The idea of computer vision as the Bayesian inverse problem to computer graphics has a long history and an appealing elegance, but it has proved difficult to directly implement. Instead, most vision tasks are approached via complex bottom-up processing pipelines. Here we show that it is possible to write short, simple …
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48 results for “computer graphics”
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.
This paper has partially a novel and partially a survey character. We start with a short review of rack (two term) homology of self distributive algebraic structures (shelves) and their connections to knot theory. We concentrate on a sub-family of quandles satisfying the graphic axiom. For a large family of graphic qua…
This paper contains a summary of mathematical researches of stochastic properties of the long time behavior of a continuously observed (and interactively controlled) quantum--field top. Applications to interactively controlled stochastic computer-graphic dynamical systems are also discussed.
We introduce and study graphic lambda calculus, a visual language which can be used for representing untyped lambda calculus, but it can also be used for computations in emergent algebras or for representing Reidemeister moves of locally planar tangle diagrams.
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…
Neighborhood regression has been a successful approach in graphical and structural equation modeling, with applications to learning undirected and directed graphical models. We extend these ideas by defining and studying an algebraic structure called the neighborhood lattice based on a generalized notion of neighborhoo…
This paper provides efficient algorithms for computing entropy and KL divergence in Bayesian networks.
problem Computing entropy and KL divergence for Bayesian networks efficiently.
method Leveraging the graphical structure of Bayesian networks, the paper provides computationally efficient algorithms.
result Reduces computational complexity of KL divergence from cubic to quadratic for Gaussian BNs.
In Sol space there are three uniparametric groups of isometries. In this work we study constant mean curvature surfaces invariant by one of these groups. We analyze the geometric properties of these surfaces by means of their computer graphics. We construct explicit examples of minimal surfaces and we shall relate …
Computes Lie algebra structure constants using a graphical calculus.
problem Computing Lie algebra structure constants efficiently.
method Graphical calculus for classical invariant theory.
result Generalizes known methods for to other Lie algebras.
Bayesian graphical models have been shown to be a powerful tool for discovering uncertainty and causal structure from real-world data in many application fields. Current inference methods primarily follow different kinds of trade-offs between computational complexity and predictive accuracy. At one end of the spectrum,…
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity constraints on model structures. In this paper, we describe two new approaches to Bay…
Consider jointly Gaussian random variables whose conditional independence structure is specified by a graphical model. If we observe realizations of the variables, we can compute the covariance matrix, and it is well known that the support of the inverse covariance matrix corresponds to the edges of the graphical model…
In this paper, we study the problem of learning the set of pure strategy Nash equilibria and the exact structure of a continuous-action graphical game with quadratic payoffs by observing a small set of perturbed equilibria. A continuous-action graphical game can possibly have an uncountable set of Nash euqilibria. We p…
Develops a graphical calculus for stable curvature invariants.
problem Calculating stable curvature invariants of Riemannian manifolds.
method Graphical calculus based on trivalent graphs with colored edges.
result Derives a curvature identity for compact Einstein manifolds.
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.
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…
Modern treatment of space curve evolutes and involutes.
problem Understanding space curve evolutes and involutes.
method Unified treatment with novel observations and computer graphics.
result Illustration of space curve evolutes and involutes with computer graphics.
Accurate model selection is a fundamental requirement for statistical analysis. In many real-world applications of graphical modelling, correct model structure identification is the ultimate objective. Standard model validation procedures such as information theoretic scores and cross validation have demonstrated poor …
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 …
Learning the hub graphical Lasso model with the structured sparsity via an efficient algorithmmath.OC
Efficiently estimates hub graphical models with structured sparsity.
problem Computational difficulty in fitting graphical models with hub nodes, especially in high-dimensional data.
method Two-phase algorithm: ADMM for initial point generation and SSN-ALM for accurate solution.
result Significantly improves estimation accuracy and efficiency compared to existing methods.
Potential games, originally introduced in the early 1990's by Lloyd Shapley, the 2012 Nobel Laureate in Economics, and his colleague Dov Monderer, are a very important class of models in game theory. They have special properties such as the existence of Nash equilibria in pure strategies. This note introduces graphical…
First DP algorithm for Wasserstein barycenters on private data.
problem Computing Wasserstein barycenters on private datasets.
method Differentially private algorithms for Wasserstein barycenters.
result High-quality private barycenters with strong accuracy-privacy tradeoffs.
New method learns dependencies in high-dimensional data without graph assumptions.
problem Learning dependencies in nonparametric and high-dimensional settings.
method Neighbourhood lattice decomposition for nonparametric CI learning.
result Compact, non-graphical representation of CI exists in any graphical model.
Develops a fast method to learn graph structures from large datasets.
problem Learning graph structures from huge datasets with computational intractability and high complexity.
method Minipatch Graph (MPGraph) estimator: breaks up the problem into minipatches, uses hard thresholding, and integrates hyperparameter tuning.
result Proves graph selection consistency and empirically shows superior accuracy and speed compared to state-of-the-art methods.
New algorithm selects relevant variables in high-dimensional graphical models.
problem Automatic selection of relevant variables in high-dimensional graphical models.
method Extends Chow and Liu's algorithm using mutual information and entropy coefficient of determination.
result Outperforms existing methods in selecting variables with explanatory power.
GPU speeds up Monte Carlo simulations for large time steps.
problem Slow convergence and inaccurate solutions with large time steps in Monte Carlo simulations.
method Generalizes the Seven League scheme for GPU acceleration.
result Significantly improved computational speed.
Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and computer security, etc. Despite of their generic applicability and wide adoptan…
A simple thresholding technique improves graph selection in neural connectivity studies.
problem Graphical model selection for functional neural connectivity in the presence of latent variables.
method Apply a hard thresholding operator to graphical Lasso, neighborhood selection, or CLIME estimators.
result Thresholded estimators outperform existing methods in graph selection consistency and empirical results.
Data visualization and interaction with large data sets is known to be essential and critical in many businesses today, and the same applies to research and teaching, in this case, when exploring large and complex mathematical objects. GAP is a computer algebra system for computational discrete algebra with an emphasis…
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…
Scalable Bayesian Structure Learning for Gaussian Graphical Models Using Marginal Pseudo-likelihoodstat.ME
Bayesian method learns graph structures from Gaussian data efficiently.
problem Scalability issue in Bayesian Gaussian graphical model inference.
method Marginal pseudo-likelihood, birth-death and reversible jump MCMC algorithms.
result Efficient graph structure learning for large graphs with over 1,000 nodes.
We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse inverse covariance (concentration) domain and solve the global eigenvalue problem …
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.
A method to select important experts for Gaussian processes to balance computational efficiency and uncertainty quantification.
problem Balancing computational efficiency and uncertainty quantification in Gaussian processes for big data.
method Using graphical models to select important experts and aggregate their predictions while ensuring uncertainty quantification.
result Substantially reduces computational cost of aggregating dependent experts while ensuring calibrated uncertainty quantification.
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.
Almost all of the work in graphical models for game theory has mirrored previous work in probabilistic graphical models. Our work considers the opposite direction: Taking advantage of recent advances in equilibrium computation for probabilistic inference. We present formulations of inference problems in Markov random f…
Traditional learning methods for training Markov random fields require doing inference over all variables to compute the likelihood gradient. The iteration complexity for those methods therefore scales with the size of the graphical models. In this paper, we propose \emph{block belief propagation learning} (BBPL), whic…
We propose a scalable, efficient and statistically motivated computational framework for Graphical Lasso (Friedman et al., 2007b) - a covariance regularization framework that has received significant attention in the statistics community over the past few years. Existing algorithms have trouble in scaling to dimensions…
Learning Massive-scale Partial Correlation Networks in Clinical Multi-omics Studies with HP-ACCORDstat.ML
Estimates complex dependency structures in multi-omics data.
problem Graphical model estimation from multi-omics data with scalability and consistency.
method Pseudolikelihood-based graphical model framework with -penalized empirical risk.
result Estimates partial correlation network from dual-omic liver cancer data.
A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the structure of such complex data, but performing these inferences is generally difficul…
We address the task of identifying densely connected subsets of multivariate Gaussian random variables within a graphical model framework. We propose two novel estimators based on the Ordered Weighted (OWL) norm: 1) The Graphical OWL (GOWL) is a penalized likelihood method that applies the OWL norm to the lowe…
Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and optimization applications. The problem is of an exponential complexity with respect to t…
Estimates sparse Gaussian graphical models using discrete optimization.
problem Learning a sparse graph from Gaussian graphical models.
method Proposes GraphL0BnB, an -penalized MIP solved with a custom BnB framework.
result Significant runtime and statistical performance improvements over existing methods.
Probabilistic graphical models (PGMs) have become a popular tool for computational analysis of biological data in a variety of domains. But, what exactly are they and how do they work? How can we use PGMs to discover patterns that are biologically relevant? And to what extent can PGMs help us formulate new hypotheses t…
The graphics processing unit (GPU) has emerged as a powerful and cost effective processor for general performance computing. GPUs are capable of an order of magnitude more floating-point operations per second as compared to modern central processing units (CPUs), and thus provide a great deal of promise for computation…
A new method for fast, non-iterative graphical model estimation.
problem Scalability issues in iterative proportional fitting for high-dimensional data.
method Non-iterative approach for positive definite graphical model estimation.
result The proposed method outperforms state-of-the-art methods in high-dimensional settings.
Bayesian method learns network structure from Gaussian process priors.
problem Computational infeasibility of Bayesian structure learning in GPNs.
method Monte Carlo and MCMC methods for sampling network structures.
result Method outperforms state-of-the-art algorithms in recovering network structure.