Improved speech recognition with TRF models combining with NN models.
problem Improving speech recognition accuracy.
method Interpolating trans-dimensional random field (TRF) models with neural network (NN) models.
result 12.1% and 17.9% relative error rate reductions for English and Chinese speech recognition respectively.
Improved neural TRF LMs for speech recognition with NCE and CNN integration.
problem Training inefficiency of neural TRF LMs on large training corpora.
method Reformulated TRFs, noise-contrastive estimation, CNN integration.
result Successful and efficient training on a 40x larger dataset with 1/3 training time and 4.7% WER reduction.
Neural TRFs improve speech recognition models with fewer parameters and faster inference.
problem Improving speech recognition models with fewer resources.
method Introducing neural TRFs that use nonlinear potentials with continuous features implemented by neural networks, combined with efficient inference techniques.
result Neural TRFs outperform discrete TRFs and LSTM LMs with fewer parameters and faster inference.
Improved neural language models trained with dynamic noise-contrastive estimation.
problem Training large-scale language models efficiently and avoiding overfitting.
method Dynamic Noise-Contrastive Estimation (DNCE) to train neural trans-dimensional random field language models.
result DNCE reduces training cost and improves model performance on large datasets.
Unified framework for efficient trans-dimensional Bayesian inference using VI and NFs.
problem Efficient trans-dimensional Bayesian inference with reduced computational cost.
method Variational inference with normalizing flows to train transport proposals.
result Our approach minimizes reverse KL divergence and reduces computational cost.
New PDMP samplers tackle variable selection in models.
problem Jointly explore model space and parameter space.
method Develop reversible jump PDMP samplers.
result New samplers mix better and are more efficient.
EFDM models spatial point processes with variable cardinality using existence variables.
problem Challenges in extending diffusion models to variable-cardinality spatial point processes.
method Existence-field diffusion model (EFDM) that jointly models spatial locations and cardinality without discrete transitions.
result EFDM achieves improved modeling capability on datasets with varying cardinality.
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.
Generative model handles varying data dimensions using jump diffusion processes.
problem Handling data of varying dimensionality in generative models.
method Formulated as a jump diffusion process, learning to approximate the process with a novel evidence lower bound.
result Effective sampling of data of varying dimensionality, better compatibility with test-time diffusion guidance imputation tasks.
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.
Study on spin random fields using chaos decomposition for cosmic microwave background modeling.
problem Modeling polarization of Cosmic Microwave Background using spin random fields.
method Explicit Wiener-Itô chaos decomposition of area measures of level sets.
result Reveals a clear difference between high frequency regime and zero spin case.
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…
Study on Gaussian random fields' singularities on manifolds.
problem Understanding singularities of Gaussian random fields on manifolds.
method Computed expected values of singularities under various conditions.
result Explicit formulae for singularities under different constraints.
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.
Develops a new model for cross-currency derivatives pricing.
problem Pricing cross-currency derivatives in a complex market model.
method Introduces a random field LIBOR market model to handle uncertainty in forward LIBOR rates.
result Derives exact and approximate pricing formulas for various derivatives.
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.
Study on points where random spherical harmonic nodal set meets tangent vector field.
problem Distribution of points on nodal sets of random spherical harmonics.
method Analysis of expected counting function and eigenvalue asymptotics.
result Asymptotic behavior of counting function is independent of the vector field.
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.
Study of cosmic microwave background polarization using spin random fields.
problem Detecting deviations from Gaussianity and anisotropies in cosmic fields.
method Explicit formula for Lipschitz-Killing curvatures of spin spherical random fields.
result Coherent with asymptotic results, providing new metric expressions.
Existence of strong randomized equilibria in mean-field games with common noise.
problem Existence of strong solutions in mean-field games of optimal stopping.
method Connection with Bank-El Karoui's representation problem and continuity assumptions.
result Existence of strong randomized mean-field equilibrium under certain conditions.
New framework models neural systems with random architecture on manifolds.
problem Complex, uncertain systems with non-Gaussian outputs.
method Latent random field on compact manifold generates neural architecture and weights.
result Synthetic neural systems can produce stochastic outputs for deterministic inputs.
The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising models with homogeneous pairwise potentials but arbitrary (inhomogeneous) unary pot…
New method calculates geodesic distances in Gaussian random field manifolds.
problem Quantifying similarity between random fields in different regimes.
method Numerical method using geodesic distances in Gaussian random field manifolds.
result Estimation of geodesic distances for various initial conditions.
Random Gaussian fields on 4D Riemannian manifolds with conformal invariance.
problem Characterizing and analyzing Gaussian fields on 4D Riemannian manifolds.
method Constructing and analyzing co-biharmonic Gaussian fields with covariance kernels defined by the Paneitz operator.
result Rigorous derivation of quantum Liouville measure for ∣ γ ∣ < 8 |γ|<\sqrt8 ∣ γ ∣ < 8 . Loopy belief propagation (LBP), which is equivalent to the Bethe approximation in statistical mechanics, is a message-passing-type inference method that is widely used to analyze systems based on Markov random fields (MRFs). In this paper, we propose a message-passing-type method to analytically evaluate the quenched a…
Gradient descent in Gaussian random fields helps understand high-dimensional optimization problems.
problem Understanding high-dimensional optimization problems in deep learning.
method Modeling loss functions as Gaussian random fields and analyzing gradient descent.
result Gradient descent's improved loss function distribution and moments are analyzed and shown to be asymptotically normal.
Random Fourier features model reconstructs wind fields from sparse measurements.
problem Reconstructing wind fields from limited data.
method Random Fourier features approximating velocity field with adaptive sampling.
result Random Fourier features model outperforms benchmarks.
A new method uses SPDEs to efficiently model random fields on complex domains.
problem Efficient representation of random fields on complex domains for engineering and machine learning.
method Uses SPDEs to develop a scalable framework for statFEM and GP regression.
result Can model anisotropic, non-stationary random fields with arbitrary smoothness.
The paper characterizes the geometry and topology of spin random fields.
problem Understanding the expected geometry and topology of spin random fields.
method Investigating the asymptotic behavior of geometric and topological functionals for spin random fields under scaling assumptions.
result Explicit results for monochromatic fields, showing non-universal asymptotic behavior and new generalized models.
DiAL uses Bayesian Dirichlet random fields for active learning with sparse labels.
problem Active learning with limited labeled data.
method Bayesian Dirichlet random field for feature-conditional class probabilities, calibrating with graph Laplacian.
result Competitive performance in low-label rate graph learning tasks.
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.
Improved susceptibility propagation for Markov random fields using diagonal matching.
problem Approximate computation of Markov random fields with robustness across network structures.
method Combines belief propagation and linear response method with diagonal matching for inverse Ising problems.
result Proposed method reduces to standard susceptibility propagation and Thouless-Anderson-Palmer equation in specific cases.
Bounds on Gaussian approximation for neural networks with novel smoothing techniques.
problem Approximating the distribution of wide random neural networks.
method Stein's method, Gaussian smoothing, Laplacian operators, Cameron-Martin space.
result First bounds on Gaussian approximation of wide random neural networks.
New method estimates multivariate Gaussian fields using sparse precision matrix.
problem Estimating covariance matrices for large multivariate Gaussian fields.
method Sparse Precision Matrix Selection (SPS) algorithm for multivariate GRFs.
result Theoretical rates of convergence for estimated covariance and parameters validated.
Study a risk model with tree-structured Poisson-Markov random field for rainfall events.
problem Dependence between rainfall frequencies in insurance portfolios.
method Tree-structured Markov random field with Poisson marginals.
result Asymptotic results for portfolio risk and risk allocation.
Reconstructing signature features from randomized vector fields in differential equations.
problem Reconstructing signature features from controlled differential equations with random vector fields.
method Using controlled ordinary differential equations driven by continuous bounded variation curves, the study explores the extent to which signature features can be reconstructed from the non-linear flow of these equations.
result The number of signature features that can be reconstructed from the non-linear flow of controlled ordinary differential equations with random vector fields is exponential in the hidden dimension, under certain conditions.
A novel framework combines deep metric learning and conditional random field for hyperspectral image classification.
problem Improving classification performance in hyperspectral image processing with limited labeled data.
method Combines spectrum-based deep metric learning and conditional random field. Uses center loss for spectrum-based features and Gaussian edge potentials for pixel-wise classification.
result Demonstrates advantages in classification accuracy and computation cost compared to classical methods.
Study on nodal components of random band-limited functions on surfaces, finding a universal law.
problem Distribution of tangencies of nodal components to a vector field on surfaces.
method Analysis of random band-limited functions on smooth compact Riemannian surfaces with vector fields.
result The distribution of tangencies to a vector field on nodal components of random band-limited functions on surfaces follows a universal deterministic law.
New test detects sparse alternatives in Gaussian random fields.
problem Detecting sparse alternatives in Gaussian random fields.
method Ad-hoc Kac Rice formula for second maximum distribution, exact spacing test.
result Exact t t t -spacing test for high power in detecting sparse alternatives. BBPL uses block updates to learn Markov random fields without full inference.
problem Training Markov random fields requires inference over all variables, scaling with model size.
method Block-coordinate updates of approximate marginals to compute approximate gradients.
result BBPL converges to the same solution as full inference, despite approximations.
Study on the smoothness of solutions to a specific type of stochastic differential equation.
problem Regularity of solutions to mean-field G G G -SDEs. method Analysis of first and second order Fréchet differentiability in the random initial condition.
result Established the Fréchet differentiability of the solution and specified the corresponding equations.
Consider a random smooth Gaussian field G ( x ) : F → R G(x):F\to\mathbb{R} G ( x ) : F → R , where F F F is a compact in R d \mathbb{R}^d R d . We derive a formula for average area of a surface generated by the equation G ( x ) = 0 G(x)=0 G ( x ) = 0 and give some applications. As an auxiliary result we obtain an integral expression for area of a surface induced by zeros of a \e…
Random neural networks mapped to statistical physics models.
problem Design questions about neural networks.
method Mapped random neural networks to lattice models in statistical physics.
result Large scale behavior of random neural networks approximated by effective field theory.
Enhances GNN robustness during inference using Conditional Random Fields.
problem Vulnerability of GNNs to adversarial attacks.
method Post-hoc approach using Conditional Random Fields (CRF).
result Improves robustness of GNNs across various models.
The paper develops methods for high-dimensional inference in Markov random fields.
problem Statistical inference for high-dimensional Markov random fields.
method Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMC-MLE) with Elastic-net regularization.
result The proposed methods achieve ℓ 1 \ell_{1} ℓ 1 -consistency and false discovery rate control. 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.
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.
Eryn is a versatile MCMC package for Bayesian inference.
problem Bayesian inference for parameter estimation and model selection.
method Markov Chain Monte Carlo (MCMC) algorithm integrated into a user-friendly toolbox.
result Eryn can handle a wide range of Bayesian inference problems, from simple to complex.