Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact solution is NP-hard even for a restricted class of Gaussian Markov random fields, calle…
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48 results for “Gaussian Markov fields”
The report explores parameter estimation methods in HMRF and related models.
problem Estimating hyper-parameters in HMRF and related models.
method Metropolis-Hastings algorithm, MCMC, pseudo-likelihood approximation, MAP estimation, EM algorithm.
result Effective parameter estimation methods for HMRF and related models.
Paper calculates KL divergence for isotropic Gaussian-Markov fields.
problem Measuring divergence between isotropic Gaussian-Markov fields.
method Derives closed-form KL divergence expressions.
result Develops new similarity measures in image processing.
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.
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.
New algorithm speeds up image denoising to linear time.
problem Bayesian image denoising with Gaussian Markov Random Field.
method Proposes a new algorithm solving in O(n) time.
result Effective in practice with hyperparameter estimation.
Region detection in Gaussian Markov fields with limited samples.
problem Consistent graph recovery in sample deficient scenarios.
method Partitioning the graph into spatial regions with similar edge parameters and regular boundaries, developing new sample complexity bounds, and introducing an efficient region growing algorithm.
result A bounded number of samples can be sufficient for consistent region recovery.
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.
CMRFs extend PGMs for topological data, capturing both conditional and marginal dependencies.
problem Limited expressiveness of PGMs for topological data.
method Introducing Colored Markov Random Fields (CMRFs) that model Gaussian edge variables on topological spaces.
result CMRFs improve distributed estimation over physical networks compared to baselines.
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.
New algorithm identifies sparse dependencies in non-Gaussian data.
problem Learning sparse probabilistic graphical models in non-Gaussian settings.
method Algorithm based on transport maps and sparsity of graphs.
result Accurately estimates sparse Markov structure of non-Gaussian distributions.
New method controls false discovery rate in learning Gaussian MRF structures.
problem Learning the structure of Gaussian MRFs from data, especially when p >> n, leads to false edges.
method Proposes nsSLOPE using sorted l1-norm regularization to control false discovery rate.
result Controls false discovery rate in learning the structure of Gaussian MRFs.
We adapt a Markov Random Field learning algorithm for continuous variables.
problem Learning sparse pairwise Markov Random Fields with continuous variables.
method Adapted Vuffray et al. (2019) algorithm for continuous variables and provided analysis.
result Sample complexity scales logarithmically with the number of variables.
The paper makes inference methods available for Gaussian models with banded precision.
problem Efficient inference for Gaussian models with banded precision.
method Develops linear algebra operators for banded matrices within automatic differentiation frameworks.
result The operators enable efficient variational inference and gradient-based sampling for Gaussian models with banded precision.
Develops a Markov Random Field model for hypergraphs to improve machine learning tasks.
problem Modeling data generation processes on hypergraphs for better machine learning.
method Hypergraph Markov Random Field model using multivariate Gaussian distribution.
result Proposed model enhances algorithm design and outperforms existing methods in structure inference and node classification.
McCullagh and Yang (2006) suggest a family of classification algorithms based on Cox processes. We further investigate the log Gaussian variant which has a number of appealing properties. Conditioned on the covariates, the distribution over labels is given by a type of conditional Markov random field. In the supervised…
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.
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…
The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models and many others. In this work, we estimate log determinants under the framework o…
PDHAMS improves sampling for discrete distributions with quadratic potential functions.
problem Sampling discrete distributions efficiently and accurately.
method Integrates a second-order approximation of the potential function and uses Gaussian integral trick.
result PDHAMS yields superior performance compared to other methods.
The paper uses MRFs to improve recommendation accuracy in collaborative filtering.
problem Improving recommendation accuracy in collaborative filtering.
method Modeling dependencies via Gaussian Markov Random Fields (MRFs) with auto-normal parameterization and pseudo-likelihood.
result The proposed approach achieved competitive ranking-accuracy and a 20% gain in accuracy on the largest data-set.
Multi-output Gaussian processes (MOGP) are probability distributions over vector-valued functions, and have been previously used for multi-output regression and for multi-class classification. A less explored facet of the multi-output Gaussian process is that it can be used as a generative model for vector-valued rando…
New method reduces model selection sample complexity for geometric graphs.
problem Model selection in Gaussian Markov fields with sample deficiency.
method Introducing spatial stationarity to geometric graphs, developing information-theoretic bounds and efficient reconstruction techniques.
result Spatial stationarity leads to significant reduction in sample complexity for consistent recovery.
New method for fluid approximation of CTMCs without population structure.
problem Approximating the macro-scale behavior of large CTMCs.
method Spectral analysis of CTMC transition matrix, diffusion maps, Gaussian process regression.
result Construct an ODE approximating CTMC mean in continuous space.
Computed tomography (CT) equivalent information is needed for attenuation correction in PET imaging and for dose planning in radiotherapy. Prior work has shown that Gaussian mixture models can be used to generate a substitute CT (s-CT) image from a specific set of MRI modalities. This work introduces a more flexible cl…
A spiking neural network model for probabilistic inference of binary Markov random fields.
problem Implementing probabilistic inference in spiking neural networks.
method Designing a spiking recurrent neural network and proving its equivalence to mean-field inference of binary Markov random fields.
result The spiking neural network model can implement inference of arbitrary binary Markov random fields.
Develops scalable model for learning velocity fields in complex traffic scenarios.
problem Learning heterogeneous and dynamic velocity fields in complex traffic scenarios.
method Nonparametric Bayesian modeling with hierarchical Dirichlet process and infinite hidden Markov model, Gaussian process prior, and scalable approximate inference.
result Demonstrates effective scalability and applicability to real-world traffic data.
New algorithm for collective Gaussian hidden Markov models inference.
problem Inference of collective Gaussian hidden Markov models from aggregate data.
method Collective Gaussian forward-backward algorithm, extending Sinkhorn belief propagation.
result Convergence guarantee and applicability to single individual Kalman filter.
New research shows how preconditioning can solve sparse linear regression problems efficiently.
problem Efficiently solving sparse linear regression problems without restrictive conditions.
method Preconditioned Lasso approach to solve sparse linear regression problems.
result Preconditioning can solve a large class of sparse linear regression problems nearly optimally.
Gaussian BP algorithm converges exponentially under walk summability for cyclic graphs.
problem Convergence rate of Gaussian BP for cyclic graphs.
method Extending known results on walk summability, proving exponential convergence rate.
result Gaussian BP converges exponentially under walk summability for cyclic graphs.
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.
Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals involving the Gaussian prior and non-conjugate likelihoods. Algorithms based on variational Gaussian (VG) approximations are widely employed since they str…
New tree-structured Markov fields with Poisson marginals for counting variables.
problem Counting variables with complex dependencies.
method Tree-structured Markov random fields with Poisson marginals.
result Straightforward sampling and joint probability calculations.
Real world systems typically feature a variety of different dependency types and topologies that complicate model selection for probabilistic graphical models. We introduce the ensemble-of-forests model, a generalization of the ensemble-of-trees model. Our model enables structure learning of Markov random fields (MRF) …
Ancestral graph models, introduced by Richardson and Spirtes (2002), generalize both Markov random fields and Bayesian networks to a class of graphs with a global Markov property that is closed under conditioning and marginalization. By design, ancestral graphs encode precisely the conditional independence structures t…
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.
Paper adapts multiplicative weights method to Gaussian graphical models.
problem Graphical model selection in Gaussian random fields.
method Adapted multiplicative weights method from Ising model to Gaussian model.
result Achieves sample complexity bound similar to existing methods.
Bayesian approach improves ODE solution accuracy.
problem Improving numerical solutions of ordinary differential equations.
method Bayesian inference with Gaussian filtering and smoothing.
result Maximum a posteriori estimate converges to true solution at polynomial rate.
Generalizes bits back coding for time-series models with latent Markov structures.
problem Efficiently compressing time-series data with latent Markov structures.
method Extends bits back coding to time-series models with latent Markov structures, including HMMs and LGSSMs.
result Effective for small scale models, promising for larger scale settings like video compression.
We present some nonparametric methods for graphical modeling. In the discrete case, where the data are binary or drawn from a finite alphabet, Markov random fields are already essentially nonparametric, since the cliques can take only a finite number of values. Continuous data are different. The Gaussian graphical mode…
New invariant metrics preserved under deformed Markov embeddings.
problem Preserving invariance in probability measure spaces under deformed embeddings.
method Deforming Markov embeddings while maintaining sufficiency, proving existence and uniqueness of invariant families.
result Existence and uniqueness of invariant families of tensor fields under deformed embeddings.
Markov models lie at the interface between statistical independence in a probability distribution and graph separation properties. We review model selection and estimation in directed and undirected Markov models with Gaussian parametrization, emphasizing the main similarities and differences. These two model classes a…
We introduce a conceptually novel structured prediction model, GPstruct, which is kernelized, non-parametric and Bayesian, by design. We motivate the model with respect to existing approaches, among others, conditional random fields (CRFs), maximum margin Markov networks (M3N), and structured support vector machines (S…
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…
Novel CMG framework improves financial sentiment forecasting.
problem Challenges in short-term sentiment forecasting of financial OHLC data.
method Integrates chaos theory, Markov chains, and Gaussian processes with transformer models.
result Consistently outperforms traditional models in accuracy and efficiency.
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov Random Field, from very limited samples. We propose a novel algorithm for solving the…
A new HMM model captures kernel dependencies using context-specific Bayesian networks.
problem Traditional HMMs struggle with non-Gaussian data and independence assumptions.
method Kernel density estimation with context-specific Bayesian networks.
result The proposed model outperforms related HMMs in likelihood and classification accuracy.
Efficient spatio-temporal Gaussian process inference method.
problem Scalable Gaussian process inference for multivariate, spatio-temporal data.
method Combines spatio-temporal filtering with natural gradient variational inference, resulting in a scalable non-conjugate GP method.
result Linear scaling with respect to time and logarithmic scaling with respect to time steps.