We consider the problem of learning the structure of a pairwise graphical model over continuous and discrete variables. We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to structure learning. In previous work, authors have considered structure learning of…
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48 results for “discrete pairwise graphical models”
Sparse logistic regression recovers any discrete pairwise graph model.
problem Recovering the Markov graph of discrete pairwise graphical models.
method Maximum conditional log-likelihood with convex optimization.
result The algorithm can recover any arbitrary discrete pairwise graphical model.
This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by the lasso. We present the Condition-on-Selection method that allows for valid s…
We investigate a generic problem of learning pairwise exponential family graphical models with pairwise sufficient statistics defined by a global mapping function, e.g., Mercer kernels. This subclass of pairwise graphical models allow us to flexibly capture complex interactions among variables beyond pairwise product. …
In this paper, we address the problem of learning the structure of a pairwise graphical model from samples in a high-dimensional setting. Our first main result studies the sparsistency, or consistency in sparsity pattern recovery, properties of a forward-backward greedy algorithm as applied to general statistical model…
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.
In this paper we consider the problem of learning undirected graphical models from data generated according to the Glauber dynamics. The Glauber dynamics is a Markov chain that sequentially updates individual nodes (variables) in a graphical model and it is frequently used to sample from the stationary distribution (to…
Generalized Root Models: Beyond Pairwise Graphical Models for Univariate Exponential Familiesstat.ML
We present a novel k-way high-dimensional graphical model called the Generalized Root Model (GRM) that explicitly models dependencies between variable sets of size k > 2---where k = 2 is the standard pairwise graphical model. This model is based on taking the k-th root of the original sufficient statistics of any univa…
The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when this algorithm will perform well. Using recent analysis of convergence and stabilit…
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 …
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.
New method learns discrete graphical models efficiently.
problem Learning discrete graphical models with minimal data.
method Interaction Screening framework for fully general discrete factor models.
result Provably learns model structure and parameters with rigorous guarantees.
Graphically discrete groups have strong rigidity properties.
problem Understanding the rigidity of group actions on graphs.
method Introducing graphical discreteness and proving rigidity properties.
result Free products of graphically discrete groups are action rigid.
Learn true model from metastable samples of discrete distributions.
problem Learning true model from samples that get stuck in metastable states.
method Conditional likelihood estimator based on strong metastability condition.
result True model can be recovered from metastable samples of discrete distributions.
Quantum method generates unbiased samples from discrete graphical models.
problem Sampling from discrete graphical models is challenging and intractable in high dimensions.
method Embedding graphical models into unitary operators and using quantum circuits.
result Provably generates unbiased and independent samples from general discrete factor models.
While graphical models for continuous data (Gaussian graphical models) and discrete data (Ising models) have been extensively studied, there is little work on graphical models linking both continuous and discrete variables (mixed data), which are common in many scientific applications. We propose a novel graphical mode…
We consider the problem of estimating undirected triangle-free graphs of high dimensional distributions. Triangle-free graphs form a rich graph family which allows arbitrary loopy structures but 3-cliques. For inferential tractability, we propose a graphical Fermat's principle to regularize the distribution family. Suc…
Unifying DAGs and UGsstat.ML
We introduce a new class of graphical models that generalizes Lauritzen-Wermuth-Frydenberg chain graphs by relaxing the semi-directed acyclity constraint so that only directed cycles are forbidden. Moreover, up to two edges are allowed between any pair of nodes. Specifically, we present local, pairwise and global Marko…
Hybrid framework combines PGMs and TNs for complex probabilistic modeling.
problem Combining quantum-like correlations into PGM models.
method Introducing decoherence to convert probabilistic TN models into PGMs.
result Hybrid models can represent and combine strengths of both PGMs and TNs.
A simple graphical model for correlated defaults is proposed, with explicit formulas for the loss distribution. Algebraic geometry techniques are employed to show that this model is well posed for default dependence: it represents any given marginal distribution for single firms and pairwise correlation matrix. These t…
We examine the effect of clamping variables for approximate inference in undirected graphical models with pairwise relationships and discrete variables. For any number of variable labels, we demonstrate that clamping and summing approximate sub-partition functions can lead only to a decrease in the partition function e…
Duality in Graphical Modelsmath.PR
Graphical models have proven to be powerful tools for representing high-dimensional systems of random variables. One example of such a model is the undirected graph, in which lack of an edge represents conditional independence between two random variables given the rest. Another example is the bidirected graph, in whic…
Researchers derive Markov properties of discrete DPPs.
problem Lack of statistical properties exploration for discrete DPPs.
method Derive Markov properties using graphical models.
result Markov properties of discrete DPPs can be expressed.
Improved score matching for non-negative data models.
problem Estimating parameters of non-negative probability density functions.
method Generalized score matching method for non-negative data.
result Improved estimation efficiency and theoretical guarantees.
We consider the problem of estimating the topology of spatial interactions in a discrete state, discrete time spatio-temporal graphical model where the interactions affect the temporal evolution of each agent in a network. Among other models, the susceptible, infected, recovered () model for interaction events fal…
Proposes SGM for modeling complex dependencies in high-dimensional systems.
problem Limited pairwise interactions in PGMs for high-dimensional systems.
method Simplicial Gaussian model (SGM) using discrete Hodge theory and independent random components.
result Maximum-likelihood inference algorithm for parameter recovery and conditional dependence structure.
Novel SVAE learns interpretable discrete data representations from deep learning.
problem Learning interpretable discrete data representations from deep learning.
method Structured variational autoencoder (SVAE) with novel optimization algorithms.
result First competitive comparisons with state-of-the-art time series models.
The paper tackles fairness in estimating graphical models, especially for protected attributes.
problem Fairness issues in estimating graphical models, particularly for sensitive characteristics.
method Integrates pairwise graph disparity error and a tailored loss function into a multi-objective optimization problem.
result Successfully mitigates bias in graphical model estimation without compromising model performance.
GTMs model complex multivariate data with varying conditional independencies.
problem Modeling multivariate data with intricate marginals and complex dependency structures.
method Semiparametric approach using penalized splines and lasso regularization.
result GTMs accurately learn complex dependencies and identify conditional independencies.
Fair GLASSO estimates fair GGMs by balancing statistical dependencies across groups.
problem Fairness in graphical models with biased data.
method Regularized graphical lasso with bias metrics, proximal gradient algorithm.
result Preserves statistical accuracy while promoting fairness across groups.
The sum-product or belief propagation (BP) algorithm is a widely-used message-passing algorithm for computing marginal distributions in graphical models with discrete variables. At the core of the BP message updates, when applied to a graphical model with pairwise interactions, lies a matrix-vector product with complex…
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.
Pairwise fairness for ranking and regression models.
problem Ensuring fairness in ranking and regression models with protected groups and attributes.
method Developed pairwise fairness metrics for ranking and regression, using constrained optimization and robust optimization techniques.
result Efficient and effective solutions for training problems, demonstrated through experiments.
Discrete geometry model approximates Willmore energy.
problem Approximating the Willmore energy for triangulated surfaces.
method A discrete energy defined in the spirit of discrete differential geometry converges to the Willmore energy.
result The discrete energy converges to the Willmore energy in the sense of -convergence.
This paper presents the R package gRapHD for efficient selection of high-dimensional undirected graphical models. The package provides tools for selecting trees, forests and decomposable models minimizing information criteria such as AIC or BIC, and for displaying the independence graphs of the models. It has also some…
We describe a mathematical link between aspects of information theory, called pairwise comparisons, and discretized gauge theories. The link is made by the notion of holonomy along the edges of a simplex. This correspondance leads to open questions in both field.
We propose Graphical Generative Adversarial Networks (Graphical-GAN) to model structured data. Graphical-GAN conjoins the power of Bayesian networks on compactly representing the dependency structures among random variables and that of generative adversarial networks on learning expressive dependency functions. We intr…
Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one is for likelihood maximization in discrete chain factor graphs, which we define …
In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a hypergraph exactly corresponds to the graphical model given by the dual hypergraph. …
Python toolbox uncovers causal relationships from data.
problem Discovering causal relationships from observational data.
method End-to-end approach using algorithms from 'Bnlearn' and 'Pcalg', including pairwise causal discovery.
result Recovery of direct dependencies and causal relationships.
NeurISE uses neural nets to learn graphical models efficiently.
problem Efficiently learning graphical models with high-order terms.
method NeurISE, a neural net-based algorithm that approximates interaction screening objective function.
result NeurISE can find parsimonious representations without prior information.
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…
PGMax: Factor Graphs for Discrete Probabilistic Graphical Models and Loopy Belief Propagation in JAXcs.LG
PGMax automates PGM inference on GPUs, improving quality and speed.
problem Efficient inference in complex discrete PGMs.
method Factor graph specification and loopy belief propagation in JAX.
result Higher-quality inference with up to 3x speedups.
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…
In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by -separation on such graphs are compositional graphoids. We focus in particular on the subclass of rib…
Bayesian inference of discrete component states in civil infrastructures using PGMs and GNNs.
problem Inferring discrete states of civil infrastructure components from measurable responses is an ill-posed inverse problem.
method The study proposes a novel Bayesian inversion paradigm based on Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs). PGMs are used to model the problem, with parameters learned from data and structural topology prior. Inference is accomplished by GNNs, and a graph property-based training strategy is developed.
result The proposed framework effectively solves the challenges of inferring the posterior PDF for discrete variables in high-dimensional problems.
We propose a method that performs anomaly detection and localisation within heterogeneous data using a pairwise undirected mixed graphical model. The data are a mixture of categorical and quantitative variables, and the model is learned over a dataset that is supposed not to contain any anomaly. We then use the model o…
Learning Planar Ising Modelsstat.ML
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of …