Constant-time approximation of partition functions for dense models.
problem Approximating partition functions in dense graphical models efficiently.
method Combining techniques from Markov Chain Monte Carlo and Variational Methods.
result An O(εn) additive approximation of the log partition function found in constant time. New solver MPLP++ outperforms existing solvers for dense graph models.
problem Efficiently solving dense, discrete Graphical Models with pairwise potentials.
method Dual Block-Coordinate Ascent with MPLP++ modification.
result MPLP++ significantly outperforms existing solvers, including TRWS.
Estimating tree structured Gaussian Graphical Model from noisy data.
problem Recover the original independence structure from noisy observations.
method Address the unidentifiability of tree structured graphical models and provide an algorithm to find the equivalence class of trees.
result An O(n^3) algorithm to find the equivalence class of trees.
OpenGM is a C++ template library for defining discrete graphical models and performing inference on these models, using a wide range of state-of-the-art algorithms. No restrictions are imposed on the factor graph to allow for higher-order factors and arbitrary neighborhood structures. Large models with repetitive struc…
New framework infers sparse inter-subject connections from dense intra-data.
problem Inferring sparse inter-subject connections from dense intra-data in neuroscience.
method Gaussian graphical models, alternative parameter estimation, and chord procedure for inference.
result Asymptotic consistency of estimator and inference method without sparsity assumption.
We analyze the sample complexity of learning graphical games from purely behavioral data. We assume that we can only observe the players' joint actions and not their payoffs. We analyze the sufficient and necessary number of samples for the correct recovery of the set of pure-strategy Nash equilibria (PSNE) of the true…
Two new estimators find groups of correlated variables in Gaussian models.
problem Identifying densely connected subsets of multivariate Gaussian variables.
method Proposes Graphical OWL (GOWL) and column-by-column Graphical OWL (ccGOWL) estimators based on the Ordered Weighted L1 (OWL) norm.
result Both methods can identify highly correlated groups and control sparsity in precision matrices.
Spectral sparsification improves Gaussian graphical models under MTP2 constraints.
problem Learning accurate, sparse graphs from data under MTP2 constraints.
method Spectral graph sparsification applied to Gaussian graphical models.
result Spectral-MTP2 preserves MTP2 and approximates the original model well.
This paper proposes a new randomized strategy for adaptive MCMC using Bayesian optimization. This approach applies to non-differentiable objective functions and trades off exploration and exploitation to reduce the number of potentially costly objective function evaluations. We demonstrate the strategy in the complex s…
We present a new notion of probabilistic duality for random variables involving mixture distributions. Using this notion, we show how to implement a highly-parallelizable Gibbs sampler for weakly coupled discrete pairwise graphical models with strictly positive factors that requires almost no preprocessing and is easy …
FuDGE estimates differences between functional graphs in high-dimensional settings.
problem Estimating differences between two undirected functional graphical models with shared structures.
method FuDGE: A method that directly estimates the functional differential graph without first estimating individual graphs.
result FuDGE consistently estimates the functional differential graph in high-dimensional settings.
Unified CI test for categorical and ordinal data maintains power in high dimensions.
problem Rapid degradation of statistical power in existing CI tests for high-dimensional conditioning variables.
method Unified CI test for categorical and ordinal data, maintaining reasonable calibration and power in high dimensions.
result Our test outperforms existing baselines in model testing and structure learning for dense directed graphical models.
Scalable method learns context-specific models for hundreds of variables.
problem Learning context-specific models for large numbers of variables.
method Order-based Markov chain Monte-Carlo search with context-specific sparsity assumption.
result Method scales to hundreds of variables and learns accurate models.
Sparse sampling method for tensor factorization and completion of high rank tensors.
problem Completion of high rank tensors with missing data in recommendation systems.
method Sparse measurements and message-passing algorithms in a high-dimensional limit.
result Theoretical insights and performance analysis of tensor factorization in dense limit.
New DL approach reveals feature construction in dense samples.
problem Understanding deep learning's effectiveness across diverse applications.
method High-density sample task with 5 unique tokens, 500 exemplars per token.
result Emergence of category structure and feature detectors observed.
The paper proposes using low rank assumption to improve causal structure learning in DAGs.
problem Challenges in learning causal structures in high-dimensional, non-sparse DAGs.
method Exploits low rank assumption of DAG adjacency matrix to adapt causal structure learning methods.
result Maximum rank is highly related to hubs, suggesting low rank for scale-free networks.
A new method learns complex dynamical systems from data efficiently.
problem Learning complex dynamical systems from large-scale data efficiently.
method Low-rank structured variational autoencoding framework for nonlinear Gaussian state-space models.
result Consistently demonstrates better predictive capabilities compared to other models.
Graphical lasso may fail to fit models when data points are insufficient.
problem When does graphical lasso fail to select and fit a graphical model?
method Computational experiments with graphical lasso.
result Graphical lasso may fail when the number of data points is less than the maximum likelihood threshold.
We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In this paper, we propose the graphical nonconvex optimization for optimal estimat…
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly…
Paper introduces a nonparametric functional graphical model for random functions.
problem Estimating probabilistic conditional independence in functional graphical models.
method Functional sufficient dimension reduction to relax Gaussian or copula Gaussian assumptions.
result Enhances estimation accuracy and retains probabilistic conditional independence.
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model. Especially, graphical models provide the following several useful properties: - Graphi…
Graphical models improve portfolio optimization for financial time series.
problem Optimizing portfolios with time-varying covariance patterns.
method Various graphical models (PCA-KMeans, autoencoders, dynamic clustering, structural learning) to capture covariance matrix patterns.
result Graphical models outperform baseline methods in generating steady returns with low risk.
Paper estimates non-causal graphical models using covariance extension and transportation distance.
problem Estimating non-causal graphical models with smoothing relations.
method Proposes a covariance extension problem and uses transportation distance to minimize error with white noise.
result Solution is a double-sided autoregressive non-causal graphical model.
Graphical models and tensor networks are shown to be dual.
problem No specific problem stated; focuses on the duality between models.
method Study of tensor hypernetworks on hypergraphs and their correspondence to graphical models.
result Tensor hypernetworks on hypergraphs correspond to graphical models of the dual hypergraph.
rags2ridges simplifies graphical modeling of high-dimensional data.
problem Graphical modeling of high-dimensional precision matrices.
method Modular framework for extraction, visualization, and analysis of Gaussian graphical models.
result Provides a one-stop-shop for graphical modeling of high-dimensional precision matrices.
Nonparametric undirected graphical model selection using diffusion models
problem Undirected graphical model selection
method Diffusion models
result Model selection consistency
Bayesian method for estimating functional graphical models from neuroimaging data.
problem Estimating dependence structures from functional data in neuroscience.
method Fully Bayesian regularization scheme, including direct Bayesian analog of functional graphical lasso and graphical horseshoe.
result Insight into brain compensation after traumatic brain injury.
AGM uses adversarial approach for robust prediction in structured prediction problems.
problem Structured prediction problems with complex relationships between variables.
method Adversarial Graphical Models (AGM) for distributionally robust prediction.
result AGM achieves Fisher consistency and flexibility in loss metrics.
Method solves Gaussian graphical models on ladder graphs efficiently.
problem Solving Gaussian graphical models on ladder graphs efficiently.
method Proposes a method that depends on the position of zeros in local covariance matrices.
result Efficiently solves Gaussian graphical models on ladder graphs under certain conditions.
New framework models complex spatial data with basis functions and graphical vectors.
problem Modeling highly-multivariate spatial processes with varying resolutions.
method Extends graphical lasso to multivariate Gaussian processes with independent graphical vectors at different resolutions, using an orthogonal basis and fusion penalty.
result Linear complexity and parsimonious conditional independence structure in multilevel graphical model.
ECM algorithm estimates graphical models efficiently in high dimensions.
problem Bayesian graphical models in high-dimensional settings are computationally infeasible.
method ECM algorithm using mixture priors for posterior exploration.
result ECM approach enables fast posterior exploration and incorporates multiple sources of information.
A new graphical model for discrete data without parametric restrictions.
problem Discrete data modeling with restrictions.
method Additive conditional independence and penalized estimation of precision operator.
result Consistency of the estimator in ultrahigh-dimensional settings.
Novel model selection method outperforms current state-of-the-art in high-dimensional graphical models.
problem Accurate model selection in high-dimensional graphical models.
method Graphical Neighbour Information (GNI) criterion.
result Demonstrates oracle performance in high-dimensional model selection, outperforming current methods.
This paper addresses the problem of neighborhood selection for Gaussian graphical models. We present two heuristic algorithms: a forward-backward greedy algorithm for general Gaussian graphical models based on mutual information test, and a threshold-based algorithm for walk summable Gaussian graphical models. Both alg…
Graphical classifier handles model uncertainty with Bayesian model averaging.
problem Model selection uncertainty in Bayesian classification.
method Particle Gibbs strategy for posterior sampling from decomposable graphical models.
result Proposed classifier outperforms standard Bayesian and other classifiers.
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit computationally convenient factorization properties and have long been a valuable tool for t…
We propose a general modeling and inference framework that composes probabilistic graphical models with deep learning methods and combines their respective strengths. Our model family augments graphical structure in latent variables with neural network observation models. For inference, we extend variational autoencode…
New method for estimating functional Gaussian graphical models for multivariate data.
problem Challenges in extending Gaussian graphical models to multivariate functional data due to compact covariance operators.
method Introducing partial separability for multivariate functional data, leading to a novel Karhunen-Loève expansion and efficient estimation through the joint graphical lasso.
result A well-defined functional Gaussian graphical model that can be identified with a sequence of finite-dimensional graphical models, each of identical fixed dimension.
New method aggregates nodes in sparse graphical models.
problem Estimating edge-sparse graphical models.
method Tree-aggregated graphical lasso (tag-lasso) method.
result Aggregates nodes in a data-driven fashion using a tree.
Graphical-GAN combines Bayesian networks and GANs for structured data modeling.
problem Modeling structured data with complex dependencies.
method Integrates Bayesian networks and GANs, introduces structured recognition model, and generalizes EP algorithm.
result Successfully learns discrete and temporal structures on visual datasets.
New graphical criteria for efficient covariate adjustment in non-parametric causal models.
problem Estimating population average treatment effects in observational studies using non-parametric causal graphical models.
method Developed new graphical criteria to determine efficient covariate adjustment sets for estimating treatment effects in non-parametric causal graphical models.
result Graphical criteria for efficient covariate adjustment can be applied in both linear and non-parametric causal models.
The paper develops methods to assess and correct model uncertainties in graphical models.
problem Model uncertainty in probabilistic graphical models.
method Information-theoretic and non-parametric stress tests.
result Ranking and correcting impactful sources of uncertainty in graphical models.
We consider the task of estimating a Gaussian graphical model in the high-dimensional setting. The graphical lasso, which involves maximizing the Gaussian log likelihood subject to an l1 penalty, is a well-studied approach for this task. We begin by introducing a surprising connection between the graphical lasso and hi…
New method scores DAGs by identifying unobserved confounding.
problem Unobserved confounding complicates causal discovery.
method Score-based causal discovery algorithm that accounts for unobserved confounding.
result Sparse linear Gaussian DAGs can be recovered from observed data.
Develops a nonparametric graphical model for conditional independence.
problem Evaluation of conditional independence without distributional assumptions.
method Nonlinear sufficient dimension reduction techniques applied to a nonparametric graphical model.
result Method outperforms existing methods in non-Gaussian settings and high-dimensional data.
Pen-and-paper exercises cover various machine learning topics.
problem None explicitly stated, focuses on learning through exercises.
method Pen-and-paper exercises on machine learning topics.
result Comprehensive coverage of machine learning concepts through exercises.
Layered graphical models improve discriminative learning efficiency.
problem Improving discriminative learning efficiency in graphical models.
method Designing layered graphical models (LGMs) in analogy to neural networks, using tensorized truncated variational inference and backpropagation.
result LGMs achieve competitive results in image classification, comparable to neural networks.