New models infer causal effects from graph-based time-series data.
problem Inferring causal effects from graph-based relational time-series data.
method Proposes causal inference models leveraging graph topology and time-series data.
result Relational time-series causal inference models accurately estimate local causal effects of individual nodes.
This chapter covers methods for identifying and inferring graph topologies.
problem Identifying and inferring graph topologies from multidimensional relational data.
method Overview of methods including correlation metrics, covariance selection, kernels, structural equations, and vector autoregressions.
result Supports both batch and online learning with convergence guarantees and leverages high-order statistical information.
Proposes GIL for semi-supervised graph classification.
problem Semi-supervised classification of graph data with limited labeled nodes.
method Graph Inference Learning framework that learns node label inference from graph topology.
result Significantly improves semi-supervised node classification performance.
Novel TRI-GNN framework improves graph classification robustness.
problem Graph neural networks suffer from over-smoothing and vulnerability to graph perturbations.
method Integrates higher-order graph information via persistent homology and local graph structure learning.
result TRI-GNN outperforms state-of-the-art baselines on node classification tasks.
Network science provides valuable insights across numerous disciplines including sociology, biology, neuroscience and engineering. A task of major practical importance in these application domains is inferring the network structure from noisy observations at a subset of nodes. Available methods for topology inference t…
Novel algorithm learns sparse signal representations over topological spaces.
problem Sparse representation of signals over combinatorial topological spaces.
method Leveraging Hodge theory, the paper embeds topology into a dictionary structure via concatenated sub-dictionaries, each as a polynomial of Hodge Laplacians, and optimizes the dictionary coefficients and sparse signal representation via iterative alternating algorithms.
result Efficiently learned sparse representations and underlying relational structure of topological signals.
Proposes a graph dynamics prior for more accurate relational inference.
problem Identifying interactions in dynamical systems from observed dynamics.
method Graph Dynamics Prior (GDP) that uses error amplification in non-local polynomial filters.
result Reconstructs graphs more accurately than previous methods, robust to under-sampling.
New methods compare neural network models using geometric and topological summaries.
problem Comparing deep representations of complex networks in models and brains.
method Develops inference methods based on topological data analysis (TDA) and graph-based techniques.
result New statistical methods enable better model comparison and inference.
Paper proposes learnable topological features for efficient phylogenetic inference.
problem Finding appropriate topological structures for phylogenetic inference tasks requires significant design effort and domain expertise.
method Combines raw node features with graph neural networks to automatically adapt to different tasks.
result Demonstrates effectiveness and efficiency on simulated and real data phylogenetic inference tasks.
GeoPhy uses geometric gradients to efficiently infer phylogenetic trees from molecular data.
problem Challenges in accurately inferring species relationships from molecular data due to combinatorially vast tree topologies.
method Introduces a novel, fully differentiable formulation of phylogenetic inference using geometric spaces and variational Bayesian methods.
result Significantly outperforms other approximate Bayesian methods in inferring phylogenetic trees.
ARTree uses deep learning to infer tree topologies efficiently.
problem Efficient phylogenetic inference from tree topologies.
method Deep autoregressive model based on graph neural networks (GNNs).
result ARTree provides a flexible family of distributions over tree topologies.
New method for inferring network topology from partial data.
problem Inferring network topology from limited node data.
method Vector autoregressive model and Gaussian mixture algorithm.
result The proposed method converges to the network combination matrix in probability.
Recent research implies that training and inference of deep neural networks (DNN) can be computed with low precision numerical representations of the training/test data, weights and gradients without a general loss in accuracy. The benefit of such compact representations is twofold: they allow a significant reduction o…
This paper proposes a new method for learning covers of geometric datasets to improve topological inference and visualization.
problem Improving topological inference and visualization of large-scale geometric datasets.
method Proposes a method for learning topologically-faithful covers of geometric datasets using optimization.
result Simplicial complexes obtained from learned covers outperform standard methods in terms of size and representation of large-scale topology.
A new method compares persistent cycles in topological data.
problem Comparing persistent homology representations of two spaces.
method Direct comparison of individual persistent cycles based on persistence intervals and spatial placement.
result Demonstrated the effectiveness of the method in topological inference.
The study explores how partial observations of network nodes can infer the graph structure.
problem How much information does observing a limited fraction of network nodes provide about the underlying graph structure?
method The article examines the inverse problem of graph learning under partial observability, focusing on decentralized processing strategies and large-scale networks.
result Partial observations of network nodes can still be sufficient to discover the graph linking the probed nodes, despite the presence of unobserved nodes.
Improved phylogenetic inference using VBPI-Mixtures for tree topology and branch length.
problem Multimodality of tree-topology posterior distributions in phylogenetic inference.
method VBPI-Mixtures algorithm that uses mixture learning within the BBVI framework.
result VBPI-Mixtures captures tree-topology distributions better than VBPI.
A distributed algorithm for training graph convolutional networks.
problem Training graph convolutional networks with sparse network topology and distributed agents.
method Formulate inference and optimization in a distributed scenario, propose a gradient descent procedure, and design communication topology.
result Convergence to stationary solutions of the GCN training problem under mild conditions.
We study the problem of cooperative inference where a group of agents interact over a network and seek to estimate a joint parameter that best explains a set of observations. Agents do not know the network topology or the observations of other agents. We explore a variational interpretation of the Bayesian posterior de…
Bayesian method infers transition matrices from incomplete graph data with topological constraints.
problem Inference of transition matrices from incomplete graph data with topological constraints.
method Bayesian approach using repeated interactions and a topological prior.
result Higher accuracy in inferring transition probabilities, improving downstream tasks.
We analyze oversquashing in topological message-passing using relational structures.
problem Oversquashing in topological message-passing remains understudied.
method A unifying axiomatic framework that bridges graph and topological message-passing.
result Potential to advance topological deep learning.
New lattice path method for statistical inference of persistent diagrams.
problem Statistical inference on persistent diagrams.
method Lattice path representation and combinatorial enumerations.
result Topological changes observed in spike proteins of COVID-19 virus.
The paper formalizes robot environments using topological concepts.
problem Determining indistinguishable environments for robots.
method Formalizing robot systems as topological dynamical systems, using covering maps and bisimulation.
result Covering maps can witness indistinguishability of environments under general conditions.
The paper develops a scalable method to infer GRNs from sparse data.
problem Inferring complex gene regulatory networks from limited and temporally sparse data.
method Bayesian optimization and kernel-based methods to construct a Gaussian Process (GP) model.
result The method efficiently searches for the topology with the highest likelihood value.
TopoFisher learns topological summaries by maximizing Fisher information, improving parameter efficiency and inference quality.
problem Simulation-based inference misses key information in low-order statistics, especially for non-Gaussian fields.
method TopoFisher uses a differentiable persistent-homology pipeline that learns topological summaries by maximizing local Gaussian Fisher information.
result TopoFisher recovers much of the available information and outperforms fixed topological vectorizations in weak gravitational lensing.
Survey on hyperplane arrangements and their topology.
problem Topology of hyperplane arrangements.
method Focus on the relationship between topology and real structure.
result Relationship between topology and real structure of hyperplane arrangements.
Improves neural relational inference for dynamic multi-agent trajectories.
problem Limited accuracy of NRI in short output sequences for relational inference in multi-agent trajectories.
method Proposes DYnamic multi-AgentRelational Inference (DYARI) model to handle changing interactions over time.
result DYARI model outperforms NRI in dynamic relational inference tasks.
New method extracts hidden phases in binary mixtures using tubular tilings.
problem Hidden phases in binary mixtures are difficult to observe.
method Introduce tubular tilings for discretizing binary mixtures on smooth manifolds.
result Recover topological information about hidden phases from observable phases and interfaces.
New method estimates causal effects in complex spaces using topological structures.
problem Challenges in estimating causal effects in non-Euclidean spaces.
method Developed a topological causal inference framework using power-weighted silhouette functions of persistence diagrams.
result Successfully quantifies topological treatment effects across various complex outcomes.
We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian Structural Inference (BSI) relies on a set of candidate unifilar HMM (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of to…
Complex biological systems have been successfully modeled by biochemical and genetic interaction networks, typically gathered from high-throughput (HTP) data. These networks can be used to infer functional relationships between genes or proteins. Using the intuition that the topological role of a gene in a network rela…
Proposes a method to infer complex network topologies from multiple graphs.
problem Learning multiple graph Laplacian matrices from heterogeneous graph signals with intricate topological patterns.
method Structured fusion regularization and ADMM algorithm for efficient computation.
result Establishes a non-asymptotic bound of the estimation error and reflects the effect of key factors on convergence rate.
A new algorithm infers causal networks from data using topological thresholds.
problem Inferring causal networks from data.
method Two methods for determining topological thresholds: one to leave no disconnected nodes, the other to find a causal large connected component.
result The novel algorithm is faster and more accurate than the PC algorithm.
Paper infers intrinsic dimension from quasi-convex measurements.
problem Inferring intrinsic dimension from measurements by quasi-convex functions.
method Developed a method using filtration of Dowker complexes based on discrete data of point orderings.
result Correct intrinsic dimension can be inferred in the limit of large data under generic assumptions.
CIFs improve VI by providing flexible posteriors for complex topologies.
problem Complex posterior distributions in VI problems.
method Using CIFs as part of an auxiliary VI scheme, exploiting conditional independence.
result CIFs yield low-variance estimators of model evidence and improve VI results.
In this study, we present and analyze a framework for geometric and topological estimation for mapping of unknown environments. We consider agents mimicking motion behaviors of cyborg insects, known as biobots, and exploit coordinate-free local interactions among them to infer geometric and topological information abou…
The abstract explains counterexamples in 4-manifold topology.
problem Understanding the equivalence relations on 4-manifolds.
method Explains and provides counterexamples for various equivalence relations.
result Illustrates the failure of potential implications between equivalence relations.
A new variational method speeds up Bayesian phylogenetic inference.
problem Slow and inefficient MCMC methods in Bayesian phylogenetic inference.
method Combining subsplit Bayesian networks with variational inference for efficient tree topology and branch length estimation.
result Variational approach provides competitive performance with significantly fewer iterations.
Estimates network topologies from shared graphon models across different networks.
problem Estimating the topology of multiple networks from nodal observations.
method Combining maximum likelihood penalty with graphon estimation schemes.
result Validated performance against competing methods in synthetic and real-world datasets.
Proposes an approach to ensure acyclic graphs in Bayesian structure learning.
problem Ensuring acyclic graphs in Bayesian structure learning.
method Integration of knowledge from topological orderings to constrain acyclicty.
result Outperforms related Bayesian score-based approaches in experiments.
Hybrid continuous-discrete models naturally represent many real-world applications in robotics, finance, and environmental engineering. Inference with large-scale models is challenging because relational structures deteriorate rapidly during inference with observations. The main contribution of this paper is an efficie…
This paper finds efficient algorithms for approximating Markov networks with k-tree topologies.
problem Efficiently approximating Markov networks with complex topologies.
method Developed O(n^{k+1})-time algorithms for finding maximum spanning k-trees (MSkT) that retain certain subgraphs.
result Optimal approximation of Markov networks with k-tree topology is achieved in polynomial time.
PIMA autoencoders discover shared features in multimodal scientific data.
problem Discovering shared information in high-throughput scientific datasets.
method Physics-informed multimodal autoencoders (PIMA) with Gaussian mixture prior and product of experts formulation.
result Accurate cross-modal inference between images and mechanical stress-strain response in lattice metamaterials.
Homflypt skein theory and string topology linked via 2-groupoids.
problem Understanding relations in Homflypt skein theory.
method Defined a 2-groupoid from the fundamental 2-groupoid of singular links, relating it to string topology.
result Relations in Homflypt skein theory are induced from a 2-groupoid.
Traditional sequential multi-object attention models rely on a recurrent mechanism to infer object relations. We propose a relational extension (R-SQAIR) of one such attention model (SQAIR) by endowing it with a module with strong relational inductive bias that computes in parallel pairwise interactions between inferre…
Studies amenable category's monotonicity and its relation to topological complexity.
problem Monotonicity of amenable category for degree-one maps.
method Uses amenable covers and compares with topological complexity.
result Establishes a relation between amenable category and topological complexity.
Stability of mapping spaces is shown to be related to the D-topology.
problem Understanding the relationship between stability and the D-topology of mapping spaces.
method Reformulation and proof of stability theorems in diffeological étale manifolds.
result Stable classes of mapping spaces are D-open.
TDL uses topological features for deep learning models, promising new insights and solutions.
problem Lack of comprehensive theoretical foundations and practical benefits in TDL.
method Discussing open problems and potential solutions in TDL.
result TDL can complement existing graph and geometric learning methods.