Efficiently infers gene regulatory networks from spatial data.
problem Inferring spatially-varying gene regulatory networks.
method Proposed an efficient optimization problem for SV-GMRFs.
result Solves large-scale SV-GMRF problems in minutes.
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
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48 results for “spatially-varying GMRFs”
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.
A scalable deep GMRF model for general graphs improves predictions and uncertainty estimates.
problem Handling generally structured data on graphs efficiently.
method A new multi-layer structure of Deep GMRFs designed for general graphs, enabling efficient training and close-to-exact Bayesian inference.
result Close-to-exact Bayesian inference for latent field predictions with uncertainty estimates.
Proposes a new method for estimating sparse precision matrices in GMRF-MM models.
problem Difficulty in learning GMMs with large parameters and limited data.
method Restricts GMM to GMRF-MM, proposes efficient optimization for sparse precision matrices, and debiases the estimates.
result Debiasing approach outperforms GLASSO in single-GMRF and GMRF-MM cases.
Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds
problem Convergent approximation of Gaussian Whittle-Matern fields on Riemannian manifolds
method Finite Element approximation of SPDEs
result Universal approximation of precision and covariance matrices
New methods reduce computational cost for Gaussian Markov Random Fields with sparse constraints.
problem Inference and simulation of GMRFs are computationally prohibitive with many constraints.
method Proposes a basis transformation into blocks of constrained and non-constrained subspaces.
result Significantly outperforms existing alternatives in computational cost.
Gaussian Markov random fields (GMRFs) are useful in a broad range of applications. In this paper we tackle the problem of learning a sparse GMRF in a high-dimensional space. Our approach uses the l1-norm as a regularization on the inverse covariance matrix. We utilize a novel projected gradient method, which is faster …
BKP R package models spatially varying binomial probabilities efficiently.
problem Modeling spatially varying binomial probabilities efficiently.
method Beta Kernel Process (BKP) combining localized kernel-weighted likelihoods with conjugate beta priors.
result Closed-form posterior inference without requiring latent variables or intensive MCMC sampling.
Proposes a deep neural network approach for image response regression.
problem Associations between medical images and covariates.
method Spatially varying coefficient models with deep neural networks.
result Explicitly accounts for spatial smoothness and subject heterogeneity.
A new method for solving complex inverse problems using deep learning.
problem Estimating complex spatially-varying parameters in high-dimensional Bayesian inverse problems.
method A variational inference method with a deep generative prior to approximate the posterior distribution.
result The method improves estimation accuracy and efficiency for solving high-dimensional inverse problems.
GWRBoost improves GWR for better spatial relationship quantification.
problem Underfitting in GWR for complex data and lack of explainable quantification.
method Geographically weighted gradient boosting model using localized additive model and gradient boosting optimization.
result Significant improvement in RMSE and AICc compared to classic GWR.
The geometric approach to diffeomorphic image registration known as "large deformation by diffeomorphic metric mapping" (LDDMM) is based on a left action of diffeomorphisms on images, and a right-invariant metric on a diffeomorphism group, usually defined using a reproducing kernel. We explore the use of left-invariant…
In this paper, we consider Bayesian image denoising based on a Gaussian Markov random field (GMRF) model, for which we propose an new algorithm. Our method can solve Bayesian image denoising problems, including hyperparameter estimation, in -time, where is the number of pixels in a given image. From the persp…
Weather2vec learns representations to adjust for non-local confounding in air pollution studies.
problem Non-local confounding in evaluating environmental policies and climate events on health outcomes.
method weather2vec framework using balancing scores to learn representations of non-local information.
result The framework effectively adjusts for confounding in air pollution studies.
Structure learning in random fields has attracted considerable attention due to its difficulty and importance in areas such as remote sensing, computational biology, natural language processing, protein networks, and social network analysis. We consider the problem of estimating the probabilistic graph structure associ…
Multioutput Gaussian Processes with Functional Data: A Study on Coastal Flood Hazard Assessmentstat.ML
A new model predicts spatially varying inland flooding from time-varying inputs.
problem Ignoring time series and spatial correlations in flood models leads to inaccurate predictions.
method Introduced a multioutput Gaussian process model with separable kernels for functional inputs and spatial locations.
result The model provides accurate predictions of spatially varying inland flooding with minimal computational time.
Bayesian spatial predictive synthesis improves spatial data predictions.
problem Model misspecification and heterogeneity in spatial data.
method Bayesian ensemble methodology capturing spatially-varying model uncertainty and performance heterogeneity.
result Synthesized predictions outperform standard methods in accuracy and uncertainty quantification.
Novel method embeds generative model into Bayesian optimization for HD cardiac model parameter estimation.
problem High-dimensional optimization of patient-specific cardiac model parameters with limited data.
method Embeds a generative variational auto-encoder into the objective function of Bayesian optimization.
result Improves accuracy of parameter estimation with more than 10x gain in efficiency.
We address the problem of inferring the causal effect of an exposure on an outcome across space, using observational data. The data is possibly subject to unmeasured confounding variables which, in a standard approach, must be adjusted for by estimating a nuisance function. Here we develop a method that eliminates the …
In this paper, we propose a nonlinear distance metric learning scheme based on the fusion of component linear metrics. Instead of merging displacements at each data point, our model calculates the velocities induced by the component transformations, via a geodesic interpolation on a Lie transfor- mation group. Such vel…
Consider a random vector with finite second moments. If its precision matrix is an M-matrix, then all partial correlations are non-negative. If that random vector is additionally Gaussian, the corresponding Markov random field (GMRF) is called attractive. We study estimation of M-matrices taking the role of inverse sec…
Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i) formulation of various graph learning problems, (ii) their probabilistic interpretatio…
New method speeds up sampling of Markov random fields.
problem Efficient sampling of Markov random fields is computationally expensive.
method Introduced a new class of Markov random fields linked to Gaussian Markov Random fields for faster sampling.
result At least 35x faster and 37x less energy consumption compared to Gibbs sampling.
We address the problem of predicting spatio-temporal processes with temporal patterns that vary across spatial regions, when data is obtained as a stream. That is, when the training dataset is augmented sequentially. Specifically, we develop a localized spatio-temporal covariance model of the process that can capture s…
In many state-of-the-art compression systems, signal transformation is an integral part of the encoding and decoding process, where transforms provide compact representations for the signals of interest. This paper introduces a class of transforms called graph-based transforms (GBTs) for video compression, and proposes…
Optimal transport learns Riemannian metrics for evolving probability measures.
problem Learning metrics for evolving probability measures on Riemannian manifolds.
method Neural parametrization of a metric tensor via optimal transport, alternating optimization scheme.
result Improved trajectory inference on scRNA and bird migration data.
New model estimates species population trends from citizen science data.
problem Interannual confounding in citizen science data.
method Double Machine Learning framework to estimate population change and propensity scores for confounding adjustment.
result Spatially detailed trend estimates from citizen science data with low error rates.
New equations reveal how cylinder power in progressive lenses depends on geodesic curvature.
problem Current understanding of cylinder power in progressive lenses is incomplete.
method Derived complete compatibility equations for spatially-varying curvature surfaces.
result Cylinder power depends on geodesic curvature, not just principal curvature.
Knowledge Matters: Importance of Prior Information for Optimization [7], by Gulcehre et. al., sought to establish the limits of current black-box, deep learning techniques by posing problems which are difficult to learn without engineering knowledge into the model or training procedure. In our work, we completely solve…
Derives continuum model from discrete -graphs with connectivity functional.
problem Modeling diffusion in networks with varying connectivity.
method Energy-based continuum limit derivation, neural-network reconstruction of connectivity.
result Error between discrete and continuum energies is , valid even with fluctuations.
Scalable Inference of Sparsely-changing Markov Random Fields with Strong Statistical Guaranteescs.LG
Efficiently infers time-varying sparse MRFs with strong statistical guarantees.
problem Inference of time-varying sparse MRFs with strong statistical guarantees.
method Constrained optimization with exact regularization, near-linear time and memory complexity.
result Sharp statistical guarantees for sparsely-changing Gaussian MRFs with as few as one sample per time.
We study linear models under heavy-tailed priors from a probabilistic viewpoint. Instead of computing a single sparse most probable (MAP) solution as in standard deterministic approaches, the focus in the Bayesian compressed sensing framework shifts towards capturing the full posterior distribution on the latent variab…
We present a neighborhood similarity layer (NSL) which induces appearance invariance in a network when used in conjunction with convolutional layers. We are motivated by the observation that, even though convolutional networks have low generalization error, their generalization capability does not extend to samples whi…
The present work deals with active sampling of graph nodes representing training data for binary classification. The graph may be given or constructed using similarity measures among nodal features. Leveraging the graph for classification builds on the premise that labels across neighboring nodes are correlated accordi…
We design non-singular cloaks enabling objects to scatter waves like objects with smaller size and very different shapes. We consider the Schrodinger equation which is valid e.g. in the contexts of geometrical and quantum optics. More precisely, we introduce a generalized non-singular transformation for star domains, a…
A new model corrects inhomogeneity in Optimal Transport with Boundary.
problem Inhomogeneity in UROT models for Optimal Transport with Boundary.
method Proposed a modified entropic regularization term to make UROT models homogeneous.
result Homogeneous UROT model preserves properties of standard UROT while correcting inhomogeneity.
GeoShapley uses game theory to measure spatial effects in ML models.
problem Measuring the impact of location on machine learning model predictions.
method Extends Shapley value framework to quantify spatial effects in various ML models.
result Validated GeoShapley values against known processes and demonstrated utility in house price modeling.
We present an adaptive regularization algorithm that can be effectively applied to the optimization problem in deep learning framework. Our regularization algorithm aims to take into account the fitness of data to the current state of model in the determination of regularity to achieve better generalization. The degree…
Efficient diffusion model for symmetric manifolds reduces training and computation costs.
problem Heat kernel computations for manifold diffusion models are computationally expensive and infeasible.
method Spatially-varying covariance diffusion model, efficient objective derived via Ito's Lemma.
result Our model reduces training time and arithmetic operations by orders of magnitude.
Bayesian optimization has proven to be a highly effective methodology for the global optimization of unknown, expensive and multimodal functions. The ability to accurately model distributions over functions is critical to the effectiveness of Bayesian optimization. Although Gaussian processes provide a flexible prior o…
Spectral variability is one of the major issue when conducting hyperspectral unmixing. Within a given image composed of some elementary materials (herein referred to as endmember classes), the spectral signature characterizing these classes may spatially vary due to intrinsic component fluctuations or external factors …
Algorithm selects variables and bandwidths for geographically weighted regression.
problem Estimating variable subsets and bandwidths for geographically weighted regression.
method Mathematical programming-based approach integrating variable selection and bandwidth estimation.
result Proposed algorithm provides stable spatially varying patterns with competitive explanatory power.
In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We present two no…
Simultaneous Monitoring of Shape and Surface Color via 4D Point Clouds: A Registration-free Approachcs.CV
A registration-free framework monitors shape and color in 4D point clouds.
problem Monitoring shape and color changes in complex parts without registration.
method Laplace-Beltrami operator spectral properties for geometric and color feature capture; combined monitoring scheme for shape and color anomalies.
result Effective detection of shape deformations and color anomalies without registration or mesh reconstruction.
PDMP samplers improve Bayesian PDE coefficient inference.
problem Efficient Bayesian inference in non-linear inverse problems with expensive likelihoods.
method Piecewise deterministic Markov process (PDMP) with surrogate-assisted thinning.
result PDMP samplers achieve higher accuracy and efficiency than traditional methods.
Mapping the magnetic field using a magnetometer array with noisy input Gaussian process regressionstat.ML
Improves magnetic field mapping using an array of magnetometers with noisy input.
problem Improving magnetic field maps in indoor environments with noisy magnetometer data.
method Uses Gaussian process regression with an array of magnetometers, incorporating known array positions and relative magnetometer locations.
result The method produces higher quality magnetic field maps compared to using a single magnetometer.
A new model predicts financial volatility across firms using spatial correlations.
problem Predicting financial volatility across firms in a network.
method Heterogeneous spatiotemporal GARCH model with local likelihood estimation.
result The model captures spatial spillovers and contagion effects in financial networks.
WNVI solves inverse problems without forward models using neural networks.
problem Solving high-dimensional Bayesian inverse problems based on PDEs.
method WNVI uses weighted residuals and SVI with neural networks to infer state variables and unknowns.
result WNVI is more accurate and efficient than traditional methods and handles ill-posed problems.