The paper develops estimators for variance in graph structures using fused lasso.
problem Variance estimation in graph-structured problems.
method Developed linear time estimator for homoscedastic case and total variation regularization estimator for heteroscedastic case.
result Minimax rates and consistency for variance estimation in various graph structures.
This paper tackles variance issues in GNN training by proposing a method to reduce both embedding and gradient variances.
problem High variance in estimating stochastic gradients in GNN training, especially in large graphs.
method The paper proposes a decoupled variance reduction strategy that employs approximate gradient information to adaptively sample nodes with minimal variance.
result The proposed method achieves faster convergence and better generalization compared to existing sampling methods.
New method discovers mean and variance causal graphs from heteroscedastic data.
problem Understanding causal relationships in data with varying variance.
method Bayesian, moment-driven approach inferring separate mean and variance causal graphs.
result Accurately recovers mean and variance structures from heteroscedastic data.
New methods solve graph sparsity optimization problems faster.
problem Complex graph sparsity optimization problems in disease outbreak monitoring and social network analysis.
method Stochastic variance-reduced gradient-based methods GraphSVRG-IHT and GraphSCSG-IHT.
result Our methods achieve linear convergence speed.
New algorithm for training GNNs with learned weights.
problem Optimal sampling for GNNs with learned weights is intractable.
method Formulated as an adversary bandit problem, optimizing exploration and exploitation.
result Asymptotically approaches optimal variance within a factor of 3.
This paper presents a bias-variance tradeoff of graph Laplacian regularizer, which is widely used in graph signal processing and semi-supervised learning tasks. The scaling law of the optimal regularization parameter is specified in terms of the spectral graph properties and a novel signal-to-noise ratio parameter, whi…
A new aggregation strategy improves GNN performance and learning dynamics.
problem Improving expressivity and learning dynamics of GNNs.
method Proposes a variance-preserving aggregation function (VPA) for GNNs.
result VPA leads to increased predictive performance and improved learning dynamics.
ES-Single uses ES to estimate gradients in unrolled graphs, reducing variance and improving performance.
problem Estimating gradients in unrolled computation graphs with low variance and stability.
method Evolution strategies (ES) applied to unrolled graphs, with a single perturbation per particle.
result ES-Single reduces variance compared to PES, leading to better performance in various tasks.
New algorithm detects changes in high-dimensional data with mean and variance.
problem Challenges in detecting changes in high-dimensional data with mean and variance.
method Complete graph-based approach to detect changes of mean and variance from low to high-dimensional online data.
result The proposed method outperforms existing methods in terms of detection power.
AB-SAGA optimizes distributed optimization over directed graphs using variance reduction and stochastic weights.
problem Optimizing distributed stochastic optimization over directed graphs with stochastic weights.
method AB-SAGA combines variance reduction and network-level gradient tracking, using both row and column stochastic weights.
result AB-SAGA converges linearly to the global optimal with a constant step-size and achieves a linear speed-up over centralized methods.
We propose Gaussian processes for signals over graphs (GPG) using the apriori knowledge that the target vectors lie over a graph. We incorporate this information using a graph- Laplacian based regularization which enforces the target vectors to have a specific profile in terms of graph Fourier transform coeffcients, fo…
Proposes deep graph persistence to address neural persistence issues in deep learning.
problem Variance of weights and lack of spatial structure in deep neural networks impact neural persistence.
method Extends neural persistence to the whole network, considering interactions between layers.
result Deep graph persistence alleviates variance-related issues and captures persistent paths through the network.
In this paper, we prove that some Gaussian structural equation models with dependent errors having equal variances are identifiable from their corresponding Gaussian distributions. Specifically, we prove identifiability for the Gaussian structural equation models that can be represented as Andersson-Madigan-Perlman cha…
Improves performance of deep GCNs by controlling node feature variance.
problem Performance degradation in deep Graph Convolutional Networks (GCNs).
method Experimentally examined the role of TRANs and PROPs in GCNs, introduced Node Normalization (NodeNorm).
result Node Normalization effectively controls node feature variance, improving GCN performance in deep models.
Push-SAGA is a decentralized algorithm for directed graphs that converges linearly.
problem Finite-sum minimization over directed graphs with stochastic gradients.
method Combines variance reduction, gradient tracking, and consensus algorithms.
result Achieves linear convergence for smooth and strongly convex problems.
Storchastic improves stochastic AD for complex models in RL and VI.
problem Handling intractable expectations in RL and VI.
method Introduces Storchastic, a framework for AD of stochastic computation graphs with various gradient estimation methods.
result Provable unbiasedness and variance reduction for higher-order gradients.
We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model, there is a directed acyclic graph describing the relationships between the variables. In Gaussian structu…
This work explores the relationship between expressivity and generalization in GNNs.
problem Understanding the trade-off between expressivity and generalization in GNNs.
method Introducing a novel framework that connects GNN generalization to the variance in graph structures they can capture.
result Theoretical findings align with empirical results, offering a deeper understanding of how expressivity enhances GNN generalization.
PES method reduces bias in gradient estimation for unrolled graphs.
problem High variance and bias in gradient estimation for unrolled computation graphs.
method Divide graph into unrolls, apply ES update, accumulate correction terms.
result PES provides unbiased, low-variance gradient estimates.
Polynomial-time algorithm learns causal graphs without parametric assumptions.
problem Learning causal graphs from data without assuming linearity or parametric forms.
method Model-free polynomial-time algorithm with finite-sample guarantees.
result Algorithm achieves linear cost in dimension and samples compared to optimal.
A new method for efficient portfolio optimization using graph structures.
problem Optimizing portfolio weights while reducing computational complexity.
method Hierarchical graph structures and Schur complement method.
result Optimal portfolio weights can be computed efficiently by inverting small submatrices.
The paper studies eigenvalues of graph Laplacians on data clouds and proves central limit theorems.
problem Asymptotic fluctuations of eigenvalues of graph Laplacians on data clouds.
method Analysis of graph Laplacian operator, asymptotic fluctuations, central limit theorems.
result Central limit theorems for eigenvalues of graph Laplacians are proven.
We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike, graphs these have some counter-intuitive properties, specifically in the limit of lar…
Bayesian method recovers causal structure in SEMs with equal error variances.
problem Recovering causal structure in SEMs with equal error variances.
method Bayesian DAG selection method using g-priors and the key property of minimum expected squared errors.
result The method consistently recovers the true graph without additional distributional assumptions.
This work relaxes GNN symmetries to approximate automorphisms, improving model performance.
problem Improving graph neural network performance on asymmetric graphs.
method Formalizing approximate symmetries via graph coarsening, introducing a bias-variance formula.
result Best generalization performance achieved by choosing a larger symmetry group than automorphisms but smaller than permutations.
Proposes SDE framework for uncertainty quantification in graph neural networks.
problem Lack of uncertainty quantification in graph neural networks.
method Introduces Latent Graph Neural Stochastic Differential Equations (LGNSDE) with Bayesian prior-posterior mechanism and Brownian motion.
result LGNSDEs provide theoretically sensible guarantees for uncertainty estimates and are robust to perturbations.
An algorithm finds optimal covariates for blocking in randomized experiments.
problem Minimizing variance in causal effect estimates from heterogeneous data.
method Using causal graphs, an algorithm identifies optimal covariates for blocking.
result An efficient algorithm reduces variance in causal effect estimates.
Study optimal adjustment sets for causal policies with hidden variables.
problem Estimating dynamic treatment regimes with hidden variables.
method Developed criteria for graphs without hidden variables to compare estimators, extended to dynamic policies and hidden variables.
result Existence and computation of optimal minimal and globally optimal adjustment sets.
LARGE adapts regularization for better graph estimation in high-dimensional data.
problem Challenges in selecting optimal regularization parameters for graph estimation.
method Locally Adaptive Regularization for Graph Estimation (LARGE) that adapts nodewise penalties.
result LARGE consistently outperforms benchmark methods in graph recovery and estimation accuracy.
Paper learns DAGs with quadratic variance functions efficiently.
problem Learning DAGs with quadratic variance functions.
method Introduces topological layers to reconstruct DAGs hierarchically.
result Efficient algorithm reduces computational cost.
GCNs improve regression tasks by aggregating neighbor signals.
problem GCNs' statistical properties in regression tasks are poorly understood.
method Examined two GCN convolutions and their impact on learning error.
result GCNs have a bias-variance trade-off that depends on neighborhood size and topology.
Study the averaging estimator on graphs with labeled nodes.
problem Understanding the quality of averaging estimators on graph data.
method Rigorously study concentration properties, variance bounds, and risk bounds.
result Contributes to theoretical understanding of graph learning.
Study improves understanding of network degree distributions using non-linear ERGs.
problem Lack of models capable of accounting for the variance of empirical degree distributions.
method Defined a fitness-induced variant of the two-star model to reproduce sample variance.
result Non-linear ERGs can reproduce the sample variance of empirical degree distributions.
Stochastic computation graphs (SCGs) provide a formalism to represent structured optimization problems arising in artificial intelligence, including supervised, unsupervised, and reinforcement learning. Previous work has shown that an unbiased estimator of the gradient of the expected loss of SCGs can be derived from a…
BSG learns dynamic network spillovers and uncertainty quantification.
problem Identifying indirect spillovers and systemic risk in dynamic networks.
method Bayesian Spillover Graphs using FEVD and Bayesian time series models.
result Significant performance gains over baselines in identifying source and sink nodes.
Proposes ENVAR for causal discovery in structural VAR models with equal noise variance.
problem Challenges in causal discovery from multivariate time series with contemporaneous effects.
method Introduces observational equivalence and the observational alignment discrepancy for structural VAR models with equal noise variance.
result Shows that multiple structural VAR parameterizations can induce the same stationary observed process law.
Proposes a new method for big portfolio selection using graph-based conditional moments.
problem Challenges in selecting portfolios for thousands of stocks.
method Graph-based Conditional Moments (GRACE) method: learns quantiles, means, variances, skewness, and kurtosis of stock returns.
result Shows superior performance compared to competitors, especially in measures of conditional variance, skewness, and kurtosis.
In this paper, we propose a perturbation framework to measure the robustness of graph properties. Although there are already perturbation methods proposed to tackle this problem, they are limited by the fact that the strength of the perturbation cannot be well controlled. We firstly provide a perturbation framework on …
Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of training examples. We analyse a challenging problem in the area of non-parametric inf…
HDT improves MCMC on graphs with history-dependent sampling.
problem Efficient sampling from target distributions on general graphs with low computational overhead.
method History-driven target (HDT) framework that replaces the original target distribution with a history-dependent one.
result Near-zero variance performance and scalability to large graphs with memory-efficient implementation.
Learning DAG or Bayesian network models is an important problem in multi-variate causal inference. However, a number of challenges arises in learning large-scale DAG models including model identifiability and computational complexity since the space of directed graphs is huge. In this paper, we address these issues in …
The reparameterization trick enables optimizing large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random variable with fixed distribution. After refactoring, the gradients of the loss propag…
Random features are improved by variance-reducing couplings, enhancing machine learning models.
problem Improving the efficiency and accuracy of random features in machine learning.
method Using optimal transport theory to find couplings that reduce variance in random features.
result Theoretical and practical gains in efficiency and accuracy for various machine learning models.
Paper explores exact recovery of communities in weighted graphs using Gaussian and exponential distributions.
problem Exact recovery of communities in weighted graphs with Gaussian and exponential distributions.
method Introduces a new semi-metric to describe conditions for exact recovery and analyzes conditions for both complete and incomplete graphs.
result Necessary and sufficient conditions for exact recovery are asymptotically tight and applicable to both complete and incomplete graphs.
Proposes counterfactual explainability for causal attribution, extending variance analysis methods.
problem Lack of mechanistic understanding in existing tools for explaining complex models.
method Extends global sensitivity analysis methods to causal explanations using directed acyclic graphs.
result Developed methods to estimate counterfactual explainability and applied to income inequality analysis.
While loopy belief propagation (LBP) performs reasonably well for inference in some Gaussian graphical models with cycles, its performance is unsatisfactory for many others. In particular for some models LBP does not converge, and in general when it does converge, the computed variances are incorrect (except for cycle-…
Improved EXACT strategy reduces GNN memory consumption and runtime.
problem Efficiently training large-scale GNNs with reduced memory usage.
method Block-wise quantization of intermediate activation maps with improved variance minimization.
result Further reduction in memory consumption (>15%) and runtime speedup (5%) with similar performance trade-offs.
New distribution simplifies covariance matrix inference.
problem Efficient inference for covariance matrices in large models.
method Incorporates Inverse G-Wishart distribution for variational message passing.
result Elegant and succinct expression of variational message passing fragments.