As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality measures rely on the assumption that the graph is perfectly known -- a premise …
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48 results for “Centrality Measures”
I show that the solution of a standard clearing model commonly used in contagion analyses for financial systems can be expressed as a specific form of a generalized Katz centrality measure under conditions that correspond to a system-wide shock. This result provides a formal explanation for earlier empirical results wh…
Decentralized learning achieves centralized performance via Gibbs measures.
problem Achieving centralized performance in decentralized machine learning.
method ERM-RER learning framework with Gibbs measures and relative-entropy regularization.
result Achieving centralized performance with Gibbs measures and specific scaling of regularization factors.
Study shows central limit theorem for counting measures in non-smooth spaces.
problem Counting measures in non-smooth spaces with coarse negative curvature.
method Established central limit theorems for actions of groups on hyperbolic spaces without properness or smoothness assumptions.
result General framework allows for applications in geometrically finite manifolds and intersection numbers.
The paper validates a centrality measure for financial networks during financial distress.
problem Systemic risk and shock propagation in financial networks.
method Statistical validation method for network centrality measures.
result The proposed centrality measure increases significantly during financial distress.
Paper uses neural networks to efficiently compute vertex centrality measures in large networks.
problem Efficiently computing vertex centrality measures in massive real-world networks.
method Neural network learning algorithms to approximate centrality measures.
result Neural network regression model outperforms other techniques in terms of solution quality and computation time.
Central limit theorem for Green metrics on hyperbolic groups.
problem Proving a central limit theorem for Green metrics on hyperbolic groups.
method Proving a central limit theorem for Green metrics on hyperbolic groups using probability measures and ordering elements.
result Proved a central limit theorem for Green metrics on hyperbolic groups.
GNNs can learn multiple graph centrality measures from a single embedding.
problem Estimating network centrality measures from graph data.
method Training a GNN to refine a single set of multidimensional embeddings and decode them into multiple outputs.
result GNN achieves 89% accuracy on random instances with up to 128 vertices.
Statistical bounds for entropic optimal transport: sample complexity and the central limit theoremmath.ST
New bounds for statistical entropic optimal transport with subgaussian measures.
problem Establishing statistical bounds for entropic optimal transport.
method Proving sample complexity and central limit theorem for entropic OT.
result Improved convergence rate and central limit theorem for empirical measures.
Machine learning speeds up centrality measure calculations for large networks.
problem High computational costs of traditional centrality measures in large networks.
method Neural network learning algorithms to approximate centrality measures.
result Regression model approximates centrality measures efficiently and accurately.
FUSE neural centrality framework improves data point measurement in high dimensions.
problem Measuring centrality in high-dimensional data is expensive and unstable.
method Combines global and local heads trained on arbitrary representations.
result Reveals meaningful classical ordering and competitive performance.
This study analyzes how cryptocurrency networks adapt to financial disruptions.
problem Understanding how cryptocurrency networks respond to financial crises.
method Vertex centrality measures to assess network stability and resilience.
result Different cryptocurrencies experienced shifts in their network roles during the FTX crisis.
Using data from 92 indices of stock exchanges worldwide, I analize the cluster formation and evolution from 2007 to 2010, which includes the Subprime Mortgage Crisis of 2008, using asset graphs based on distance thresholds. I also study the survivability of connections and of clusters through time and the influence of …
Paper proves a Central Limit Theorem for Random Forest Permutation Importance Measure.
problem Lack of theoretical analysis of Random Forest Permutation Importance Measure (RFPIM).
method Formal proof using U-Statistics theory, deviating from conventional Random Forest model.
result Established a Central Limit Theorem for RFPIM.
The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for interval-valued datasets. We propose a geometrical approach in the determination of s…
History estimation in random recursive trees: Pointwise approach via iterated Jordan centralitiesmath.PR
Estimate arrival times in random recursive trees using iterated Jordan centralities.
problem Estimate arrival times in random recursive trees.
method Pointwise approach using iterated Jordan centralities.
result Tail bounds for relative estimation error.
New risk-dependent centrality measures assess node importance in financial networks.
problem Understanding how external risk levels affect network node importance.
method Developed risk-dependent centrality measures based on SI model of epidemics.
result Observed ranking interlacement phenomenon where nodes can swap positions due to external risk changes.
Study improves accuracy of risk measures using advanced algorithms.
problem Computing accurate risk measures for financial losses.
method Nested stochastic approximation and multilevel acceleration.
result Established central limit theorems for estimation errors.
This paper compares various graph centrality methods for portfolio optimization.
problem Investment risk and return optimization using network theory.
method Graph centrality measures applied to portfolio optimization.
result Graph-theoretical methods yield higher risk-adjusted returns.
Generalizes k-means to graphs using PageRank.
problem Clustering nodes in directed and undirected graphs.
method Utilizes PageRank to compute node centrality in graphs.
result Robustly computes centrality in graphs and metric spaces.
Paper estimates the order of vertices in random recursive trees.
problem Estimating the order of arrival of vertices in random recursive trees.
method Proposes an order estimator based on the Jordan centrality measure and defines risk measures.
result Establishes a nearly optimal estimator for the problem.
A new method selects important variables for clustering from dependency networks.
problem Variable selection for clustering in high-cost data scenarios.
method Create dependency networks, rank variables by centrality, select top-n variables.
result Top-n variables improve clustering performance compared to existing methods.
Develops thermodynamic formalism for quasimorphisms on negatively curved spaces.
problem Analyzing quasimorphisms on negatively curved spaces.
method Thermodynamic formalism framework, Banach isomorphism, weak Livšic cohomology.
result Establishes Central Limit Theorem and invariance principle for unbounded quasimorphisms.
Novel risk matrix for optimal portfolio choice with tail risk considerations.
problem Optimal portfolio choice with tail risk events.
method Risk matrix with Value-at-Risk and Delta-CoVaR measures, derived conditions for closed-form solution, examination of portfolio risk and centrality, demonstration of asset centrality's impact on optimal weight allocation.
result Portfolio risk is not necessarily increasing with stock centrality and can be improved by high connectivity.
Decentralization illusion in Decentralized Finance: Evidence from tokenized voting in MakerDAO pollscs.CR
MakerDAO's governance is centralized despite its decentralized claim.
problem Decentralization illusion in Decentralized Finance (DeFi) governance.
method Empirical analysis using financial, transaction, network, and sentiment indicators.
result Centralized governance impacts Maker protocol and voting power distribution.
The paper studies billiards in symmetric tables and finds a measure bound for maximizing orbits.
problem Understanding the measure of maximizing orbits in symmetric billiard tables.
method Introduced a closed invariant set of locally maximizing orbits and gave an effective bound on its measure.
result An effective bound on the measure of the invariant set in terms of the isoperimetric defect of the curve.
Embedding graph nodes into a vector space can allow the use of machine learning to e.g. predict node classes, but the study of node embedding algorithms is immature compared to the natural language processing field because of a diverse nature of graphs. We examine the performance of node embedding algorithms with respe…
Multi-centrality Graph Spectral Decompositions and their Application to Cyber Intrusion Detectioncs.SI
Many modern datasets can be represented as graphs and hence spectral decompositions such as graph principal component analysis (PCA) can be useful. Distinct from previous graph decomposition approaches based on subspace projection of a single topological feature, e.g., the Fiedler vector of centered graph adjacency mat…
Improved nested simulation for financial risk measurement.
problem Efficiently estimating nested risk measures in financial engineering.
method Reusing inner simulation outputs to improve efficiency and accuracy.
result The proposed approach outperforms standard nested simulation and regression methods.
This paper reviews incompatibilities of comonotonic risk measures.
problem Incompatibilities of comonotonic risk measures with central properties.
method Literature review and Choquet representation of comonotonic additive risk measures.
result Comonotonic additive risk measures cannot be surplus invariant.
Extends Milnor's invariants to 3-manifolds, solving an open problem.
problem Extract transfinite Milnor invariants for 3-manifolds.
method Develops a theory of transfinite invariants for 3-manifold groups.
result Realizes nontrivial values of transfinite Milnor invariants.
Study loop ensembles on graphs, linking group theory and topology.
problem Understanding loop homotopy classes and homologies on graphs.
method Determined distributions of loop homotopy classes and homologies using the lower central series of the fundamental group.
result Distributions of loop homotopy classes and homologies defined by the lower central series of the fundamental group.
Network theory assesses systemic risk in the insurance sector.
problem Detecting critical insurance companies in systemic risk.
method Complex network approach with weighted effective resistance centrality.
result Identifies companies with significant influence on network robustness.
Transformer models improve financial sentiment measurement.
problem Capturing nuanced sentiment from financial news articles.
method Transformer-based language models for sentiment classification and aggregation.
result Transformer models outperform traditional dictionary-based methods in sentiment classification.
In the wake of the still ongoing global financial crisis, bank interdependencies have come into focus in trying to assess linkages among banks and systemic risk. To date, such analysis has largely been based on numerical data. By contrast, this study attempts to gain further insight into bank interconnections by tappin…
We show that any objective risk measurement algorithm mandated by central banks for regulated financial entities will result in more risk being taken on by those financial entities than would otherwise be the case. Furthermore, the risks taken on by the regulated financial entities are far more systemically concentrate…
In 1978 Brakke introduced the mean curvature flow in the setting of geometric measure theory. There exist multiple variants of the original definition. Here we prove that most of them are indeed equal. One central point is to correct the proof of Brakke's §3.5, where he develops an estimate for the evolution of the mea…
The paper examines how loss aversion impacts multi-armed bandit decisions over long periods.
problem The impact of loss aversion on multi-armed bandit decisions over long periods.
method A new central limit theorem for measures with history-dependent variances, derived under risk aversion in gains and risk loving in losses.
result Consequences of loss aversion for asymptotic properties are derived in analytical results.
SM-netFusion estimates brain network atlas by considering multiple topological measures.
problem Limited BNA estimation methods that overlook topological measures and lack discriminative power.
method Supervised multi-topology network cross-diffusion framework using degree, closeness, and eigenvector centrality measures.
result SM-netFusion produces more centered and representative templates, and improves classification accuracy.
Stock market as temporal networkq-fin.ST
Financial networks have become extremely useful in characterizing the structure of complex financial systems. Meanwhile, the time evolution property of the stock markets can be described by temporal networks. We utilize the temporal network framework to characterize the time-evolving correlation-based networks of stock…
Measuring comodules are defined and shown to provide a useful generalization of the set of maps between modules with a broad range of applications. Three applications are described. Connections on bundles are described in terms of measuring comodules, enabling curvature to be defined under general algebraic circumstanc…
Network metrics form a fundamental part of the network analysis toolbox. Used to quantitatively measure different aspects of the network, these metrics can give insights into the underlying network structure and function. In this work, we connect network metrics to modern probabilistic machine learning. We focus on the…
Study measures invariant under horospherical subgroups for finitely generated Kleinian groups.
problem Investigating measures invariant under horospherical subgroups for finitely generated Kleinian groups.
method Combining results from Landesberg and Lindenstrauss with 3-manifold theory, including the Tameness Theorem.
result Identified all Radon measures on quotient space that are ergodic and invariant under horospherical subgroup.
This paper was presented and written for two seminars: a national UK University Risk Conference and a Risk Management industry workshop. The target audience is therefore a cross section of Academics and industry professionals. The current ongoing global credit crunch has highlighted the importance of risk measurement i…
The paper studies empirical processes from nearest neighbors in regression.
problem Estimating conditional cumulative distribution functions and local linear regression.
method Uniform central limit theorem and non-asymptotic bound under local bracketing entropy and uniform entropy numbers.
result Gaussian limit of empirical process with simple covariance.
We study non-abelian differentiable gerbes over stacks using the theory of Lie groupoids. More precisely, we develop the theory of connections on Lie groupoid -extensions, which we call "connections on gerbes", and study the induced connections on various associated bundles. We also prove analogues of the Bianchi id…
We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk meas…
Study financial markets using synchronization measures and clustering algorithms.
problem Analyze high-frequency trading dynamics and market states.
method Ordinal pattern series, information-theoretic synchronization measure, clustering algorithms, Markov model.
result Identify two coherent seasons of centralized and decentralized synchronicity.