TGGM models nonlinear learning using truncated Gaussian variables.
problem Designing statistical models for nonlinear learning.
method Introducing TGGM, integrating latent nonnegative variables, using EM algorithm, breaking inference into TGGM problems.
result TGGM models induce non-Gaussian, nonlinear relations among variables.
Paper introduces a new GGM variant for efficient inference and unsupervised learning.
problem Limited modeling abilities of traditional Gaussian graphical models.
method Introduces a novel variant of Gaussian graphical models with truncated normal distributions and bipartite structure.
result Efficient inference and unsupervised learning capabilities demonstrated.
The paper efficiently estimates parameters from truncated Gaussian and linear models.
problem Estimating parameters from truncated Gaussian and linear models.
method Minimizes finite population negative log-likelihood function with an l1-regularization term.
result Efficient estimation of parameters from truncated samples.
Unified probabilistic framework for nonlinearities in neural networks.
problem Lack of a unified approach to incorporating nonlinearities in neural networks.
method Doubly truncated Gaussian distributions for generating various nonlinearities.
result Performance improvements in RBM, temporal RBM, and TGGM when nonlinearities are learned alongside weights.
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 methods for scalable causal discovery from complex data.
problem Learning causal structures from nonlinear, continuous or mixed data.
method BF-BIC score and BF-LRT test for scalable causal discovery.
result BF-BIC score and BF-LRT test enable scalable causal discovery with competitive accuracy and runtime.
Optimal algorithm learns Gaussian under halfspace truncation with minimal samples.
problem Learning a Gaussian distribution truncated to an unknown halfspace.
method Efficient algorithm using n = i l d e O ( d 2 / ε 2 ) n = ilde{O}(d^2/\varepsilon^2) n = i l d e O ( d 2 / ε 2 ) samples and runtime dominated by empirical covariance matrix computation. result Optimal sample and time complexity bounds for learning a Gaussian under halfspace truncation.
Proposes a new method to improve estimation in Gaussian graphical models.
problem Optimal estimation in high-dimensional Gaussian graphical models.
method Graphical nonconvex optimization, approximated by a sequence of convex programs.
result Achieves the oracle rate of convergence and outperforms other methods.
High-dimensional inference for sparse spectral precision matrices
problem Inference on the spectral precision matrix at a fixed frequency
method Full likelihood-based inference using neighboring discrete Fourier transforms
result Simultaneous control of regularization, finite-sample truncation, and smoothing biases
Estimates unnormalized models with missing data using imputation and noise contrastive estimation.
problem Statistical models with intractable normalization constants and missing data.
method Combines imputation techniques with estimators for unnormalized models like noise contrastive estimation and score matching.
result Effective statistical inference with unnormalized models from missing data.
The paper analyzes and mitigates biases in scalable Gaussian Process methods.
problem Modeling biases in scalable Gaussian Process methods.
method Randomized truncation estimators to eliminate bias in exchange for increased variance.
result Randomized truncation estimators meaningfully outperform biased counterparts with minimal additional computation.
Algorithm estimates Gaussian parameters under unknown truncation sets.
problem Estimating Gaussian parameters when samples are truncated to unknown sets.
method Efficient algorithm for arbitrary unknown truncation sets, using Gaussian surface area as complexity measure.
result Algorithm works for large families of sets including intersections of halfspaces and general convex sets.
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…
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.
Optimal statistical test for identifying edges in Gaussian graphical models.
problem Identifying the correct edges in Gaussian graphical models from a sample.
method Developed a Neyman-type multiple decision procedure to minimize the combined error rates of Type I and Type II errors.
result The developed procedure is optimal, minimizing the linear combination of Type I and Type II error rates.
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.
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.
Paper proves almost all Gaussian graphical models are perfect.
problem Determining when Gaussian graphical models are perfect.
method Direct approach to Gaussian graphical models, extending Lněnička and Matúš's construction.
result Almost all Gaussian graphical models are perfect.
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.
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.
Lower bound shows super-polynomial gap for estimating truncated Gaussian means.
problem Estimating mean of truncated Gaussian distribution with limited samples.
method Statistical Query (SQ) lower bounds for learning.
result Super-polynomial information-computation gap for the task.
This paper addresses the problem of scalable optimization for L1-regularized conditional Gaussian graphical models. Conditional Gaussian graphical models generalize the well-known Gaussian graphical models to conditional distributions to model the output network influenced by conditioning input variables. While highly …
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 sampling method for leaky RBM using Gaussian annealing.
problem Sampling from leaky RBM with numerical stability issues.
method Anneal leakiness from Gaussian to ReLU units.
result Efficient sampling with improved likelihood estimation and faster mixing.
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.
Bayesian method learns Gaussian graphical models without decomposability constraints.
problem Learning non-decomposable Gaussian graphical models efficiently and accurately.
method Fractional pseudo-likelihood and sparsity-inducing prior.
result Consistent estimator of graph structure for high-dimensional data.
Introduces a new model for directed relationships in Gaussian data.
problem Learning directed relationships in Gaussian data.
method Developed a new directed graphical model (GGIM) from Gaussian data, leveraging stationary Gaussian processes on graphs.
result GGIMs can be framed as a LASSO problem and have a bound on the difference from the l 1 l_1 l 1 -norm penalized maximum log-likelihood estimate. 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.
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.
The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gauss…
The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically d…
Efficiently clusters nodes in Gaussian graphical models from data.
problem Clustering nodes in Gaussian graphical models directly from data.
method Clusters nodes based on the similarity of their network neighborhoods defined by partial correlations. Uses matrix factors for limited data.
result Demonstrates improved clustering of nodes in Gaussian graphical models.
Proposes PLA-GGM for estimating variable associations with confounders.
problem Estimating associations between variables distorted by confounders.
method Partially linear additive Gaussian graphical model (PLA-GGM) with L 1 L_1 L 1 -regularized maximal pseudo-profile likelihood estimator (MaPPLE). result Proves n \sqrt{n} n -sparsistency and superior performance in synthetic and real-world datasets. Estimates multiple dependent Gaussian graphical models for gene expression data.
problem Dependence among gene expression data from different tissues and the whole body.
method Decomposes the problem into systemic and category-specific layers, estimates them jointly using graphical EM.
result Estimation consistency and selection sparsistency of the proposed estimator.
New Bayesian method uses momentum-space renormalization for image modeling.
problem Bayesian image modeling challenges in Gaussian graphical models.
method Combines marginal likelihood maximization with momentum-space renormalization.
result Scheme for computing hyperparameters and mean square errors.
The paper shows cross-validation fails in learning Gaussian graphical model structures.
problem Cross-validation's failure in learning Gaussian graphical model structures.
method Finite-sample bounds on misidentification probability of Lasso estimator.
result Cross-validation is inconsistent for learning Gaussian graphical model structures.
Proposes a method to estimate sparse Gaussian graphical models with hidden clustering structure.
problem Modeling statistical relationships between variables with sparsity and clustering.
method Two-phase algorithm using sGS-ADMM for initial point and pALM for solution.
result Demonstrates good performance and efficiency of the proposed model and algorithm on synthetic and real data.
Paper compares two methods for inferring network structures in presence of latent confounders.
problem Inferring network structures in presence of latent confounders.
method Gaussian graphical models with latent variables (LVGGM) and PCA-based removal of confounding (PCA+GGM).
result Proposes a new method combining strengths of LVGGM and PCA+GGM, proving consistency and convergence rate.
Unified framework for mean testing under truncation bias.
problem High-dimensional mean testing under arbitrary truncation.
method Characterizes fundamental limits and develops a simple second-order test.
result Unified framework connects finite-moment, sub-Gaussian, and median-regular structural regimes.
In this paper, we propose a semiparametric approach, named nonparanormal skeptic, for efficiently and robustly estimating high dimensional undirected graphical models. To achieve modeling flexibility, we consider Gaussian Copula graphical models (or the nonparanormal) as proposed by Liu et al. (2009). To achieve estima…
Two algorithms learn Gaussian graphical models from Glauber dynamics trajectories.
problem Learning Gaussian graphical models from dependent data.
method Two complementary approaches: local edge-testing and burn-in/thinning reduction.
result Both approaches provide finite-sample recovery guarantees and empirical comparisons.
ISEE method efficiently estimates large precision matrices in Gaussian graphical models.
problem Estimating large precision matrices in ultra-large Gaussian graphical models.
method ISEE method combines sparse modeling and large covariance matrix estimation.
result ISEE method can recover graphical structure with significant probability and efficient estimation of link strengths.
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…
k-means derived from Gaussian mixture models with isotropic Gaussians.
problem Clustering with Gaussian mixture models.
method Truncated variational EM approximations applied to Gaussian Mixture Models.
result k-means is a special case of variational EM for Gaussian Mixture Models.
We provide a correction to the expression for scoring Gaussian directed acyclic graphical models derived in Geiger and Heckerman [Ann. Statist. 30 (2002) 1414-1440] and discuss how to evaluate the score efficiently.
Novel method for learning Gaussian graphical models from paired data.
problem Learning Gaussian graphical models for dependent groups.
method Introducing twin order to explore the search space more efficiently.
result The twin order makes the model space a distributive lattice, leading to more efficient model exploration.
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…
Surveying joint Gaussian graphical models to identify shared structures across domains.
problem Estimating shared structures across different data sources.
method Statistical inference of joint Gaussian graphical models.
result Improved estimation power for high-dimensional data.