmentation results, and a G‐CRF is used to refine the segmentation. Second, epistemic and aleatory uncertainties in the model and database are considered to overcome the disadvantages of traditional deep‐learning methods. Last, probability‐based rejection is conducted to remove unreasonable segmentations. The proposed method is evaluated on a data set of images that were obtained from 16 highways. The proposed integration segments pavement distresses from digital images with desirable performance. It also provides a satisfactory means to improve the accuracy and generalization performance of pavement defect detection without introducing a delay into the segmentation process.

Predictive Risk Management for Dynamic Tree Trimming Scheduling for Distribution Networks

This paper introduces a predictive method for distribution feeder vegetation management based on a risk framework. The state of risk is calculated for each feeder section using a variety of factors extracted from network parameters and historical outage data, historical weather data and weather forecasts, and a variety of vegetation indices. The framework implements the spatiotemporal correlation of all the collected data. The prediction model used is the Gaussian conditional random field, which takes into account spatial interdependencies between different feeder sections. This enables better prediction accuracy, and also offers the capability to deal with missing and bad data. Based on the calculated risk, the dynamic optimal tree trimming schedule, which minimizes the overall risk for the system under a given predetermined budget, is developed. Results obtained on a real utility network show that optimal tree trimming based on the developed risk framework for vegetation management could significantly decrease the overall risk of the feeder outages without increasing the budget.

Background Extraction Based on Joint Gaussian Conditional Random Fields

Background extraction is generally the first step in many computer vision and augmented reality applications. Most existing methods, which assume the existence of a clean background during the reconstruction period, are not suitable for video sequences such as highway traffic surveillance videos, whose complex foreground movements may not meet the assumption of a clean background. Therefore, we propose a novel joint Gaussian conditional random field (JGCRF) background extraction algorithm for estimating the optimal weights of frame composition for a fixed-view video sequence. A maximum a posteriori problem is formulated to describe the intra- and inter-frame relationships among all pixels of all frames based on their contrast distinctness and spatial and temporal coherence. Because all background objects and elements are assumed to be static, patches that are motionless are good candidates for the background. Therefore, in the algorithm method, a motionless extractor is designed by computing the pixel-wise differences between two consecutive frames and thresholding the accumulation of variation across the frames to remove possible moving patches. The proposed JGCRF framework can flexibly link extracted motionless patches with desired fusion weights as extra observable random variables to constrain the optimization process for more consistent and robust background extraction. The results of quantitative and qualitative experiments demonstrated the effectiveness and robustness of the proposed algorithm compared with several state-of-the-art algorithms; the proposed algorithm also produced fewer artifacts and had a lower computational cost.

Graphical Model Selection for Gaussian Conditional Random Fields in the Presence of Latent Variables

ABSTRACTWe consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random field into the sum of a sparse and a low-rank matrix. We derive convergence bounds for this estimator and show that it is well-behaved in the high-dimensional regime as well as “sparsistent” (i.e., capable of recovering the graph structure). We then show how proximal gradient algorithms and semi-definite programming techniques can be employed to fit the model to thousands of variables. Through extensive simulations, we illustrate the conditions required for identifiability and show that there is a wide range of situations in which this model performs significantly better than its counterparts, for example, by accommodating more latent variables. Finally, the suggested method is applied to two datasets comprising individual level data on genetic variants and metabolites levels. We show our results replicate better than alternative approaches and show enriched biological signal. Supplementary materials for this article are available online.

Efficient image super-resolution integration

The super-resolution (SR) problem is challenging due to the diversity of image types with little shared properties as well as the speed required by online applications, e.g., target identification. In this paper, we explore the merits and demerits of recent deep learning-based and conventional patch-based SR methods and show that they can be integrated in a complementary manner, while balancing the reconstruction quality and time cost. Motivated by this, we further propose an integration framework to take the results from FSRCNN and A+ methods as inputs and directly learn a pixel-wise mapping between the inputs and the reconstructed results using the Gaussian conditional random fields. The learned pixel-wise integration mapping is flexible to accommodate different upscaling factors. Experimental results show that the proposed framework can achieve superior SR performance compared with the state of the arts while being efficient.

Sparse Gaussian Conditional Random Fields on Top of Recurrent Neural Networks

Predictions of time-series are widely used in different disciplines. We propose CoR, Sparse Gaussian Conditional Random Fields (SGCRF) on top of Recurrent Neural Networks (RNN), for problems of this kind. CoR gains advantages from both RNN and SGCRF. It can not only effectively represent the temporal correlations in observed data, but can also learn the structured information of the output. CoR is challenging to train because it is a hybrid of deep neural networks and densely-connected graphical models. Alternative training can be a tractable way to train CoR, and furthermore, an end-to-end training method is proposed to train CoR more efficiently. CoR is evaluated by both synthetic data and real-world data, and it shows a significant improvement in performance over state-of-the-art methods.

Multi-PSF fusion in image restoration of range-gated systems

For the task of image restoration, an accurate estimation of degrading PSF/kernel is the premise of recovering a visually superior image. The imaging process of range-gated imaging system in atmosphere associates with lots of factors, such as back scattering, background radiation, diffraction limit and the vibration of the platform. On one hand, due to the difficulty of constructing models for all factors, the kernels from physical-model based methods are not strictly accurate and practical. On the other hand, there are few strong edges in images, which brings significant errors to most of image-feature-based methods. Since different methods focus on different formation factors of the kernel, their results often complement each other. Therefore, we propose an approach which combines physical model with image features. With an fusion strategy using GCRF (Gaussian Conditional Random Fields) framework, we get a final kernel which is closer to the actual one. Aiming at the problem that ground-truth image is difficult to obtain, we then propose a semi data-driven fusion method in which different data sets are used to train fusion parameters. Finally, a semi blind restoration strategy based on EM (Expectation Maximization) and RL (Richardson-Lucy) algorithm is proposed. Our methods not only models how the lasers transfer in the atmosphere and imaging in the ICCD (Intensified CCD) plane, but also quantifies other unknown degraded factors using image-based methods, revealing how multiple kernel elements interact with each other. The experimental results demonstrate that our method achieves better performance than state-of-the-art restoration approaches.

Gaussian conditional random fields extended for directed graphs

For many real-world applications, structured regression is commonly used for predicting output variables that have some internal structure. Gaussian conditional random fields (GCRF) are a widely used type of structured regression model that incorporates the outputs of unstructured predictors and the correlation between objects in order to achieve higher accuracy. However, applications of this model are limited to objects that are symmetrically correlated, while interaction between objects is asymmetric in many cases. In this work we propose a new model, called Directed Gaussian conditional random fields (DirGCRF), which extends GCRF to allow modeling asymmetric relationships (e.g. friendship, influence, love, solidarity, etc.). The DirGCRF models the response variable as a function of both the outputs of unstructured predictors and the asymmetric structure. The effectiveness of the proposed model is characterized on six types of synthetic datasets and four real-world applications where DirGCRF was consistently more accurate than the standard GCRF model and baseline unstructured models.

Structured Regression on Multiscale Networks

Structure-based regression algorithms generally suffer substantive speed losses and have exacting memory requirements compared to their structureless counterparts. Gaussian conditional random field (GCRF) models are one of the most time- and memory-efficient approaches to structured regression. The authors' previous speedups for the GCRF method allow for exact solutions on networks of up to 100,000 nodes and 10 million links. Using multiscale networks, the exact solution for networks of millions of nodes and trillions of links can be solved in a similar amount of time. They walk through the intuitiveness of using multiple scales of networks on a real-life health informatics application. The time and memory demands from using this approach are logarithmic compared to naive implementations.

Joint Estimation of Multiple Conditional Gaussian Graphical Models.

In this paper, we propose a joint conditional graphical Lasso to learn multiple conditional Gaussian graphical models, also known as Gaussian conditional random fields, with some similar structures. Our model builds on the maximum likelihood method with the convex sparse group Lasso penalty. Moreover, our model is able to model multiple multivariate linear regressions with unknown noise covariances via a convex formulation. In addition, we develop an efficient approximated Newton's method for optimizing our model. Theoretically, we establish the asymptotic properties of our model on consistency and sparsistency under the high-dimensional settings. Finally, extensive numerical results on simulations and real data sets demonstrate that our method outperforms the compared methods on structure recovery and structured output prediction. To the best of our knowledge, the joint learning of multiple multivariate regressions with unknown covariance is first studied.

Machine Learning Approach for Predicting Wall Shear Distribution for Abdominal Aortic Aneurysm and Carotid Bifurcation Models.

Computer simulations based on the finite element method represent powerful tools for modeling blood flow through arteries. However, due to its computational complexity, this approach may be inappropriate when results are needed quickly. In order to reduce computational time, in this paper, we proposed an alternative machine learning based approach for calculation of wall shear stress (WSS) distribution, which may play an important role in mechanisms related to initiation and development of atherosclerosis. In order to capture relationships between geometric parameters, blood density, dynamic viscosity and velocity, and WSS distribution of geometrically parameterized abdominal aortic aneurysm (AAA) and carotid bifurcation models, we proposed multivariate linear regression, multilayer perceptron neural network and Gaussian conditional random fields (GCRF). Results obtained in this paper show that machine learning approaches can successfully predict WSS distribution at different cardiac cycle time points. Even though all proposed methods showed high potential for WSS prediction, GCRF achieved the highest coefficient of determination (0.930-0.948 for AAA model and 0.946-0.954 for carotid bifurcation model) demonstrating benefits of accounting for spatial correlation. The proposed approach can be used as an alternative method for real time calculation of WSS distribution.

Extending the Modelling Capacity of Gaussian Conditional Random Fields while Learning Faster

Gaussian Conditional Random Fields (GCRF) are atype of structured regression model that incorporatesmultiple predictors and multiple graphs. This isachieved by defining quadratic term feature functions inGaussian canonical form which makes the conditionallog-likelihood function convex and hence allows findingthe optimal parameters by learning from data. In thiswork, the parameter space for the GCRF model is extendedto facilitate joint modelling of positive and negativeinfluences. This is achieved by restricting the modelto a single graph and formulating linear bounds on convexitywith respect to the models parameters. In addition,our formulation for the model using one networkallows calculating gradients much faster than alternativeimplementations. Lastly, we extend the model onestep farther and incorporate a bias term into our linkweight. This bias is solved as part of the convex optimization.Benefits of the proposed model in terms ofimproved accuracy and speed are characterized on severalsynthetic graphs with 2 million links as well as on ahospital admissions prediction task represented as a humandisease-symptom similarity network correspondingto more than 35 million hospitalization records inCalifornia over 9 years.

Gaussian Conditional Random Fields for Aggregation of Operational Aerosol Retrievals

We present a Gaussian conditional random field model for the aggregation of aerosol optical depth (AOD) retrievals from multiple satellite instruments into a joint retrieval. The model provides aggregated retrievals with higher accuracy and coverage than any of the individual instruments while also providing an estimation of retrieval uncertainty. The proposed model finds an optimal temporally smoothed combination of individual retrievals that minimizes the root-mean-squared error of AOD retrieval. We evaluated the model on five years (2006-2010) of satellite data over North America from five instruments (Aqua and Terra MODIS, MISR, SeaWiFS, and the Ozone Monitoring Instrument), collocated with ground-based Aerosol Robotic Network ground-truth AOD readings, clearly showing that the aggregation of different sources leads to improvements in the accuracy and coverage of AOD retrievals.