Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian -stable distribution received much interest in the literature. Here, we introduce a type of expectation maximization algorithm that e…
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We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered stable processes, we deal with density transformations and compute their -var…
This paper extends stable blanket theory to models with hidden variables and causal cycles.
problem Identifying stable predictors in models with hidden variables and causal cycles.
method Use acyclic directed mixed graphs (ADMGs) and directed graphs (DGs) with -separation and -separation to characterize and construct intervention-stable predictor sets.
result Graphical characterizations of Markov blankets, stable frontiers, and stable blankets in models with hidden variables and cycles.
This paper models cryptocurrencies using -stable distributions, outperforming other models.
problem Modeling the highly speculative and leptokurtic nature of cryptocurrencies.
method Used -stable distribution and compared it with other heavy tailed distributions. Employed maximum likelihood method for estimation.
result The -stable distribution fits cryptocurrency return data better than other models.
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.
Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically, we prove stable recurrent neural networks are well approximated by feed-forward …
Beyond Perturbation Stability: LP Recovery Guarantees for MAP Inference on Noisy Stable Instancesstat.ML
New LP method recovers MAP solution from noisy stable instances.
problem MAP inference on noisy stable instances.
method Designing an algorithm to find nearby perturbation stable instances and using LP relaxation.
result LP approximately recovers the MAP solution from noisy stable instances.
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…
New financial models use tempered stable subordination for better correlation dynamics.
problem Building financial models with better correlation dynamics.
method Introducing tempered stable Sato subordinators and additive inhomogeneous processes.
result The new process has time-dependent correlation, improving fit for financial data.
Stability of recurrent models is closely linked with trainability, generalizability and in some applications, safety. Methods that train stable recurrent neural networks, however, do so at a significant cost to expressibility. We propose an implicit model structure that allows for a convex parametrization of stable mod…
Retraining stabilizes model influence on data.
problem Performativity in predictive models leads to feedback loops.
method Developed the stable signal principle to address retraining dynamics.
result Repeated risk minimization converges geometrically to stable signal direction.
Proposes a method to learn stable invariant sets in dynamical systems.
problem Learning stable invariant sets in general dynamical systems.
method Generalizes Manek and Kolter's approach by introducing projection onto latent space shapes and using invertible neural networks.
result Validates the method and shows its usefulness for long-term prediction.
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.
In this article, we first propose the modified Hannan-Rissanen Method for estimating the parameters of the autoregressive moving average (ARMA) process with symmetric stable noise and symmetric stable generalized autoregressive conditional heteroskedastic (GARCH) noise. Next, we propose the modified empirical character…
We offer new formulas for European option pricing under tempered stable processes.
problem Pricing European options under tempered stable processes.
method Series expansions for tempered stable densities and European option prices.
result Our formulas are hyperparameter-free and competitive with traditional methods.
New method estimates tempered stable Lévy models with high accuracy.
problem Estimating volatility and jump intensity of tempered stable Lévy processes.
method Iterative method combining Truncated Realized Quadratic Variations and small-time approximations.
result Method outperforms existing alternatives in various scenarios.
New mathematical foundations for stable RKHSs improve system identification.
problem Improving stability tests and modeling of impulse responses.
method Providing new structural properties and stability conditions for stable RKHSs.
result Any stable kernel admits feature maps induced by orthogonal eigenvectors in l2.
The study extends GBM to include stable nonzero prices and finds a pronounced potential well.
problem The standard GBM model cannot describe stable nonzero prices in financial dynamics.
method Generalized GBM with polynomial drift of order q, model selection, and Markov chain Monte Carlo ensembles of potential functions.
result The optimal model for financial data is q=2, indicating the existence of a stable price.
New representations for surface groups in PU(2,1) are stable and larger than convex cocompact ones.
problem Characterizing representations of surface groups in PU(2,1).
method Introducing simple-stable representations and proving their properties.
result The set of conjugacy classes of simple-stable representations is a domain of discontinuity strictly larger than convex cocompact representations.
FlowMM models stable crystal structures efficiently.
problem Predicting and proposing stable crystalline structures.
method Riemannian Flow Matching generalized to crystal symmetries.
result 3x more efficient at finding stable materials.
We give a method to construct stable vector bundles whose rank divides the degree over curves of genus bigger than one. The method complements the one given by Newstead. Finally, we make some systematic remarks and observations in connection with rationality of moduli spaces of stable vector bundles.
Fitting Generalized Tempered Stable distribution: Fractional Fourier Transform (FRFT) Approachq-fin.ST
The paper uses FRFT to fit GTS distribution to asset returns.
problem Modeling asset returns with GTS distribution.
method Fractional Fourier Transform (FRFT) for fitting.
result GTS distribution fits SPY ETF and Bitcoin BTC returns.
A new nonparametric approach for system identification has been recently proposed where the impulse response is seen as the realization of a zero--mean Gaussian process whose covariance, the so--called stable spline kernel, guarantees that the impulse response is almost surely stable. Maximum entropy properties of the …
Kyle's equilibrium model stability proven for 1-2 trading times, but not for 3 or more.
problem Stability of Kyle's equilibrium model in a dynamic trading setting.
method Proof of stability for 1-2 trading times, non-stability for 3 or more trading times, independent of input parameters.
result Kyle's equilibrium model is stable for 1-2 trading times but not for 3 or more trading times.
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.
Study examines crypto-backed stable derivatives in DeFi, focusing on DAI.
problem Stability of crypto-backed stablecoins in DeFi.
method Introduced a belief parameter to simulate DAI, proposed a mathematical model, analyzed risk factors.
result Belief parameter improves simulation of DAI price stability.
The fields of compressed sensing (CS) and matrix completion have shown that high-dimensional signals with sparse or low-rank structure can be effectively projected into a low-dimensional space (for efficient acquisition or processing) when the projection operator achieves a stable embedding of the data by satisfying th…
Stable Torsion Lengthmath.GR
Study on stable torsion length in groups, showing it vanishes in crystallographic groups and providing algorithms for computation.
problem Understanding the stable torsion length in groups, especially in crystallographic and free products of groups.
method Developed linear programming and exact algorithms to compute stable torsion length in free products of groups and finite groups.
result Showed that stable torsion length vanishes in crystallographic groups and provided exact computations for nontrivial examples.
Study on stable translation lengths of surface homeomorphisms and their approximations.
problem Understanding stable translation lengths of homeomorphisms and their finite approximations.
method Comparing stable translation lengths of homeomorphisms and their finite approximations on curve graphs.
result Stable translation length of homeomorphisms with dense periodic points equals the supremum of their approximations.
Paper proves convex domains have one maximum for semi-stable solutions.
problem Analyzing critical points of semi-stable solutions on convex domains.
method Relating critical points to an auxiliary function and using topological degree.
result Positive, semi-stable solutions have exactly one non-degenerate critical point.
Proposes a new model for clustering with heavier tails.
problem Clustering with heavy-tailed data.
method Finite mixture of skewed sub-Gaussian stable distributions, maximum likelihood estimation, EM algorithm.
result The proposed model can robustly handle heavy-tailed data.
The paper extends stable minimal hypersurface results to δ-stable hypersurfaces in R^(n+1).
problem Extending stable minimal hypersurface results to δ-stable hypersurfaces.
method Regularity and compactness theorems for immersed δ-stable minimal hypersurfaces in R^(n+1).
result Optimal range of δ for δ-stable hypersurfaces.
Model selection on validation data is an essential step in machine learning. While the mixing of data between training and validation is considered taboo, practitioners often violate it to increase performance. Here, we offer a simple, practical method for using the validation set for training, which allows for a conti…
We show that stable commutator length is rational on free products of free Abelian groups amalgamated over , a class of groups containing the fundamental groups of all torus knot complements. We consider a geometric model for these groups and parameterize all surfaces with specified boundary mapping to th…
We propose a new blind source separation algorithm based on mixtures of alpha-stable distributions. Complex symmetric alpha-stable distributions have been recently showed to better model audio signals in the time-frequency domain than classical Gaussian distributions thanks to their larger dynamic range. However, infer…
The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure between components are investigated. We discuss a random number generating procedu…
The gradient flow of the Yang-Mills action acts pointwise on closed loops of gauge fields. We construct a topologically nontrivial loop of SU(2) gauge fields on S4 that is locally stable under the flow. The stable loop is written explicitly as a path between two gauge fields equivalent under a topologically nontrivial …
Stable solutions found for a specific physics model.
problem Stability of solutions to the -Yang-Mills-Higgs model.
method Gluing method and detailed analysis of linearized operators.
result Found a family of stable critical points in higher dimensions.
Proposes a new risk model using stable laws to manage company-wide losses.
problem Managing aggregate risks and pricing policies in the presence of systematic risk.
method Develops a modified risk model using multivariate stable distributions to account for various risk phenomena.
result Computes the Tail Conditional Expectation of aggregate risks and corresponding allocations.
CV inference can be invalid for relatively unstable model comparisons.
problem The validity of cross-validation for model comparison is questioned when models are relatively unstable.
method The study proves that simple, individually stable models can generate relatively unstable comparisons, invalidating CV inference.
result The Lasso and soft-thresholding generate relatively unstable comparisons, invalidating CV inferences.
New algorithm learns stable LDSs with lower error and better control performance.
problem Learning stable LDSs from data with minimal reconstruction error and stability constraints.
method Proposes an optimization method using a recent characterization of stable matrices, iteratively improving reconstruction error and ensuring stability.
result Achieves orders-of-magnitude improvement in reconstruction error compared to existing methods.
Study on stable Hamiltonian topology finds non-density of certain structures.
problem Non-density of stable hypersurfaces and Hamiltonian structures.
method Proving non-density results for stable hypersurfaces and Hamiltonian structures in various dimensions.
result Non-density of stable hypersurfaces and Hamiltonian structures in specific isotopy and homotopy classes.
The study proves that certain stable minimal hypersurfaces must be cylindrical.
problem Characterizing stable minimal hypersurfaces in Euclidean space.
method Analyzing the density at infinity and using stable area minimizing hypercone properties.
result Stable minimal hypersurfaces with specific conditions are cylindrical.
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.
Stable minimal hypersurfaces in math.DG
Flat stable minimal hypersurfaces in 5D are always flat.
problem Characterizing stable minimal hypersurfaces in higher dimensions.
method Analyzing properties of stable minimal hypersurfaces in \(\mathbf{R}^5\).
result Complete, two-sided stable minimal hypersurfaces in \(\mathbf{R}^5\) are flat.
Refines Khovanov homology using signed Burnside categories.
problem Stable homotopy refinement of Khovanov homology.
method Signed Burnside category approach to compare Blanchet and Khovanov chain complexes.
result Stable homotopy type construction for link diagrams.
Standard bubbles and partitions are stable in various model spaces.
problem Stability of standard bubbles and partitions in different model spaces.
method New conjugated Brascamp-Lieb inequality and conformally flattening boundary potential.
result Stability of standard bubbles and partitions in , , and .
Spectral densities of Wishart-Levy free stable random matrices: Analytical results and Monte Carlo validationcond-mat.stat-mech
Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails, that can be modelled with Levy stable distributions. We review comprehensively …