New framework detects time-varying economic persistence.
problem Time-varying persistence in economic shocks.
method Localized regression techniques to identify evolving heterogeneity.
result Substantial persistence variations align with macroeconomic events.
We examine how the most prevalent stochastic properties of key financial time series have been affected during the recent financial crises. In particular we focus on changes associated with the remarkable economic events of the last two decades in the mean and volatility dynamics, including the underlying volatility pe…
A novel topological method analyzes fMRI data over time.
problem Analyzing time-varying fMRI data due to noise and person-to-person variation.
method Encoding each time point as a persistence diagram of topological features.
result Time-varying persistence diagrams can cluster participants and study brain state trajectories.
Algorithm estimates parameters over time-varying graphs without special assumptions.
problem Estimating parameters over time-varying graphs without assuming independence.
method Decentralized online regularized learning with innovation, consensus, and regularization terms.
result Estimations converge almost surely under certain conditions.
Paper introduces SCI to distinguish market signals from coordination.
problem Unclear signals in prediction markets.
method Formalizes SCI, introduces weighted and time-varying extensions.
result Discriminates between market signals and coordination.
We study soft persistence (existence in subsequent temporal layers of motifs from the initial layer) of motif structures in Triangulated Maximally Filtered Graphs (TMFG) generated from time-varying Kendall correlation matrices computed from stock prices log-returns over rolling windows with exponential smoothing. We ob…
We measure the influence of different time-scales on the dynamics of financial market data. This is obtained by decomposing financial time series into simple oscillations associated with distinct time-scales. We propose two new time-varying measures: 1) an amplitude scaling exponent and 2) an entropy-like measure. We a…
New method improves neural network robustness to adversarial attacks.
problem Improving adversarial robustness of neural networks.
method Inspired by adaptive control theory, the approach uses persistency of excitation to constrain gradient descent updates.
result Networks trained with the PoE-motivated learning rate schedule are significantly more robust to adversarial attacks.
New measure EC assesses node contributions in nonlinear, time-varying systems.
problem Existing node contribution measures assume linear, time-invariant dynamics, failing for complex, real-world systems.
method Defined 'emergent contribution (EC)' as a dynamical leverage measure from Jacobians of differentiable models.
result EC diverges from average controllability under persistent regime switching and sign reversal, identifying limits of local linearization.
A big challenge in environmental monitoring is the spatiotemporal variation of the phenomena to be observed. To enable persistent sensing and estimation in such a setting, it is beneficial to have a time-varying underlying environmental model. Here we present a planning and learning method that enables an autonomous ma…
TDA-based portfolios show better risk-adjusted returns than classical methods.
problem Traditional portfolio selection methods fail to capture complex asset dynamics.
method Topological Data Analysis (TDA) using persistence landscapes to quantify portfolio risk.
result TDA-based portfolios outperform classical models in excess mean return and financial ratios.
Study examines how industrial emissions evolve over time in response to various factors.
problem Understanding how firm-level emissions change over time in response to environmental regulation, economic conditions, and organizational constraints.
method Used a time-varying mean-group estimator to link emissions data with firm characteristics and macroeconomic indicators over 1992-2023.
result Firm-level characteristics and aggregate conditions have different impacts on emissions growth at different times.
Stable topological summary captures evolving dependency structure in dynamic Bayesian networks.
problem Missing larger-scale patterns in evolving dependency structures in dynamic Bayesian networks.
method Topological approach using Dynamic Bayesian Graphs and persistent homology.
result Stable topological summary (barcodes) captures evolving dependency structure in DBNs.
A hybrid framework for American option pricing under time-varying rough volatility.
problem Pricing American options under time-varying rough volatility.
method Signature method combined with gradient-boosted ensemble for Hurst parameter estimation, regime switch, and Random Fourier Features for acceleration.
result The proposed hybrid framework improves performance over fixed-roughness baselines and reduces duality gaps in some regimes.
This letter revisits the informational efficiency of the Bitcoin market. In particular we analyze the time-varying behavior of long memory of returns on Bitcoin and volatility 2011 until 2017, using the Hurst exponent. Our results are twofold. First, R/S method is prone to detect long memory, whereas DFA method can dis…
This study develops a dynamic inverse optimization framework to recover hidden, time-varying preferences from observed allocation trajectories.
problem The gap between classical optimization theory and real-world practice, especially in the presence of drift and shocks.
method Dynamic inverse optimization framework using a drift-aware estimator grounded in convex analysis and online learning theory.
result Sharp static and dynamic regret bounds for the framework, demonstrating its responsiveness to gradual drift and sudden shocks.
Machining processes are most accurately described using complex dynamical systems that include nonlinearities, time delays, and stochastic effects. Due to the nature of these models as well as the practical challenges which include time-varying parameters, the transition from numerical/analytical modeling of machining …
SPO optimizes LLMs by eliminating group-based baselines and variance issues.
problem Frequent degenerate groups and synchronization barriers in group-based policy optimization methods.
method Single-stream Policy Optimization (SPO) replaces per-group baselines with a persistent, KL-adaptive value tracker and global advantage normalization.
result SPO converges more smoothly and attains higher accuracy than GRPO, improving maj@32 by +3.4 pp across five math benchmarks.
This work classifies monodromy in vineyards using singularity theory.
problem Understanding and predicting monodromy in vineyards for topological data analysis.
method Using a connection with singularity theory, the study classifies monodromy in vineyards of 1-manifolds in R^2.
result Monodromy in vineyards occurs only if they contain a specific singularity of the distance function.
Extends tracking guarantees for time-varying variational inequalities.
problem Tracking solutions of time-varying variational inequalities.
method Extends existing results to sublinear solution paths and periodic problems.
result Discrete dynamical systems of periodic time-varying VI can exhibit chaotic behavior or converge to the solution.
New method tracks time-varying parameters in data.
problem Tracking unknown time-varying parameters in data.
method Stochastic gradient descent-based recursive scheme with log-likelihood as gain function.
result Convergence in mean-square error in a suitable neighborhood of the unknown parameter.
Approaches for approximating persistent homology for large datasets.
problem Inability to compute persistent homology for large datasets.
method Multiple subsampling framework for statistical approximation of persistent homology.
result Derivation of finite sample convergence rates for empirical means of persistent homology.
Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an associated kernel. The main advantage of this summary is that it allows one to apply tools from statistics and machine lea…
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.
Paper proves k-means clustering works on persistence diagrams.
problem Complex geometry of persistence diagram space.
method Proves convergence of k-means on persistence diagram space. result Performance of k-means on persistence diagrams and measures is superior. Formula for interleaving distance of rectangle persistence modules.
problem Calculating distances between rectangle persistence modules.
method Formulas based on rectangle geometry, extended to decomposable modules.
result Closed formulas for interleaving and bottleneck distances.
Paper proposes BOCPD for real-time order flow and market impact prediction.
problem Persistent order flow patterns in financial markets.
method Bayesian online change-point detection (BOCPD) with score-driven approach.
result Model outperforms existing models in predicting order flow and market impact.
We propose a dynamic network model where two mechanisms control the probability of a link between two nodes: (i) the existence or absence of this link in the past, and (ii) node-specific latent variables (dynamic fitnesses) describing the propensity of each node to create links. Assuming a Markov dynamics for both mech…
This paper demonstrates the flaws of co-persistence theory proposed by Bollerslev and Engle (1993) which cause the theory can hardly be applied. With the introduction of the half-life of decay coefficient as the measure of the persistence, and both the weak definition of persistence and co-persistence in variance, this…
Optimizes wavelets for graph classification using spectral wavelet signatures and persistence diagrams.
problem Graph classification with geometric properties encoded in persistence diagrams.
method Optimizes spectral wavelets for graph datasets to capture best-suited features for classification.
result Competitive performance in graph classification problems compared to other persistence-based architectures.
New method for analyzing multiparameter persistence modules from smooth functions.
problem Analyzing multiparameter persistence modules from smooth functions.
method Generalized Morse theory applied to cobordism and Cerf theory.
result Complete description of persistence modules as direct sums of indecomposables.
Develops robust persistence diagrams using kernel methods.
problem Persistence diagrams are sensitive to data perturbations.
method Constructs robust persistence diagrams from superlevel filtrations of robust density estimators using reproducing kernels.
result Robust persistence diagrams are consistent estimators in bottleneck distance.
This paper interprets critical scales in persistent homology for compact metric spaces.
problem Understanding critical scales in persistent homology for general compact metric spaces.
method Analyzing local minima of the distance function and their impact on persistence.
result Each decrease in zero-dimensional persistence and increase in one-dimensional persistence is induced by local minima of the distance function.
MuRiT efficiently computes multi-parameter persistence barcodes.
problem Efficient computation of multi-parameter persistent homology.
method Vietoris-Rips transformation to reduce multi-parameter to single-parameter computation.
result MuRiT computes pathwise persistence barcodes for multi-filtered flag complexes.
Develops a method to predict stock returns with time-varying risk premia.
problem Predicting stock returns with time-varying risk premia while maintaining no-arbitrage restrictions.
method Penalized two-pass regression with time-varying factor loadings, incorporating penalization in the first pass and grouping in the second pass.
result The proposed method reduces prediction errors compared to other approaches.
Persistent homology can recognize knotting in curves.
problem Recognizing knotting in curves
method Compute one-dimensional persistent homology, extract cycle representatives, and assign a hypergraph curvature-based score.
result Systematic differences between knotted and unknotted structures are revealed.
This article analyzes the relationship between co-persistence and hedging which indicates co-persistence ratio is just the long-term hedging ratio. The new method of exhaustive search algorithm for deriving co-persistence ratio is derived in the article. And we also develop a new hedging strategy of combining co-persis…
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come. In this article, by considering the space of persistence diagrams as a space of d…
Persistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their {\em diagram distances}, most of the recent attempts at using persistence diagrams in machine learning have been done through kernel methods, i.e., embeddings of …
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a …
A new approach to reinforcement learning improves policy performance by adjusting control frequency.
problem Improving reinforcement learning performance by optimizing control frequency.
method Introducing action persistence and a novel algorithm, PFQI, to learn optimal value function at a given persistence.
result PFQI effectively learns optimal value function with action persistence, improving reinforcement learning performance.
Given a compact geodesic space X we apply the fundamental group and alternatively the first homology group functor to the corresponding Rips or Čech filtration of X to obtain what we call a persistence. This paper contains the theory describing such persistence: properties of the set of critical points, their preci…
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.
Time-varying neural network improves stock return prediction.
problem Predicting stock returns in a time-varying market.
method Online early stopping algorithm for neural network training.
result The proposed algorithm outperforms current methods in predicting monthly U.S. stock returns.
Improved persistence spheres map measures to functions, stable under partial transport.
problem Representing and comparing measures in topological machine learning.
method Persistence spheres map measures to continuous functions on the sphere, stable under 1-Wasserstein partial transport.
result Persistence spheres provide a stable, parameter-free representation of measures, improving upon existing methods.
Enhanced multivariate GARCH model using LSTM for better volatility forecasting.
problem Limitations of traditional multivariate GARCH in capturing persistent volatility and co-movement.
method Integrates deep learning (LSTM) into multivariate GARCH models to capture nonlinear and dynamic dependence structures.
result Superior out-of-sample portfolio risk forecast compared to traditional methods.
We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric descriptions of the "life span" or "persistence" of a homology class. As a case study, …
This article addresses persistent tangles. These are tangles whose presence in a knot diagram forces that diagram to be knotted. We provide new methods for constructing persistent tangles. Our techniques rely mainly on the existence of non-trivial colorings for the tangles in question. Our main result in this article i…