scholarly journals Variational Message Passing and Local Constraint Manipulation in Factor Graphs

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 807
Author(s):  
İsmail Şenöz ◽  
Thijs van de Laar ◽  
Dmitry Bagaev ◽  
Bert de de Vries
Keyword(s):  
Free Energy ◽  
Latent Variables ◽  
Message Passing ◽  
Factor Graph ◽  
Estimation Accuracy ◽  
Attractive Alternative ◽  
Factor Graphs ◽  
Data Set ◽  
Bethe Free Energy ◽  
Model Evidence

Accurate evaluation of Bayesian model evidence for a given data set is a fundamental problem in model development. Since evidence evaluations are usually intractable, in practice variational free energy (VFE) minimization provides an attractive alternative, as the VFE is an upper bound on negative model log-evidence (NLE). In order to improve tractability of the VFE, it is common to manipulate the constraints in the search space for the posterior distribution of the latent variables. Unfortunately, constraint manipulation may also lead to a less accurate estimate of the NLE. Thus, constraint manipulation implies an engineering trade-off between tractability and accuracy of model evidence estimation. In this paper, we develop a unifying account of constraint manipulation for variational inference in models that can be represented by a (Forney-style) factor graph, for which we identify the Bethe Free Energy as an approximation to the VFE. We derive well-known message passing algorithms from first principles, as the result of minimizing the constrained Bethe Free Energy (BFE). The proposed method supports evaluation of the BFE in factor graphs for model scoring and development of new message passing-based inference algorithms that potentially improve evidence estimation accuracy.

scholarly journals Message Passing-Based Inference for Time-Varying Autoregressive Models

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 683
Author(s):  
Albert Podusenko ◽  
Wouter M. Kouw ◽  
Bert de Vries
Keyword(s):  
Message Passing ◽  
Synthetic Data ◽  
Model Performance ◽  
Ar Model ◽  
Factor Graph ◽  
Time Varying ◽  
Real World Data ◽  
Data Set ◽  
Inference Problem ◽  
Stationary Signals

Time-varying autoregressive (TVAR) models are widely used for modeling of non-stationary signals. Unfortunately, online joint adaptation of both states and parameters in these models remains a challenge. In this paper, we represent the TVAR model by a factor graph and solve the inference problem by automated message passing-based inference for states and parameters. We derive structured variational update rules for a composite “AR node” with probabilistic observations that can be used as a plug-in module in hierarchical models, for example, to model the time-varying behavior of the hyper-parameters of a time-varying AR model. Our method includes tracking of variational free energy (FE) as a Bayesian measure of TVAR model performance. The proposed methods are verified on a synthetic data set and validated on real-world data from temperature modeling and speech enhancement tasks.

scholarly journals Properties of Bethe Free Energies and Message Passing in Gaussian Models

2011 ◽  
Vol 41 ◽  
pp. 1-24 ◽  
Author(s):  
B. Cseke ◽  
T. Heskes
Keyword(s):  
Free Energy ◽  
Message Passing ◽  
Probabilistic Models ◽  
Mean Field ◽  
Necessary Condition ◽  
Free Energies ◽  
Gaussian Models ◽  
Message Passing Algorithm ◽  
Bethe Free Energy ◽  
The Moment

We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. We define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals, derive a lower and an upper bound on the fractional Bethe free energy and establish a necessary condition for the lower bound to be bounded from below. It turns out that the condition is identical to the pairwise normalizability condition, which is known to be a sufficient condition for the convergence of the message passing algorithm. We show that stable fixed points of the Gaussian message passing algorithm are local minima of the Gaussian Bethe free energy. By a counterexample, we disprove the conjecture stating that the unboundedness of the free energy implies the divergence of the message passing algorithm.

scholarly journals Effect of snow microstructure variability on Ku-band radar snow water equivalent retrievals

2019 ◽  
Vol 13 (11) ◽  
pp. 3045-3059 ◽  
Author(s):  
Nick Rutter ◽  
Melody J. Sandells ◽  
Chris Derksen ◽  
Joshua King ◽  
Peter Toose ◽  
...  
Keyword(s):  
Spatial Variability ◽  
Layer Thickness ◽  
Snow Water Equivalent ◽  
Estimation Accuracy ◽  
Snow Layer ◽  
Data Set ◽  
Snow Water ◽  
Retrieval Errors ◽  
Snow Microstructure ◽  
The Impact

Abstract. Spatial variability in snowpack properties negatively impacts our capacity to make direct measurements of snow water equivalent (SWE) using satellites. A comprehensive data set of snow microstructure (94 profiles at 36 sites) and snow layer thickness (9000 vertical profiles across nine trenches) collected over two winters at Trail Valley Creek, NWT, Canada, was applied in synthetic radiative transfer experiments. This allowed for robust assessment of the impact of estimation accuracy of unknown snow microstructural characteristics on the viability of SWE retrievals. Depth hoar layer thickness varied over the shortest horizontal distances, controlled by subnivean vegetation and topography, while variability in total snowpack thickness approximated that of wind slab layers. Mean horizontal correlation lengths of layer thickness were less than a metre for all layers. Depth hoar was consistently ∼30 % of total depth, and with increasing total depth the proportion of wind slab increased at the expense of the decreasing surface snow layer. Distinct differences were evident between distributions of layer properties; a single median value represented density and specific surface area (SSA) of each layer well. Spatial variability in microstructure of depth hoar layers dominated SWE retrieval errors. A depth hoar SSA estimate of around 7 % under the median value was needed to accurately retrieve SWE. In shallow snowpacks <0.6 m, depth hoar SSA estimates of ±5 %–10 % around the optimal retrieval SSA allowed SWE retrievals within a tolerance of ±30 mm. Where snowpacks were deeper than ∼30 cm, accurate values of representative SSA for depth hoar became critical as retrieval errors were exceeded if the median depth hoar SSA was applied.

A GAMMA MOVING AVERAGE PROCESS FOR MODELLING DEPENDENCE ACROSS DEVELOPMENT YEARS IN RUN-OFF TRIANGLES

2020 ◽  
pp. 1-22
Author(s):  
Luis E. Nieto-Barajas ◽  
Rodrigo S. Targino
Keyword(s):  
Latent Variables ◽  
Moving Average ◽  
Real Data ◽  
Model Parameters ◽  
Average Process ◽  
Moving Average Process ◽  
Data Set ◽  
Run Off ◽  
Average Form ◽  
Reserve Estimates

ABSTRACT We propose a stochastic model for claims reserving that captures dependence along development years within a single triangle. This dependence is based on a gamma process with a moving average form of order $p \ge 0$ which is achieved through the use of poisson latent variables. We carry out Bayesian inference on model parameters and borrow strength across several triangles, coming from different lines of businesses or companies, through the use of hierarchical priors. We carry out a simulation study as well as a real data analysis. Results show that reserve estimates, for the real data set studied, are more accurate with our gamma dependence model as compared to the benchmark over-dispersed poisson that assumes independence.

A combined local and global structure module for human pose estimation

2021 ◽  
pp. 1-11
Author(s):  
Zhihui Yang ◽  
Xiangyu Tang ◽  
Lijuan Zhang ◽  
Zhiling Yang
Keyword(s):  
Pose Estimation ◽  
Computational Cost ◽  
Hybrid Structure ◽  
Estimation Accuracy ◽  
Structure Model ◽  
Data Set ◽  
Human Pose ◽  
Human Joints ◽  
Residual Block ◽  
Keypoints Detection

Human pose estimate can be used in action recognition, video surveillance and other fields, which has received a lot of attentions. Since the flexibility of human joints and environmental factors greatly influence pose estimation accuracy, related research is confronted with many challenges. In this paper, we incorporate the pyramid convolution and attention mechanism into the residual block, and introduce a hybrid structure model which synthetically applies the local and global information of the image for the analysis of keypoints detection. In addition, our improved structure model adopts grouped convolution, and the attention module used is lightweight, which will reduce the computational cost of the network. Simulation experiments based on the MS COCO human body keypoints detection data set show that, compared with the Simple Baseline model, our model is similar in parameters and GFLOPs (giga floating-point operations per second), but the performance is better on the detection of accuracy under the multi-person scenes.

scholarly journals OPTIMIZING RADIOMETRIC PROCESSING AND FEATURE EXTRACTION OF DRONE BASED HYPERSPECTRAL FRAME FORMAT IMAGERY FOR ESTIMATION OF YIELD QUANTITY AND QUALITY OF A GRASS SWARD

2018 ◽  
Vol XLII-3 ◽  
pp. 1305-1310 ◽  
Author(s):  
R. Näsi ◽  
N. Viljanen ◽  
R. Oliveira ◽  
J. Kaivosoja ◽  
O. Niemeläinen ◽  
...  
Keyword(s):  
Feature Extraction ◽  
3D Structure ◽  
Point Clouds ◽  
Estimation Accuracy ◽  
Spectral Features ◽  
Data Set ◽  
Area Of Interest ◽  
Evaluation Task ◽  
Corrected Data ◽  
Grass Sward

Light-weight 2D format hyperspectral imagers operable from unmanned aerial vehicles (UAV) have become common in various remote sensing tasks in recent years. Using these technologies, the area of interest is covered by multiple overlapping hypercubes, in other words multiview hyperspectral photogrammetric imagery, and each object point appears in many, even tens of individual hypercubes. The common practice is to calculate hyperspectral orthomosaics utilizing only the most nadir areas of the images. However, the redundancy of the data gives potential for much more versatile and thorough feature extraction. We investigated various options of extracting spectral features in the grass sward quantity evaluation task. In addition to the various sets of spectral features, we used photogrammetry-based ultra-high density point clouds to extract features describing the canopy 3D structure. Machine learning technique based on the Random Forest algorithm was used to estimate the fresh biomass. Results showed high accuracies for all investigated features sets. The estimation results using multiview data provided approximately 10&amp;thinsp;% better results than the most nadir orthophotos. The utilization of the photogrammetric 3D features improved estimation accuracy by approximately 40&amp;thinsp;% compared to approaches where only spectral features were applied. The best estimation RMSE of 239&amp;thinsp;kg/ha (6.0&amp;thinsp;%) was obtained with multiview anisotropy corrected data set and the 3D features.

scholarly journals Mosaicking Weather Radar Retrievals from an Operational Heterogeneous Network at C and X Band for Precipitation Monitoring in Italian Central Apennines

2022 ◽  
Vol 14 (2) ◽  
pp. 248
Author(s):  
Stefano Barbieri ◽  
Saverio Di Fabio ◽  
Raffaele Lidori ◽  
Francesco L. Rossi ◽  
Frank S. Marzano ◽  
...  
Keyword(s):  
Atmospheric Precipitation ◽  
Weather Radar ◽  
Geographic Area ◽  
Single Frequency ◽  
Estimation Accuracy ◽  
Central Apennines ◽  
Data Set ◽  
Area Of Interest ◽  
Spatial Coverage ◽  
Network Pattern

Meteorological radar networks are suited to remotely provide atmospheric precipitation retrieval over a wide geographic area for severe weather monitoring and near-real-time nowcasting. However, blockage due to buildings, hills, and mountains can hamper the potential of an operational weather radar system. The Abruzzo region in central Italy’s Apennines, whose hydro-geological risks are further enhanced by its complex orography, is monitored by a heterogeneous system of three microwave radars at the C and X bands with different features. This work shows a systematic intercomparison of operational radar mosaicking methods, based on bi-dimensional rainfall products and dealing with both C and X bands as well as single- and dual-polarization systems. The considered mosaicking methods can take into account spatial radar-gauge adjustment as well as different spatial combination approaches. A data set of 16 precipitation events during the years 2018–2020 in the central Apennines is collected (with a total number of 32,750 samples) to show the potentials and limitations of the considered operational mosaicking approaches, using a geospatially-interpolated dense network of regional rain gauges as a benchmark. Results show that the radar-network pattern mosaicking, based on the anisotropic radar-gauge adjustment and spatial averaging of composite data, is better than the conventional maximum-value merging approach. The overall analysis confirms that heterogeneous weather radar mosaicking can overcome the issues of single-frequency fixed radars in mountainous areas, guaranteeing a better spatial coverage and a more uniform rainfall estimation accuracy over the area of interest.

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