Neural Operator Variational Inference based on Regularized Stein Discrepancy for Deep Gaussian Processes

Deep Gaussian Process (DGP) models offer a powerful nonparametric approach for Bayesian inference, but exact inference is typically intractable, motivating the use of various approximations. However, existing approaches, such as mean-field Gaussian assumptions, limit the expressiveness and efficacy of DGP models, while stochastic approximation can be computationally expensive. To tackle these challenges, we introduce Neural Operator Variational Inference (NOVI) for Deep Gaussian Processes. NOVI uses a neural generator to obtain a sampler and minimizes the Regularized Stein Discrepancy in L2 space between the generated distribution and true posterior. We solve the minimax problem using Monte Carlo estimation and subsampling stochastic optimization techniques. We demonstrate that the bias introduced by our method can be controlled by multiplying the Fisher divergence with a constant, which leads to robust error control and ensures the stability and precision of the algorithm. Our experiments on datasets ranging from hundreds to tens of thousands demonstrate the effectiveness and the faster convergence rate of the proposed method. We achieve a classification accuracy of 93.56 on the CIFAR10 dataset, outperforming SOTA Gaussian process methods. Furthermore, our method guarantees theoretically controlled prediction error for DGP models and demonstrates remarkable performance on various datasets. We are optimistic that NOVI has the potential to enhance the performance of deep Bayesian nonparametric models and could have significant implications for various practical application

Double Normalizing Flows: Flexible Bayesian Gaussian Process ODEs Learning

Recently, Gaussian processes have been utilized to model the vector field of continuous dynamical systems. Bayesian inference for such models \cite{hegde2022variational} has been extensively studied and has been applied in tasks such as time series prediction, providing uncertain estimates. However, previous Gaussian Process Ordinary Differential Equation (ODE) models may underperform on datasets with non-Gaussian process priors, as their constrained priors and mean-field posteriors may lack flexibility. To address this limitation, we incorporate normalizing flows to reparameterize the vector field of ODEs, resulting in a more flexible and expressive prior distribution. Additionally, due to the analytically tractable probability density functions of normalizing flows, we apply them to the posterior inference of GP ODEs, generating a non-Gaussian posterior. Through these dual applications of normalizing flows, our model improves accuracy and uncertainty estimates for Bayesian Gaussian Process ODEs. The effectiveness of our approach is demonstrated on simulated dynamical systems and real-world human motion data, including tasks such as time series prediction and missing data recovery. Experimental results indicate that our proposed method effectively captures model uncertainty while improving accuracy

Petrography and Organic Geochemistry Characterizations of Lower Paleozoic Organic-Rich Shale in the Northwestern Upper Yangtze Plate: Niutitang Formation and Longmaxi Formation, Dabashan Foreland Belt

Measurements of total organic carbon, Rock-Eval pyrolysis, X-ray diffraction, scanning electron microscope, maceral examination, gas chromatography, and gas chromatography-mass spectrometry were conducted on the organic-rich shale of Lower Paleozoic Niutitang Formation and Longmaxi Formation in Dabashan foreland belt to discuss the organic matter characteristic, organic matter origin, redox condition, and salinity. The results indicate that the Niutiang Formation and Longmaxi Formation organic-rich shale are good and very good source rocks with Type I kerogen. Both of the shales have reached mature stage for generating gas. Biomarker analyses indicate that the organic matter origin of Niutitang Formation and Longmaxi Formation organic-rich shale are all derived from the lower bacteria and algae, and the organic matter are all suffered different biodegradation degrees. During Niutitang Formation and Longmaxi Formation period, the redox conditions are both anoxic with no stratification and the sedimentary water is normal marine water

Multi scale lung extraction based on an improved feature-guided geodesic active contour model

Conference Name:2014 5th IEEE International Conference on Software Engineering and Service Science, ICSESS 2014. Conference Address: Beijing, China. Time:June 27, 2014 - June 29, 2014.Object extraction is usually a hot and challenging problem in medical area. Within this area, variational methods are used largely when showing their stunning performance. However, they are still often confronted with the obstacles of local minima issues, which prevent the optimization process converging to the right optima significantly. In this paper, an improved multi-scale object extraction based on feature-guided active contour model with its application in lung segmentation is proposed, which is based on novel constrained variational framework. The experimental results show that the proposed algorithm has a better performance over traditional relative methods. ? 2014 IEEE

Comparative analysis of the complete chloroplast genome sequences in psammophytic Haloxylon species (Amaranthaceae)

The Haloxylon genus belongs to the Amaranthaceae (formerly Chenopodiaceae) family. The small trees or shrubs in this genus are referred to as the King of psammophytic plants, and perform important functions in environmental protection, including wind control and sand fixation in deserts. To better understand these beneficial plants, we sequenced the chloroplast (cp) genomes of Haloxylon ammodendron (HA) and Haloxylon persicum (HP) and conducted comparative genomic analyses on these and two other representative Amaranthaceae species. Similar to other higher plants, we found that the Haloxylon cp genome is a quadripartite, double-stranded, circular DNA molecule of 151,570 bp in HA and 151,586 bp in HP. It contains a pair of inverted repeats (24,171 bp in HA and 24,177 bp in HP) that separate the genome into a large single copy region of 84,214 bp in HA and 84,217 bp in HP, and a small single copy region of 19,014 bp in HA and 19,015 bp in HP. Each Haloxylon cp genome contains 112 genes, including 78 coding, 30 tRNA, and four ribosomal RNA genes. We detected 59 different simple sequence repeat loci, including 44 mono-nucleotide, three di-nucleotide, one tri-nucleotide, and 11 tetra-nucleotide repeats. Comparative analysis revealed only 67 mutations between the two species, including 44 substitutions, 23 insertions/deletions, and two micro-inversions. The two inversions, with lengths of 14 and 3 bp, occur in the petA-psbJ intergenic region and rpl16 intron, respectively, and are predicted to form hairpin structures with repeat sequences of 27 and 19 bp, respectively, at the two ends. The ratio of transitions to transversions was 0.76. These results are valuable for future studies on Haloxylon genetic diversity and will enhance our understanding of the phylogenetic evolution of Amaranthaceae

Comparative analysis of the complete chloroplast genome sequences in psammophytic Haloxylon species (Amaranthaceae)

The Haloxylon genus belongs to the Amaranthaceae (formerly Chenopodiaceae) family. The small trees or shrubs in this genus are referred to as the King of psammophytic plants, and perform important functions in environmental protection, including wind control and sand fixation in deserts. To better understand these beneficial plants, we sequenced the chloroplast (cp) genomes of Haloxylon ammodendron (HA) and Haloxylon persicum (HP) and conducted comparative genomic analyses on these and two other representative Amaranthaceae species. Similar to other higher plants, we found that the Haloxylon cp genome is a quadripartite, double-stranded, circular DNA molecule of 151,570 bp in HA and 151,586 bp in HP. It contains a pair of inverted repeats (24,171 bp in HA and 24,177 bp in HP) that separate the genome into a large single copy region of 84,214 bp in HA and 84,217 bp in HP, and a small single copy region of 19,014 bp in HA and 19,015 bp in HP. Each Haloxylon cp genome contains 112 genes, including 78 coding, 30 tRNA, and four ribosomal RNA genes. We detected 59 different simple sequence repeat loci, including 44 mono-nucleotide, three di-nucleotide, one tri-nucleotide, and 11 tetra-nucleotide repeats. Comparative analysis revealed only 67 mutations between the two species, including 44 substitutions, 23 insertions/deletions, and two micro-inversions. The two inversions, with lengths of 14 and 3 bp, occur in the petA-psbJ intergenic region and rpl16 intron, respectively, and are predicted to form hairpin structures with repeat sequences of 27 and 19 bp, respectively, at the two ends. The ratio of transitions to transversions was 0.76. These results are valuable for future studies on Haloxylon genetic diversity and will enhance our understanding of the phylogenetic evolution of Amaranthaceae

Deformation Test System of Transmission Tower Based on Binocular Vision Method

A test system to measure the deformation of the transmission tower based on binocular vision method is introduced in this work. The test system can achieve the accurate monitoring of the transmission tower deformation, and provide deformation data for the reliability analysis of the transmission tower provides both in static and dynamic measurement. The test system is successfully applied in a tower type test

Deformation Test System of Transmission Tower Based on Binocular Vision Method

A test system to measure the deformation of the transmission tower based on binocular vision method is introduced in this work. The test system can achieve the accurate monitoring of the transmission tower deformation, and provide deformation data for the reliability analysis of the transmission tower provides both in static and dynamic measurement. The test system is successfully applied in a tower type test

An approach to cross-calibrating multi-mission satellite data for the open ocean

Synchronous observations with similar illumination-observation and meteorological conditions are critical components of cross-calibration analysis. This study outlines data quality control criteria for obtaining the stable synchronous data needed for developing and evaluating a cross-calibration algorithm. With image data from the Visible Infrared Imaging Radiometer (VIIRS) and Medium Resolution Spectral Imager II (MERSI II), we developed a cross-calibration algorithm using 35 image pairs of four ocean gyres, and we evaluated the data using 11 image pairs of the global ocean. We found that our new algorithm provided well-calibrated MERSI II reflectance at the top-of-atmosphere. The coefficients of determination (R-2) were greater than 0.89, and the mean absolute percent difference (MAPD) varied from 1.13% to 8.37% in the visible bands, which was significantly superior to an algorithm developed from a data set constrained by existing data quality controls. When the satellite data were preprocessed with the new cross-calibration algorithm, the MERSI II instrument provided inter-mission remote sensing reflectance for the North Pacific Gyre that was consistent with the VIIRS instrument. Furthermore, we derived consistent estimates of remote sensing reflectance and backscattering coefficients (b(b)) from VIIRS and the cross-calibrated MERSI II reflectance data for four typically turbid coastal waters. The VIIRS bb coastal images had special distribution patterns, such as tongue-shaped plumes and mesoscale eddies, which accurately reappeared in the MERSI II images. The inter-mission MAPD values varied from 16%-24% for the coastal waters. This uncertainty level was much lower than the bb data quantified from the original MERSI II data with no cross-calibration. Our results suggest that our data quality control criteria provide good quality synchronous data for cross-calibration analysis. MERSI II could provide good ocean color products for oceanic communications after cross-calibration, even though the radiance calibration for the original MERSI II reflectance data are imperfect