The speed with which a learning algorithm converges as it is presented with more data is a central problem in machine learning --- a fast rate of convergence means less data is needed for the same level of performance. The pursuit of fast rates in online and statistical learning has led to the discovery of many conditi…
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
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48 results for “centrality conditions”
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.
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.
In this study, we give the relationships between the conical curvatures of ruled surfaces drawn by the unit vectors of the ruling, central normal and central tangent of a regular ruled surface in the Euclidean -space. We obtain the differential equations characterizing slant ruled surfaces and if the reference ruled su…
Paper introduces input perturbation for privacy in machine learning models.
problem Protecting both training data and model parameters while maintaining privacy.
method Add noise to training data and train with perturbed data for differential privacy.
result Achieves (ε,δ)-differential privacy on the final model with privacy on original data.
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…
The problem of portfolio optimization is one of the most important issues in asset management. This paper proposes a new dynamic portfolio strategy based on the time-varying structures of MST networks in Chinese stock markets, where the market condition is further considered when using the optimal portfolios for invest…
Solved a specific case of Salter's question on Burau representation.
problem Under what conditions are matrices in the image of the Burau representation of .
method Algorithmically constructed a counterexample to Salter's specific question.
result The central quotient of the Burau image group is not the central quotient of a certain subgroup of the unitary group.
Study Drinfeld centralizers and Rouquier complexes in homotopy categories.
problem Interplay between Drinfeld centralizers and Rouquier complexes in homotopy categories.
method Study Drinfeld centralizers and Rouquier complexes in homotopy categories.
result Proved folklore facts about conjugation by Rouquier complexes in the Hecke category.
The article considers the problem of existence and uniqueness of centrally symmetrical convex body for which the projection curvature radius function coincides with a given flag function. A necessary and sufficient condition is found that ensures a positive answer. An algorithm for construction the body in question is …
This paper strengthens the central limit theorem for order statistics using relative entropy.
problem Establishing a stronger mode of convergence for central limit behavior of order statistics.
method Using relative entropy to ensure a stronger mode of convergence for central limit behavior of order statistics.
result An order rate of convergence is established under mild conditions.
Study compares costs and arbitrage in CEXs vs DEXs, finding DEXs better for large trades.
problem Comparing transaction costs and arbitrage in crypto exchanges.
method Comprehensive dataset analysis of transaction costs and no-arbitrage deviations.
result Fixed gas fees in DEXs impose a significant burden on small trades, while CEXs offer more competitive costs for larger trades.
Simple construction of Lie 2-groups from loop group extensions.
problem Constructing Lie 2-groups from loop group extensions.
method Using conjugation action of loop group on its central extension.
result Simple construction of string 2-group as a strict Fréchet Lie 2-group.
The paper studies groups of surface automorphisms and their representations.
problem Understanding the structure of groups of surface automorphisms and their representations.
method Analyzes group homomorphisms between and .
result Provides conditions for the image of the homomorphism to have finite index or no finite nonzero orbit.
The paper establishes CLTs for Markov chains and improves sampling algorithms for heavy-tailed distributions.
problem Establishing central limit theorems for ergodic averages of Markov chains.
method Drift conditions to provide necessary and sufficient conditions for CLTs, including lower bounds on convergence rates.
result Sharp conditions and convergence rates for various MCMC algorithms on heavy-tailed targets.
Geometric invariant theory introduces stability conditions mirroring abelian category theory.
problem Stability conditions in geometric invariant theory.
method Axiomatic notion of central charge and stability condition on schemes and stacks.
result Introduction of stability conditions for polarized schemes and smooth projective varieties.
This paper proves a central limit theorem for differential privacy in high dimensions.
problem Understanding optimal noise distributions for privacy-accuracy trade-offs in high-dimensional settings.
method Developed a central limit theorem approach to analyze differential privacy mechanisms.
result Gaussian mechanisms achieve the optimal privacy-accuracy trade-off in high dimensions.
Equilibrium pricing of securities in the co-presence of cooperative and non-cooperative populationsq-fin.MF
Develops an equilibrium model for securities pricing in a mixed cooperative and non-cooperative market.
problem Equilibrium pricing of securities in a market with cooperative and non-cooperative agents.
method Conditional extended mean-field control for cooperative agents, mean-field model for both cooperative and non-cooperative agents.
result Existence of a unique equilibrium for both finite-agent and mean-field models under certain conditions.
We give a refined value group for the collection of triple linking numbers of links in the 3-sphere. Given two links with the same pairwise linking numbers we show that they have the same refined triple linking number collection if and only if the links admit homeomorphic surface systems. Moreover these two conditions …
Node centrality is one of the most important and widely used concepts in the study of complex networks. Here, we extend the paradigm of node centrality in financial and economic networks to consider the changes of node "importance" produced not only by the variation of the topology of the system but also as a consequen…
Study Q-learning with averaging for reinforcement learning, proving efficient inference and error bounds.
problem Efficient inference and error bounds for Q-learning with averaging.
method Functional central limit theorem and asymptotic linear estimator for optimal Q-value function.
result Standardized partial-sum process converges weakly to a rescaled Brownian motion, matching instance-dependent lower bound for error.
Centralized systemic risk control in the interbank system: Weak formulation and Gamma-convergencemath.OC
Paper studies central bank's strategy to control systemic risk in interbank system.
problem Minimizing average distance between log-monetary reserves and target levels.
method Weak formulation, Ekeland's variational principle, Gamma-convergence, stochastic Fokker-Planck-Kolmogorov equation.
result Proves convergence of optimal strategies as number of banks increases.
This paper extends rack and quandle covering theory using higher categorical Galois theory.
problem Developing a higher covering theory of racks and quandles.
method Applying techniques from higher categorical Galois theory to extend and clarify the foundations of rack and quandle coverings.
result Identification of meaningful higher-dimensional centrality conditions defining higher coverings of racks and quandles.
This paper contains a feasibility study of deep neural networks for the classification of Euro banknotes with respect to requirements of central banks on the ATM and high speed sorting industry. Instead of concentrating on the accuracy for a large number of classes as in the famous ImageNet Challenge we focus thus on c…
Study finds central points of double heptagon surface are not connection points.
problem Identifying connection points on double heptagon translation surfaces.
method Used a gcd algorithm to determine hyperbolic directions and found non-connection points.
result Central points of heptagons are not connection points on double heptagon translation surfaces.
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.
For , we present a generalized central limit theorem for -stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential equations (PIDEs). A classical generalized central limit theorem is recovered as a special case, p…
We give conditions under which the normalized marginal distribution of a semimartingale converges to a Gaussian limit law as time tends to zero. In particular, our result is applicable to solutions of stochastic differential equations with locally bounded and continuous coefficients. The limit theorems are subsequently…
Counterexamples show Salter's question on Burau image is negative for n=4.
problem Conditions for a matrix to be in the Burau image of .
method Analyzing the central quotient and using counterexamples.
result The central quotient of the Burau image group does not coincide with the central quotient of a specific subgroup of the unitary group for .
Study efficient algorithms for one-shot federated conformal prediction.
problem Valid prediction sets in one-shot federated learning.
method Quantile-of-quantiles family of estimators and split conformal prediction.
result No significant loss in coverage and length compared to centralized setting.
A new subdivision scheme for Heisenberg group values with central smoothness loss.
problem Regularity of limit curves in Heisenberg group-valued subdivision schemes.
method Interpolatory subdivision scheme with central correction based on group law.
result Central part of limit curve converges to a continuous limit with logarithmic modulus of continuity.
New map connects stability conditions to Teichmüller space.
problem Stability conditions and Teichmüller space relationship.
method Using harmonic maps and 3-Calabi-Yau categories.
result Natural map between stability conditions and Teichmüller space.
Develops CLTs for Markov chain transition probabilities and policies.
problem Estimating transition probabilities and policies in controlled Markov chains.
method Non-parametric estimator for transition matrices; CLTs for value, Q-, and advantage functions; goodness-of-fit tests.
result Asymptotic normality of estimators under specific logging policies.
In this work we study the problem of existence of symplectic structures on free nilpotent Lie algebras. Necessary and sufficient conditions are given for even dimensional ones. The one dimensional central extension for odd dimensional free nilpotent Lie algebras is also considered.
Geometrically constructs Virasoro-Bott group from circle diffeomorphisms.
problem Constructing the Virasoro-Bott group from circle diffeomorphisms.
method Analogous to loop group construction, using disc diffeomorphisms with special boundary conditions.
result Identifies Virasoro-Bott group as a quotient of disc diffeomorphisms with identified Lie algebra.
New method allocates capital based on tail central moments for financial risk assessment.
problem Inability of CTE-based capital allocation to reflect tail behavior of losses.
method Developed TCM-based capital allocation for normal mean-variance mixture distributions.
result TCM-based method captures tail risk contributions not detected by CTE.
Characterizes periodic elements in Artin-Tits groups via stability conditions.
problem Understanding periodic elements in Artin-Tits groups.
method Dynamical characterization via 2-Calabi-Yau category and stability conditions.
result An element is periodic if and only if it has a fixed point in the stability manifold.
Second part of a series on higher coverings of racks and quandles.
problem Characterizing higher-dimensional centrality conditions in racks and quandles.
method Applying higher categorical Galois theory to racks and quandles.
result Identification and characterization of higher coverings, trivial coverings, and normal coverings.
We consider a distributed parameter estimation problem, in which multiple terminals send messages related to their local observations using limited rates to a fusion center who will obtain an estimate of a parameter related to observations of all terminals. It is well known that if the transmission rates are in the Sle…
We prove central limit theorems for the random walks on either the mapping class group of a closed, connected, orientable, hyperbolic surface, or on , each time under a finite second moment condition on the measure (either with respect to the Teichmüller metric, or with respect to the Lipschitz metric …
Paper improves SDR estimation speed and conditions.
problem Improving sufficient dimension reduction for multi-index models.
method Estimating expected smoothed gradient outer product.
result Achieves fast parametric convergence rate of .
The paper establishes a central limit theorem for estimating the influence parameter in a partially observed Hawkes process system.
problem Estimating the influence parameter in a partially observed Hawkes process system.
method Central limit theorem applied to an estimator of the influence parameter in a partially observed system of Hawkes processes.
result Establishes a central limit theorem for the estimator of the influence parameter under the subcritical condition.
Traffic congestion in metropolitan areas is a world-wide problem that can be ameliorated by traffic lights that respond dynamically to real-time conditions. Recent studies applying deep reinforcement learning (RL) to optimize single traffic lights have shown significant improvement over conventional control. However, o…
Federated survival analysis outperforms local and centralized training, with RSF offering the best balance of discrimination, calibration, and robustness.
problem Survival analysis models require large, diverse cohorts but are limited by privacy regulations and lack of centralized data.
method Federated learning (FL) is used to train shared models without exchanging raw data.
result FL consistently outperforms local training and approaches, and occasionally exceeds centralized performance.
Study 1-Lefschetz contact solvmanifolds, proving their characterization.
problem Characterize 1-Lefschetz contact solvmanifolds.
method Prove the 1-Lefschetz condition on Lie algebras via 1-dimensional central extensions and explicit cohomology relations.
result Unimodular symplectic Lie algebras are 1-Lefschetz if and only if their contactizations are.
Paper studies nonnegative Tucker decomposition identifiability with sparsity conditions.
problem Identify nonnegative Tucker decomposition factors uniquely.
method Adapting NMF identifiability results, derive procedures using tensor unfoldings or slices.
result Nonnegative Tucker decomposition factors are identifiable under certain sparsity conditions.
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 paper introduces fixed-point centralities for networks and graphons.
problem Defining network centralities for networks and graphons.
method Fixed-point centralities defined via permutation equivariant mappings and graphons.
result Variation bounds of fixed-point centralities under mild assumptions.