Researchers study the geometric properties of a specific type of stable processes.
problem Understanding the information geometry of tempered stable processes.
method Derivation of α-divergence, Fisher information matrices, and α-connections.
result Obtained Fisher information matrices and α-connections for statistical manifolds.
New method identifies optimal subset of stable information to transfer for better model generalization.
problem Non-reliability of machine learning models to dataset shifts.
method Causal minimax learning approach to identify optimal subset of stable information.
result Proposed algorithm efficiently searches for optimal subset with minimal worst-case risk.
We study here some aspects of the topology of the space of smooth, stable, genus 0 curves in a Riemannian manifold X, i.e. the Kontsevich stable curves, which are not necessarily holomorphic. We use the Hofer-Wysocki-Zehnder polyfold structure on this space and some natural characteristic classes, to show that for $X…
Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In this paper, we introduce stable graphical (SG) models, a class of multivariate st…
We develop methods to estimate lag and parameters for multiple stable autoregressive processes.
problem Estimating lag and parameters for multiple stable autoregressive processes with unknown lag.
method Use convex programming to simultaneously select lag and estimate parameters across multiple processes.
result The estimated process is stable, and forecasting errors can outperform known rates.
Non-compact manifolds prevent C0-stable mappings from being dense.
problem Density of C0-stable mappings on non-compact manifolds. method Using topologically critical points to show non-density.
result The set of C0-stable mappings is never dense on non-compact manifolds. Algorithm identifies optimal stable matching in uncertain two-sided markets.
problem Sequential learning in two-sided markets with unknown preferences.
method Pure exploration approach with elimination-based algorithms exploiting partial preference information.
result Identification of pervasive stable matching for optimal stable matching identification.
I-SPEC learns stable models from data without full causal knowledge.
problem Learning models that generalize well across shifts in environment.
method End-to-end framework using partial ancestral graph to learn stable interventional distribution.
result I-SPEC can learn robust models without full causal knowledge.
SFB uses stable features to adapt unstable ones for better performance.
problem Improving classifier performance on out-of-distribution data by leveraging stable features.
method SFB learns a predictor that separates stable and unstable features, then adapts unstable predictions using stable predictions.
result SFB can learn an asymptotically-optimal predictor without test-domain labels.
Paper introduces a method to generate stable shapes using Grassmann manifolds.
problem Generating stable shapes with minimal extraneous transformations.
method Continuous normalization flows on Grassmann manifolds to eliminate extraneous transformations.
result The method significantly outperforms state-of-the-art methods in generating high-quality samples.
Weaved helices form mechanically stable 3D structures.
problem Creating stable 3D structures from helical elements.
method Exploiting screw symmetry and invariant cylindrical rod packing to form triply periodic arrangements.
result Demonstrated nineteen triply periodic arrangements of interwoven helices.
Develops information geometry for Lévy processes in finance.
problem Understanding the statistical properties of Lévy processes for financial modeling.
method Deriving α-divergences from Lévy triplets, identifying Fisher information matrix and α-connection. result Identifies statistical implications and differential-geometric structures of Lévy processes.
A Smale flow is a structurally stable flow with one dimensional invariant sets. We use information from homology and template theory to construct, visualize and in some cases, classify, nonsingular Smale flows in the 3-sphere.
Modeling risk and performance with Levy-stable distributions.
problem Understanding risk and performance in financial markets with non-Gaussian distributions.
method Developed a finite-horizon model using Levy-stable scaling, identified parameters from data, derived formulas for various financial ratios.
result Horizon-correct formulas for risk measures are derived and validated across different horizons.
Algorithm identifies and transfers unstable features to create robust classifiers.
problem Developing unbiased classifiers from input-label pairs alone.
method Contrast different data environments in source tasks to encode unstable features, then cluster target task data and minimize worst-case risk.
result Our method maintains robustness across synthetic and real-world environments.
Default-ERM shortcut learning persists even without additional information.
problem Default-ERM shortcut learning in perception tasks despite stable feature sufficiency.
method Studied linear perception task; developed margin control (MARG-CTRL) loss functions.
result Margin control mitigates shortcut learning on various tasks.
This paper analyzes deep Stable neural networks, showing convergence rates under different growth settings.
problem Analyzing the behavior of deep Stable neural networks as width increases.
method Large-width asymptotic analysis and convergence rates for fully connected feed-forward deep Stable NNs.
result The rescaled deep Stable NN converges weakly to a Stable SP under joint growth, with sup-norm convergence rates established.
A faster, more stable method for optimizing topological functions.
problem Optimizing topological functions is computationally expensive and unstable.
method Introduces a novel backpropagation scheme for faster and more robust optimization.
result Produces more robust optima and stable visualizations.
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.
Paper introduces S-SSE for stable sparse subspace embedding.
problem Inefficient sparse random projection matrices with uneven non-zero distribution.
method Uses uniform sampling without replacement to create a stable sparse subspace embedded matrix (S-SSE).
result S-SSE maintains Euclidean distance better after dimension reduction.
Paper introduces stable vectorization for multiparameter PH using signed barcodes.
problem Lack of stable vectorization methods for multiparameter persistent homology.
method Signed barcodes as measures for stable vectorization of MPH.
result Stable feature vectors from signed barcodes improve performance in data science.
Proposes a new method to optimize graph neural network architectures on heterogeneous information networks.
problem Weaknesses in instability and inflexibility of existing graph neural architecture search methods.
method Partial Message Meta Multigraph search (PMMM) using a differentiable framework to search for a meaningful meta multigraph.
result Significantly more stable and effective than state-of-the-art heterogeneous GNNs.
FADE adapts machine learning models to evolving data efficiently.
problem Sequential covariate shift in dynamic environments.
method FADE uses Fisher information geometry for robust learning under SCS.
result FADE achieves up to 19% higher accuracy under severe shifts.
We propose a mathematical procedure for finding informed trader activities in European-style options and their underlying asset. The regression model (9) with moving average component was written. Being added to it ARMA-process for log-price differences of underlying asset, the generalized model is written as Vector AR…
Alpha-based performance evaluation may fail to capture correlated residuals due to model errors. This paper proposes using the Generalized Information Ratio (GIR) to measure performance under misspecified benchmarks. Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is deriv…
We prove a general homological stability theorem for certain families of groups equipped with product maps, followed by two theorems of a new kind that give information about the last two homology groups outside the stable range. (These last two unstable groups are the "edge" in our title.) Applying our results to auto…
Stable Hadamard Memory improves reinforcement learning by efficiently managing memory.
problem Memory models struggle in partially observable reinforcement learning environments.
method Introduces a novel memory model using the Hadamard product for efficient memory management and updates.
result Significantly outperforms state-of-the-art memory-based methods on challenging benchmarks.
Unified framework for robust, stable, and efficient density ratio estimation.
problem Density-chasm and support-chasm problems in density ratio estimation.
method Dequantified diffusion-Schrödinger bridge (D3RE) framework with DDBI and DSBI.
result Offers uniform approximation and bounded time scores in theory and empirical performance.
New algorithm reduces RL policy optimization gap.
problem Insufficient theoretical understanding of policy optimization methods.
method Reference-based Policy Optimization with Stable at Any Time guarantee (RPO-SAT)
result Achieves nearly minimax optimal policy-based algorithm for tabular RL.
Stable actions of hyperbolic groups on their boundaries.
problem Stability of group actions on boundaries.
method Dynamical coding and semi-conjugacy analysis.
result Topological stability of actions on hyperbolic group boundaries.
Study of parabolic Higgs bundles on curves with special fixed points.
problem Understanding fixed points of Cimes-action on moduli spaces of Higgs bundles. method Analyzing Cimes-action on moduli spaces, classifying fixed points, and studying Bialynicki-Birula flows. result Classification of very stable fixed points and their relation to Hitchin maps.
Proposes SVI for covariate-shift generalization with sparse variable independence.
problem Covariate-shift generalization with limited data and unstable variables.
method Introduces sparsity constraint and combines reweighting and selection in an iterative way.
result Improves covariate-shift generalization performance on synthetic and real-world datasets.
Enhances OOD detection using latent diffusion for more robust and efficient training.
problem Improving reliability of machine learning models in real-world scenarios.
method Proposes Outlier-Aware Learning (OAL) framework that generates synthetic OOD data in latent space and uses MICL and KD modules.
result Demonstrates superior performance on benchmark datasets.
New algorithm detects and adapts to changes in real-time data streams.
problem Adapting to fast-changing data in real-time systems.
method Concept drift detection followed by prototype-based adaptation.
result Stable and quick adjustments during model adaptation.
Entropy data replaces classical charts for smooth manifolds.
problem Establishing smooth structures on topological manifolds.
method Using entropy data to define admissible coordinate functions and reconstruct smooth atlases.
result Entropy-smooth structures are equivalent to classical smooth structures and stable under perturbations.
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are certified stable to input deformations. This stability to deformations can be interp…
Proposes a dynamic matching algorithm for two-sided online markets.
problem Dynamic preferences in two-sided online matching platforms.
method Dynamic Matching Bandit Algorithm with statistical preference ranking estimation.
result Agent-optimal stable matching result with logarithmic regret bound.
Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persist…
The paper analyzes cryptocurrency trading networks using pairwise and high-order dependencies.
problem Understanding information flows and dependencies in cryptocurrency markets.
method Defined a cryptocurrency trading network using weekly log returns, analyzed using Granger causality and O-information.
result High-order dependencies reveal that stable coins play a major role in high-order effects.
The paper develops methods for calculating equivariant homology from Morse functions.
problem Calculating equivariant homology from equivariant Morse functions.
method Alter equivariant Morse functions to stable ones, use generic equivariant metrics, and analyze the Morse spectral sequence.
result Equivariant Morse functions induce a filtration that computes equivariant homology.
Stable algebraic filters improve neural network performance.
problem Improving neural network stability to deformations.
method Analyzed stability of algebraic filters and neural networks under deformations of the homomorphism.
result Stable algebraic filters have frequency responses whose derivative is inversely proportional to frequency.
Recent developments in system identification have brought attention to regularized kernel-based methods, where, adopting the recently introduced stable spline kernel, prior information on the unknown process is enforced. This reduces the variance of the estimates and thus makes kernel-based methods particularly attract…
We decompose the squared price-of-risk premium into three components: intervention-stable premium, confounding wedge, and information loss.
problem Decomposing the squared price-of-risk premium into its components
method Identifying an order-three obstruction to aggregation across portfolios
result The decomposition is estimable and detectable with a permutation-calibrated screen
A method removes treatment-covariate dependence for counterfactual prediction without adversarial training.
problem Counterfactual prediction under assignment bias.
method Information-theoretic approach learning a stochastic representation Z to minimize mutual information with outcomes.
result The method performs favorably in likelihood, counterfactual error, and policy evaluation compared to adversarial baselines.
New method reconstructs stable sentiment signals from sparse news data.
problem Transforming raw news sentiment outputs into reliable temporal series.
method Modular three-stage pipeline: aggregation, gap filling, and smoothing.
result Three-week lead-lag pattern between reconstructed sentiment and stock prices.
We tackle the challenge of disentangled representation learning in generative adversarial networks (GANs) from the perspective of regularized optimal transport (OT). Specifically, a smoothed OT loss gives rise to an implicit transportation plan between the latent space and the data space. Based on this theoretical obse…
Novel neural GP kernels learn stable, flexible covariance structures.
problem Scalable and flexible covariance kernels for Gaussian processes.
method Directly learn kriging coefficients and conditional standard deviations using deep neural architectures exploiting permutation-equivariant structure.
result Improved training stability and data efficiency with expressive, non-stationary kernels.
Enhances graph neural networks with spectral and topological information.
problem Improving graph neural networks' expressivity beyond Weisfeiler-Leman hierarchy.
method Integrates spectral information into Persistent Homology diagrams.
result SpectRe is strictly more expressive than PH and spectral information alone.