We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank algorithm, recently introduced in the literature. The mechanics of di…
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48 results for “linear propagator”
Susceptibility Propagation by Using Diagonal Consistencycond-mat.stat-mech
Improved susceptibility propagation for Markov random fields using diagonal matching.
problem Approximate computation of Markov random fields with robustness across network structures.
method Combines belief propagation and linear response method with diagonal matching for inverse Ising problems.
result Proposed method reduces to standard susceptibility propagation and Thouless-Anderson-Palmer equation in specific cases.
This paper proposes an alternating back-propagation algorithm for learning the generator network model. The model is a non-linear generalization of factor analysis. In this model, the mapping from the continuous latent factors to the observed signal is parametrized by a convolutional neural network. The alternating bac…
LNPE enhances local connections in embeddings using extended neighbor propagation.
problem Improving local connections and interactions in nonlinear dimensionality reduction.
method Inspired by GCN, LNPE extends 1-hop neighbors to n-hop neighbors in LLE.
result LNPE produces more faithful and robust embeddings with better topological and geometrical properties.
Study various numerical methods for expectation propagation in machine learning.
problem Improving the convergence and stability of the expectation propagation algorithm for large-scale learning tasks.
method Numerical approximation strategies including Laplace method, Gaussian quadrature, and variational sampling.
result Variational sampling yields the best convergence for the expectation propagation algorithm in training linear binary classifiers.
New method CROWN-IBP combines IBP and CROWN for efficient verifiable robust neural networks.
problem Training verifiably robust neural networks is challenging and computationally expensive.
method CROWN-IBP combines interval bound propagation and linear relaxation for efficient training.
result CROWN-IBP achieves significant improvements in verifiable robustness on MNIST and CIFAR datasets.
The interconnected wealth of nations: Shock propagation on global trade-investment multiplex networksphysics.soc-ph
Model quantifies how global economic shocks propagate through interconnected trade and investment networks.
problem Understanding and predicting the global propagation of economic crises.
method Coupled epidemic and internal contagion dynamics on a multiplex network of trade and investment interactions.
result Linear relation between a country's shock magnitude and its global impact, influenced by internal contagion and intercountry propagation.
New -BP algorithm improves belief propagation for graphs with loops.
problem Uncertainty in belief propagation for graphs with loops.
method Derive -BP algorithm motivated by minimizing -divergence.
result Proves convergence conditions for -BP.
Paper learns dynamic generator models for video sequences.
problem Modeling spatial-temporal processes like dynamic textures and actions.
method Alternating back-propagation through time algorithm to learn latent state vectors and generator model.
result Trains realistic models for dynamic textures and actions.
Gaussian BP converges geometrically for pairwise linear Gaussian models.
problem Analyzing convergence of Gaussian belief propagation for pairwise linear Gaussian models.
method Analytical study of updating information matrix and belief mean vector convergence.
result Gaussian BP converges geometrically to a unique positive definite matrix.
The paper proposes a scalable framework for uncertainty quantification and propagation in surrogate-based Bayesian inference.
problem Uncertainty in surrogate models and its impact on inference and decision-making.
method Bayesian inference methods for surrogate models with measurement data.
result Scalable framework for uncertainty quantification and propagation in surrogate models.
Develops a new approach to study nonlinear PDEs and their singularities.
problem Understanding the propagation domains of solutions to nonlinear PDEs.
method Derived geometric machinery and sheaf theory to study nonlinear PDEs and their singular supports.
result Estimates the domains of propagation for solutions of non-linear systems.
IIC decouples causal identification into two phases, significantly reducing the HTC gap in linear SEMs.
problem Determining causal effect coefficients in linear SEMs with latent confounders using the Half-Trek Criterion (HTC) leaves a gap of inconclusive causal effects.
method Iterative Identification Closure (IIC) framework that decouples causal identification into two phases: a seed function S_0 and Reduced HTC propagation.
result IIC strictly subsumes both HTC and ancestor decomposition, reducing the HTC gap by over 80% with combined seeds.
Study finds price impact is universal in anonymous markets.
problem Understanding price impact in anonymous electronic markets.
method Analysis of proprietary dataset and linear propagator model.
result Magnitude and time dependence of price impact are universal in anonymous markets.
The back-propagation algorithm is widely used for learning in artificial neural networks. A challenge in machine learning is to create models that generalize to new data samples not seen in the training data. Recently, a common flaw in several machine learning algorithms was discovered: small perturbations added to the…
Endogenous business cycles explain higher comovement across countries.
problem Standard models struggle to explain high comovement in business cycles across countries.
method Developed a demand-driven reduced-form model with strategic complementarities and international trade linkages.
result Combining endogenous business cycles with exogenous shocks matches empirical comovement levels.
A decentralized MARL algorithm for value propagation in non-linear settings.
problem Decentralized coordination in multi-agent systems with different local rewards.
method Decentralized optimization and value propagation algorithm.
result Non-asymptotic convergence rate of 1/T in nonlinear function approximation.
Improved accuracy in community detection with vertex labels.
problem Efficient inference in stochastic block models with vertex labels.
method Linearized belief propagation algorithm with vertex labels.
result Belief propagation achieves highest accuracy when a function of network parameters has a unique fixed point.
Proposes a method to estimate neural network statistics analytically for normalization.
problem Estimating statistics of hidden units in neural networks for better initialization and normalization.
method Analytic moment propagation of mean and variance through the network structure.
result Analytic estimates of statistics are useful for initialization and normalization, independent of batch input.
The paper uses belief propagation to analyze rankings and partial orders from partial information.
problem Analyzing rankings and partial orders from incomplete data.
method Continuous spin system and belief propagation algorithm.
result Computes marginal distribution and approximates number of linear extensions.
New method identifies extreme risk propagation in financial networks.
problem Understanding extreme risk in financial networks.
method Max-linear structural equation model, hard-thresholding, Hamming distance.
result Sparse DAG for extreme risk propagation estimated.
Two graph auto-encoders decouple feature propagation from graph convolution layers.
problem Designing efficient graph auto-encoders with fixed receptive fields.
method L-GAE and L-VGAE using linear matrix computation before auto-encoder input.
result Comparable performance to VGAEs with smaller, simpler networks.
Bayesian model for sparse regression with spatial-temporal structure.
problem Sparse linear regression with spatio-temporal constraints.
method Hierarchical Gaussian process prior and Expectation Propagation algorithm.
result Model successfully applied to real data.
Paper analyzes convergence of distributed inference using BP in linear Gaussian models.
problem Distributed inference convergence in linear Gaussian models.
method Factor graphs, Gaussian belief propagation, local computation, message passing.
result Message information matrix converges to a unique positive definite limit matrix at a doubly exponential rate.
Study probabilistic safety of BNNs under adversarial attacks.
problem Evaluate vulnerability of BNNs to adversarial attacks.
method Relaxation techniques from non-convex optimization to compute probabilistic safety bounds.
result Certify probabilistic safety of BNNs with millions of parameters.
A framework for designing and evaluating new GCN variants.
problem Designing and evaluating new graph convolutional network (GCN) variants.
method Propose a framework to compose networks using building blocks of GCN.
result Several newly composed variants are useful alternatives and competitive with original GCNs.
Proposes a new deep learning model for uncertainty quantification and propagation.
problem High-dimensional uncertainty quantification and propagation problems.
method Integrates U-net with Gaussian Gated Linear Network (GGLN) to create GLU-net.
result Less complex architecture with 44% fewer parameters than existing models.
Constructs a solution operator for hyperbolic gluing in higher dimensions.
problem Solving the linearized constant scalar curvature equation at hyperbolic space.
method Constructs a solution operator with good support propagation properties.
result Extends the Mao-Oh-Tao gluing method to the hyperbolic setting, gaining two derivatives.
Bayesian EP solves CS problems more accurately than other methods.
problem Finding sparse solutions to underdetermined linear systems with constraints.
method Bayesian inference with Expectation Propagation (EP) for marginal distribution computation.
result EP outperforms other methods in solving CS problems with correlated sensing matrices.
Exact inference in the linear regression model with spike and slab priors is often intractable. Expectation propagation (EP) can be used for approximate inference. However, the regular sequential form of EP (R-EP) may fail to converge in this model when the size of the training set is very small. As an alternative, we …
New method improves neural network verification by considering multivariate input space of ReLU neurons.
problem Improving the effectiveness of neural network verification algorithms.
method A new tightened convex relaxation for ReLU neurons considering multivariate input space.
result Our convex relaxation is significantly stronger than the commonly used univariate-input relaxation.
Improved Gaussian Process model for predicting trajectories without independence assumption errors.
problem Incorrect independence assumption in previous work on Gaussian Process uncertainty propagation.
method Proposed a novel piecewise linear approximation to correct the independence assumption in continuous models.
result Corrected the independence assumption in Gaussian Process models for predicting trajectories.
It is known that fixed points of loopy belief propagation (BP) correspond to stationary points of the Bethe variational problem, where we minimize the Bethe free energy subject to normalization and marginalization constraints. Unfortunately, this does not entirely explain BP because BP is a dual rather than primal algo…
Paper proposes methods to reduce financial contagion by targeted cash injections.
problem Financial contagion through interconnected networks.
method Dynamic model of payments with external control term for corrective cash injections.
result Targeted cash injections can significantly reduce default propagation.
State Space Expectation Propagation: Efficient Inference Schemes for Temporal Gaussian Processesstat.ML
Unified framework for efficient Gaussian process inference.
problem Efficient inference in non-conjugate Gaussian process models.
method Combines expectation propagation with linearization for improved efficiency.
result Unified view of various inference schemes, including classical smoothers and EP.
Two EP frameworks ensure integrable beliefs in Bayesian estimation problems.
problem Non-integrable beliefs in EP can lead to infeasible solutions.
method Proposes two EP frameworks to keep messages non-integrable.
result Ensures integrable beliefs in EP, even with non-integrable messages.
Two new algorithms improve Q* approximation in batch RL with linear error propagation.
problem Improving Q* approximation in batch reinforcement learning.
method Two novel algorithms that estimate Bellman error directly, without quadratic dependence.
result Linear-in-horizon error propagation for batch RL algorithms.
New methods for uncertainty in neural networks with leaky ReLU activations.
problem Uncertainty in feed-forward neural networks with random input perturbations.
method Analytical expressions for PDF and moments of neural network output, linearization of leaky ReLU, Gaussian copula surrogate models.
result Accurate statistical results for large input perturbations, excellent agreement with Monte Carlo simulations.
A Framework for Analyzing Cross-correlators using Price's Theorem and Piecewise-Linear Decompositioncs.LG
The paper proposes new cross-correlators using Price's Theorem and piecewise-linear decomposition.
problem Optimal method for estimating cross-correlations using finite samples.
method General mathematical framework using Price's Theorem and piecewise-linear decomposition.
result Some cross-correlators based on Huber's loss functions, MP functions, and LSE functions have higher SNR.
Deep networks trained with Hebbian updates perform similarly to back-propagation on image datasets.
problem Training deep networks with realistic asymmetric connections and updates.
method Use Hebbian updates with separate feedforward and feedback weights, and local rule for updates.
result Similar performance to back-propagation achieved with Hebbian updates on challenging image datasets.
Unified diffusive bounds for non-linear parabolic equations.
problem Proving diffusive upper bounds for parabolic equations.
method Simple exponential deformation argument.
result Unified diffusive upper bounds for a wide class of non-linear parabolic equations.
We introduce a new class of lower bounds on the log partition function of a Markov random field which makes use of a reversed Jensen's inequality. In particular, our method approximates the intractable distribution using a linear combination of spanning trees with negative weights. This technique is a lower-bound count…
GP-SUM filters complex non-Gaussian states using Gaussian Processes.
problem Stochastic dynamic filtering and state propagation with complex beliefs.
method GP-SUM combines sampling and probabilistic Bayes filters, using Gaussian Processes for dynamic and observation models.
result GP-SUM outperforms other filters on benchmarks and predicts non-Gaussian states accurately.
Identifies root causes of outliers in unknown cyclic graphs.
problem Outliers in unknown cyclic graphs with linear structural equations.
method Identifies a short list of potential root causes based on strong perturbation and structural equations.
result The shortlist includes true root causes and their parents on the cycle.
Graph neural network simplifies to linear model with attention mechanisms.
problem Semi-supervised learning with limited labeled data.
method Proposes a graph neural network removing fully-connected layers and replacing them with attention mechanisms.
result Attention-based graph neural network outperforms existing methods on benchmark datasets.
Market impact is a key concept in the study of financial markets and several models have been proposed in the literature so far. The Transient Impact Model (TIM) posits that the price at high frequency time scales is a linear combination of the signs of the past executed market orders, weighted by a so-called propagato…
Deep learning framework for uncertainty quantification in physics.
problem Uncertainty in systems governed by non-linear differential equations.
method Physics-informed neural networks with adversarial inference.
result Effective training of deep generative models for physical systems.
It is of increasing importance to develop learning methods for ranking. In contrast to many learning objectives, however, the ranking problem presents difficulties due to the fact that the space of permutations is not smooth. In this paper, we examine the class of rank-linear objective functions, which includes popular…