Deep learning approximates system moments from data.
problem Approximating moments of spatial probabilistic systems.
method Dynamic Boltzmann Distributions (DBDs) with deep Boltzmann machines (DBMs).
result Learned moment closures improve generalization over traditional methods.
The study optimizes sampling in complex systems with probabilistic response distributions.
problem Calibrating and optimizing complex systems with probabilistic response distributions.
method Non-parametric Bayesian approach to modeling spatial fields of probability distributions, introducing adaptive sampling strategies.
result Adaptive sampling strategies improve system evaluations by guiding focus towards key features.
DCK improves air quality index prediction with probabilistic spatial models.
problem Non-Gaussian, complex spatial structure of air quality index.
method Deep classifier kriging (DCK) for non-Gaussian, nonlinear spatial prediction.
result DCK outperforms conventional methods in predictive accuracy and uncertainty quantification.
Graph-EFM models weather uncertainty with graph-based ensembles.
problem Accurately capturing forecast uncertainty in chaotic weather.
method Flexible latent-variable formulation with hierarchical graph construction.
result Graph-EFM ensembles achieve equivalent or lower errors than deterministic models.
Bayesian Empirical Bayes extends EB to complex structures using probabilistic symmetry.
problem Improving simultaneous inference in complex settings like arrays and graphs.
method Generalized empirical Bayes approach based on probabilistic symmetry.
result BEB outperforms existing methods in denoising arrays and spatial data.
Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous exploration are typically adressed with specialised methods, often relying on detailed …
CNNs improve wind speed forecasts in the Netherlands.
problem Limited spatial patterns in current post-processing methods.
method Convolutional Neural Networks (CNNs) for spatial wind speed information.
result CNNs produce better probabilistic forecasts with higher Brier skill scores.
Probabilistic STNs improve image classification and robustness.
problem Training and robustness issues in STNs.
method Probabilistic extension of STNs that estimates stochastic transformations.
result Improved classification performance, robustness, and model calibration.
ProFnet models HDFTS with neural networks, offering scalable probabilistic forecasts.
problem Modeling high-dimensional functional time series with nonlinear trends and high spatial dimensions.
method Integrates feedforward and deep neural networks with probabilistic modeling.
result Superior performance in forecasting Japan's mortality rates.
Many data-driven approaches exist to extract neural representations of functional magnetic resonance imaging (fMRI) data, but most of them lack a proper probabilistic formulation. We propose a group level scalable probabilistic sparse factor analysis (psFA) allowing spatially sparse maps, component pruning using automa…
Probabilistic programming aids in automatically dating ice cores, reducing manual error and uncertainty.
problem Automatically dating ice cores with high accuracy and capturing uncertainty.
method Probabilistic models and probabilistic programming for automatic inference.
result Demonstrated the use of probabilistic programming for ice core dating, showcasing its benefits and limitations.
Probabilistic atlases provide essential spatial contextual information for image interpretation, Bayesian modeling, and algorithmic processing. Such atlases are typically constructed by grouping subjects with similar demographic information. Importantly, use of the same scanner minimizes inter-group variability. Howeve…
DDPMs can reproduce medical image context, showing interpolation between samples.
problem Understanding DDPMs' ability to learn spatial context in medical imaging.
method Used stochastic context models (SCMs) to produce training data and assess DDPMs' performance.
result DDPMs can generate contextually correct images, interpolating between samples.
ProGen improves spatiotemporal forecasting with SDEs and diffusion models.
problem Complex spatial and temporal dependencies in spatiotemporal data.
method ProGen uses Stochastic Differential Equations and diffusion-based generative models.
result ProGen outperforms state-of-the-art models on traffic datasets.
New framework for 3D spatial topology enumeration and identification.
problem Efficient navigation through complex engineering system topologies.
method Mathematical spatial graph theory to represent, enumerate, and identify unique topological classes.
result Identification of distinctive 3D topological classes for engineering systems.
Generative networks minimize predictive scoring rules for probabilistic forecasting.
problem Evaluating and improving probabilistic forecasts using generative models.
method Training generative networks to minimize predictive-sequential scoring rules on temporal sequences.
result Our method outperforms adversarial approaches in probabilistic calibration.
SPACE models complex scenes by decomposing objects and backgrounds.
problem Scalability and unsupervised object-oriented scene representation learning.
method Generative latent variable model combining spatial-attention and scene-mixture approaches.
result SPACE achieves factorized object representations and decomposes complex scenes.
Probabilistic Bisection Algorithm performs root finding based on knowledge acquired from noisy oracle responses. We consider the generalized PBA setting (G-PBA) where the statistical distribution of the oracle is unknown and location-dependent, so that model inference and Bayesian knowledge updating must be performed s…
The 2008 financial crisis revealed banking consolidation paradoxically increased systemic fragility and global financial contagion with negligible spatial decay.
problem Fundamental vulnerabilities in interconnected banking systems during the 2008 financial crisis were inadequately addressed by existing frameworks.
method Developed a unified spatial-network framework using spectral analysis of network Laplacian operators combined with spatial difference-in-differences identification.
result Banking consolidation paradoxically increased systemic fragility and global financial contagion with negligible spatial decay.
Unsupervised fire and smoke segmentation from IR videos.
problem Early detection of fire from infrared videos.
method Spatial, temporal, and motion information fusion using optical flow, divergence, and intensity values.
result Markov Random Field outperforms other clustering algorithms in fire and smoke segmentation.
Enhances POU-Nets with probabilistic noise model for efficient spatial data clustering.
problem Improving the efficiency and accuracy of deep learning models for spatial data.
method Integrates Gaussian noise model into POU-Nets to enable gradient-based optimization and hierarchical refinement.
result Achieves sharp spatial partitions and higher-order polynomial approximation without regularizers.
This study prioritizes temporal resolution over spatial in energy systems models due to higher influence.
problem The impact of spatial and temporal resolution on energy system models.
method Global sensitivity analysis to compare structural aspects, spatial, and temporal resolution.
result Temporal resolution has a higher influence on all results parameters compared to spatial resolution.
Sum-Product Networks (SPNs) are hierarchical, graphical models that combine benefits of deep learning and probabilistic modeling. SPNs offer unique advantages to applications demanding exact probabilistic inference over high-dimensional, noisy inputs. Yet, compared to convolutional neural nets, they struggle with captu…
New model predicts weekly earthquakes with better tail risk assessment.
problem Violation of Poisson assumption in seismic data.
method Neural network for per-cell overdispersion estimation.
result 8.6% reduction in mean pinball deviation, 12.5% lower CRPS in tail events.
Spatially positioned neurons in neural networks mimic biological systems.
problem Creating neural networks that can perform multiple tasks efficiently.
method Added spatial positions and proximity penalties to artificial neurons.
result Neurons naturally cluster, each responsible for a specific task.
Proposes a transformer model with geostatistical inductive bias for spatio-temporal forecasting.
problem Combining probabilistic rigor of geostatistics with flexible deep learning representations.
method Spatially-informed transformer with learnable covariance kernel.
result Successfully recovers spatial decay parameters end-to-end via backpropagation.
Hybrid model predicts flow and pressure in water systems.
problem Predicting flow and pressure in water distribution systems with complex spatial-temporal correlations.
method Hybrid dual-stage spatial-temporal attention-based recurrent neural networks (hDS-RNN).
result Our model outperformed 9 baseline models in flow and pressure series prediction.
New approach to Lagrangian systems using intrinsic geometry.
problem Developing a new framework for Lagrangian systems.
method Direct reformulation of Hamiltonian formalism, introduction of spatial equation and spatial-gauge symmetry.
result Covariant and non-covariant canonical variational principles demonstrated for Maxwell equations.
We propose a simple probabilistic model to explain the spatial structure of the rent distribution of housing market in city of Sapporo. Here we modify the mathematical model proposed by Gauvin et. al. Especially, we consider the competition between two distances, namely, the distance between house and center, and the d…
The paper explores new quandle systems for handlebody-links and spatial graphs.
problem Developing new invariants for handlebody-links and spatial graphs.
method Investigates and constructs new algebraic systems (quandles) to generalize existing ones.
result Provides necessary conditions for colouring invariants of knotted handlebodies.
The paper calibrates geophysical predictions using marginal distributions and machine learning.
problem Sensitivity to initial conditions in geophysical systems leads to large deviations in long-term forecasts.
method The method introduces a calibration algorithm based on normalization and Kernelized Stein Discrepancy (KSD) to enhance ML predictions.
result The method improves the fidelity of ML predictions to known physical distributions, ensuring consistency with non-local statistical structures.
Bayesian method improves segmentation accuracy with noisy labels.
problem Annotation errors in semantic segmentation due to mislabeling and spatial correlations.
method Approximate Bayesian estimation with spatially correlated discrete distributions and variational inference.
result The method achieves performance comparable to clean labels under moderate noise levels.
The paper examines uncertainty calibration for object detection models in autonomous driving.
problem Uncertainty in object detection predictions and its calibration.
method Definition and evaluation of semantic and spatial uncertainty, calibration methods for uncertainty distributions.
result Calibrated uncertainty improves the overall performance of object detection models in real-world scenarios.
We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity of target data. The proposed model can effectively make use of auxiliary data set…
Future stability of FLRW solutions in expanding 3D space is shown for compact perturbations.
problem Future stability of expanding FLRW solutions with spatial topology R^3.
method Nonlinear stability analysis of spherically symmetric perturbations.
result Decay rates of energy momentum tensor components compared to Minkowski space.
Signature kernel scoring rule improves weather forecasting by capturing temporal and spatial dependencies.
problem Lack of suitable scoring rules for probabilistic weather forecasting.
method Reframe weather variables as continuous paths using iterated integrals (signature kernels) to capture temporal and spatial dependencies.
result Signature kernel scoring rule outperforms conventional methods in weather forecasting, especially for long-term forecasts.
New model predicts travel demand uncertainty with high accuracy.
problem Uncertainty and sparsity in sparse travel demand prediction.
method Spatial-Temporal Zero-Inflated Negative Binomial Graph Neural Network (STZINB-GNN).
result STZINB-GNN outperforms benchmarks in predicting travel demand uncertainty.
Forward inference techniques such as sequential Monte Carlo and particle Markov chain Monte Carlo for probabilistic programming can be implemented in any programming language by creative use of standardized operating system functionality including processes, forking, mutexes, and shared memory. Exploiting this we have …
Probabilistic method combines space and time uncertainties in PDEs.
problem Separate treatment of space and time in PDE solvers obscures interactions and error quantification.
method Gaussian process interpretation of finite difference methods interacting with probabilistic ODE solvers.
result Joint quantification of space- and time-uncertainty possible without sacrificing ODE solver performance.
Hybrid model integrates GATv2 and geostatistics for better spatial prediction and uncertainty.
problem Accurate spatial prediction and uncertainty quantification in epidemiology and risk analysis.
method Integrates Graph Attention Network (GATv2) with model-based geostatistics (MBG) to capture relational and spatial dependencies.
result Hybrid model improves predictive accuracy and uncertainty quantification compared to standalone models.
This paper examines how voter concentration affects election outcomes in district-based systems.
problem How does the spatial concentration of electors impact election results?
method The authors frame the spatial distribution of electors in a probabilistic setting and explore models to capture intra-district polarization. They use Likelihood-free Inference under the Approximate Bayesian Computation framework and supervised regression methods to estimate parameters.
result The models can capture statistical properties of real elections and show how voter distributions can change election results.
Extracts intrinsic spatial coordinates for complex agent systems to learn PDEs.
problem Modeling collective dynamics of heterogeneous agents.
method Data-driven extraction of intrinsic spatial coordinates, learning PDEs in emergent space.
result Collective dynamics can be approximated through learned PDEs in emergent coordinates.
Dynamic models learn from sparse, interacting sub-systems.
problem Learning robust models for systems with local views and spatial locations.
method Abstracting the system as a collection of sparsely interacting sub-systems, each with a learned topology informed by spatial structure.
result Models are more robust to the number of available views and generalize better to novel tasks.
Probabilistic solvers improve stability for stiff systems.
problem Performance penalties for small steps in stiff systems.
method Probabilistic exponential integrators that include fast linear dynamics in the prior.
result Proven L-stability and probabilistic error accounting.
Compact Gaussian model approximates deep ensemble predictions.
problem Efficiently approximating deep ensemble models for image prediction.
method Sparse-structured multivariate Gaussian with Cholesky parameterization trained to match pre-trained ensemble outputs.
result Compact representation captures uncertainty and structured correlations explicitly.
This paper tackles Bayesian system identification with probabilistic numerical methods.
problem Accurately modeling nonlinear dynamic systems from noisy data.
method Probabilistic Sequential Monte Carlo (SMC) combined with probabilistic numerical integration.
result Efficient identification of latent states and system parameters from noisy measurements.
Deep GMRFs improve spatial data modeling and prediction.
problem Modeling spatial dependencies in data.
method Established connection between GMRFs and CNNs, allowing for multi-layer architectures.
result Deep GMRFs outperform state-of-the-art models in satellite temperature prediction.
Probabilistic programming allows specification of probabilistic models in a declarative manner. Recently, several new software systems and languages for probabilistic programming have been developed on the basis of newly developed and improved methods for approximate inference in probabilistic models. In this contribut…