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.
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.
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.
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.
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.
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.
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…
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.
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…
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…
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.
In this work, we formalize the problem of causal inference over graph-based relational time-series data where each node in the graph has one or more time-series associated to it. We propose causal inference models for this problem that leverage both the graph topology and time-series to accurately estimate local causal…
Paper improves tree probability estimation using stochastic optimization and variance reduction.
problem Improving tree probability estimation in phylogenetic inference.
method Introduces computationally efficient methods for training SBNs and variance reduction for optimization.
result Methods outperform previous baseline methods in tree topology probability estimation and Bayesian phylogenetic inference.
Paper uses diffusion models to design electric aircraft quickly.
problem Designing electric aircraft efficiently and accurately.
method Simulation-based inference with hierarchical diffusion models.
result Rediscovers known aircraft design trends and laws.
Directed networks are pervasive both in nature and engineered systems, often underlying the complex behavior observed in biological systems, microblogs and social interactions over the web, as well as global financial markets. Since their structures are often unobservable, in order to facilitate network analytics, one …
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.
A topological approach to stratification learning is developed for point cloud data drawn from a stratified space. Given such data, our objective is to infer which points belong to the same strata. First we define a multi-scale notion of a stratified space, giving a stratification for each radius level. We then use met…
Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. This paper is a brief introduction, through a few selected topics, to basic fundamental and practical aspects of \tda\ for non experts.
Researchers create benchmarks to compare graph inference methods.
problem Comparing graph inference methods is difficult due to varying downstream tasks.
method Developed benchmarks for various graph tasks.
result Contrasted prominent graph inference techniques.
Study infers tree topology from customer data using contrastive learning.
problem Inferring local network topology from customer data.
method Contrastive learning approach for binary event encoding from continuous time series.
result Preliminary results show potential for valuable encoder learning.
Bayesian method infers network topology and dynamics from noisy, sparse measurements.
problem Learning network topology and dynamics from partial, noisy data.
method Developed method uses dynamical structure functions derived from linear stochastic differential equations.
result Method outperforms state-of-the-art methods in various network types.
New method detects uncertainty in neural networks for out-of-distribution detection.
problem Detecting out-of-distribution inputs to ensure model reliability.
method Predictive topological uncertainty (pTU) based on persistent homology.
result pTU provides a statistical framework for OOD detection.
A new method for state estimation on complex networks.
problem Reconstructing latent dynamics from multivariate time-series on topological cell complexes.
method Topology-aware state space framework derived from stochastic partial differential equations, with state evolution following heat-like topological diffusion.
result The proposed method successfully recovers latent states and topological structures in real-world networks.
In this work, we address semi-supervised classification of graph data, where the categories of those unlabeled nodes are inferred from labeled nodes as well as graph structures. Recent works often solve this problem via advanced graph convolution in a conventionally supervised manner, but the performance could degrade …
A new model encodes distances and topology in latent variables.
problem Modeling dissimilarity data with latent variables and invariances.
method Isometric Gaussian Process Latent Variable Model using Riemannian geometry and variational inference.
result The model can encode invariances in learned manifolds.
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.
New method robustifies topological data analysis against outliers.
problem Outliers make topological data analysis unstable.
method Proposed a robust distance function (MoM Dist) for persistent homology.
result MoM Dist sublevel filtrations and weighted filtrations are consistent estimators in adversarial settings.
TabPFN's internal geometry topology correlates with dataset reliability.
problem Understanding TabPFN's behavior on structurally difficult tabular geometries.
method Using zigzag persistent homology, studying TabPFN's internal representations on synthetic tabular tasks with known topology.
result Topology of TabPFN's internal representation geometry is strongly associated with dataset-level reliability.
The financial market is a complex dynamical system composed of a large variety of intricate relationships between several entities, such as banks, corporations and institutions. At the heart of the system lies the stock exchange mechanism, which establishes a time-evolving network of trades among companies and individu…
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…
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.
Method interprets deep learning models using topological data analysis.
problem Lack of interpretability in deep learning models, especially in high-risk applications.
method Topological and geometric data analysis to infer features and decision-making mechanisms of DL models.
result Extracted subgraphs reveal relevant features for model decisions, demonstrating model's reliance on pertinent data.
Attack graphs provide compact representations of the attack paths that an attacker can follow to compromise network resources by analysing network vulnerabilities and topology. These representations are a powerful tool for security risk assessment. Bayesian inference on attack graphs enables the estimation of the risk …
A hierarchical clustering algorithm for data clouds without structure assumptions.
problem Exploring data clouds without making structure assumptions.
method Hierarchical topological clustering algorithm that infers persistence of outliers and clusters of arbitrary shape from data hierarchy.
result The algorithm can provide meaningful clusters in complex datasets.
The paper optimizes LLM inference systems through queueing theory.
problem Efficient LLM inference for AI agents under various routing topologies.
method Developed a fluid-limit framework for multi-class batched processing networks under K-FCFS scheduling.
result Proved that work-conserving scheduling algorithms maximize throughput for LLM inference.
This study redefines probability for finite outcomes using axioms and examples.
problem Defining probability for finite outcomes and preserving information.
method Developed three axioms for relative probability functions and provided examples and a system for their composition.
result Proved the topological closure of the relative probability space, preserving information under limits.
Estimates multiple networks using graphons for non-aligned graphs.
problem Estimating 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.
We present a new family of zero-field Ising models over N binary variables/spins obtained by consecutive "gluing" of planar and O(1)-sized components and subsets of at most three vertices into a tree. The polynomial-time algorithm of the dynamic programming type for solving exact inference (computing partition func…