Estimates differences in brain connectivity graphs using latent variables.
problem Estimating differences in latent variable graphical models.
method Two-stage procedure: initialization and convergence stages using projected alternating gradient descent.
result Nonconvex procedure outperforms existing methods on synthetic and real data.
We investigate the problem of learning discrete, undirected graphical models in a differentially private way. We show that the approach of releasing noisy sufficient statistics using the Laplace mechanism achieves a good trade-off between privacy, utility, and practicality. A naive learning algorithm that uses the nois…
Paper efficiently infers differential parameters in time-varying models using time score matching.
problem Efficiently inferring differential parameters in time-varying probabilistic models.
method Directly estimates the differential parameter using time score matching and proves consistency of the method.
result Consistent estimation of parameter derivatives in high-dimensional settings.
Paper analyzes multi-attribute data to estimate differences in Gaussian graphical models.
problem Estimating differences in two Gaussian graphical models with similar structure.
method Group lasso penalized D-trace loss function and ADMM algorithm for optimization.
result Consistency in support recovery and estimation in high-dimensional settings established.
Paper estimates differences in multi-attribute Gaussian graphical models using non-convex penalties.
problem Estimating differences in multi-attribute Gaussian graphical models with similar structure.
method Penalized D-trace loss function with non-convex (log-sum and SCAD) penalties, proximal gradient descent methods.
result Theoretical analysis and numerical examples support consistency in support recovery and estimation.
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.
New method for tuning Graphical Lasso hyperparameters.
problem Tuning hyperparameters of Graphical Lasso.
method Bilevel optimization with first-order method.
result Derivation of Graphical Lasso Jacobian.
Paper develops differentially private methods for estimating precision matrices.
problem Estimating precision matrices from sensitive data while maintaining privacy.
method Differential privacy framework, ridge estimator, graphical lasso estimator, ADMM algorithm.
result The proposed methods provide utility in estimating precision matrices from private data.
PACE-GGM uses Gaussian mechanism for private covariance estimation.
problem Private estimation of covariance matrices in high dimensions.
method Data-adaptive selection of entries, Gaussian mechanism, maximum-entropy reconstruction.
result Consistent improvements in estimation error compared to Gaussian mechanism and baselines.
Method estimates differences between two functional graphs.
problem Estimating differences between two functional undirected graphical models.
method Direct estimation of graph difference, avoiding separate estimation.
result Method is consistent in high-dimensional settings.
We present a technique to characterize differentially expressed genes in terms of their position in a high-dimensional co-expression network. The set-up of Gaussian graphical models is used to construct representations of the co-expression network in such a way that redundancy and the propagation of spurious informatio…
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.
Automates hair color digitization using imaging and deep learning.
problem Challenges in capturing and rendering realistic hair colors.
method Combines imaging, path-tracing, and self-supervised machine learning.
result Accurately captures and renders hair color with synthetic images.
SG-PALM learns interpretable tensor models for high-dimensional data.
problem Learning interpretable tensor models for high-dimensional data.
method SG-PALM combines Sylvester generative model and fast proximal alternating linearized minimization.
result SG-PALM converges linearly to global optimum and scales to high dimensions.
Paper develops a consistent algorithm for learning graph structure from continuous-time stochastic differential equations.
problem Learning structure from continuous-time stochastic differential equations.
method Score-based structure learning using Neural Ordinary Differential Equations with adaptive regularization.
result The method consistently recovers directed graphs of local independencies in systems of stochastic differential equations.
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.
This document aims to provide a review on learning with deep generative models (DGMs), which is an highly-active area in machine learning and more generally, artificial intelligence. This review is not meant to be a tutorial, but when necessary, we provide self-contained derivations for completeness. This review has tw…
Directed graphical models (DGMs) are a class of probabilistic models that are widely used for predictive analysis in sensitive domains, such as medical diagnostics. In this paper we present an algorithm for differentially private learning of the parameters of a DGM with a publicly known graph structure over fully obser…
New method controls latent variables in graphical models to improve causal inference and prediction.
problem Uncertainty in causal relationships due to unobserved confounders.
method Iteratively derives proxies for latent variables from model residuals.
result Improves structural inference and prediction performance of causal models.
Many privacy mechanisms reveal high-level information about a data distribution through noisy measurements. It is common to use this information to estimate the answers to new queries. In this work, we provide an approach to solve this estimation problem efficiently using graphical models, which is particularly effecti…
TAMIS improves MIA on synthetic data, reducing cost and requiring less knowledge.
problem Empirical assessment of privacy in machine learning algorithms.
method Improves MAMA-MIA by recovering graphical model from synthetic data and introducing a more accurate attack score.
result TAMIS achieves better or similar performance to MAMA-MIA on synthetic data challenges.
Perfect adaptation in systems is identified and tested using graphical tools.
problem Identifying perfect adaptation in dynamical systems.
method Causal ordering algorithm and graphical representations of dynamical systems.
result Sufficient graphical and testing conditions for perfect adaptation.
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.
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.
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 Γ-convergence. 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.
Based on differential privacy (DP) framework, we introduce and unify privacy definitions for the multi-armed bandit algorithms. We represent the framework with a unified graphical model and use it to connect privacy definitions. We derive and contrast lower bounds on the regret of bandit algorithms satisfying these def…
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently, probabilistic graphical models for reciprocal processes have been provided. This …
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…
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…
We focus on the problem of estimating the change in the dependency structures of two p-dimensional Gaussian Graphical models (GGMs). Previous studies for sparse change estimation in GGMs involve expensive and difficult non-smooth optimization. We propose a novel method, DIFFEE for estimating DIFFerential networks via…
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.
Nonparametric undirected graphical model selection using diffusion models
problem Undirected graphical model selection
method Diffusion models
result Model selection consistency
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.
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.
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.
Paper estimates differences in conditional independence graphs from time-dependent data.
problem Estimating changes in conditional dependencies between two time series with known similar structure.
method Penalized D-trace loss function approach in the frequency domain, using Wirtinger calculus, with convex and non-convex penalties.
result Established sufficient conditions for consistency and graph recovery in high-dimensional settings.
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.
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra)…
Paper presents voxel graph operators for vector data models.
problem Efficient conversion and analysis of geometric models.
method Topological voxelization, graph construction, differential operator derivation.
result Discrete differential and integral operators from voxel complexes.
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.
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…
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…