Shapley values criticized for feature selection, leading to new insights.
problem Using Shapley values for feature selection is problematic.
method Introduced and critiqued Shapley values as feature selection tools, using counterexamples and simulations.
result Shapley values may not always align with feature selection goals.
The paper compares LOCO and Shapley values for feature importance, highlighting their limitations and suggesting improvements.
problem Quantifying feature importance in the presence of feature correlation.
method LOCO and Shapley Values, critiquing their axioms and proposing new measures.
result Shapley values do not eliminate feature correlation, and a modified LOCO is recommended.
Study Vassiliev invariants and periodic orbits of Axiom A flows.
problem Calculating Vassiliev invariants and writhe for periodic orbits of Axiom A flows.
method Asymptotic analysis of Vassiliev invariants and writhe.
result Obtained asymptotics for Vassiliev invariants and writhe of periodic orbits.
The paper develops methods for clustering directed dissimilarity networks.
problem Clustering directed dissimilarity networks.
method Admissible methods based on axioms of value and transformation.
result Unique admissible clustering method exists when modifying the axiom of value.
The paper develops axioms for uniquely decomposing functions with real arguments.
problem Decomposing functions with real arguments while preserving their overall structure.
method Developing axioms to uniquely decompose Borel measurable functions.
result Unique decompositions for all Borel measurable functions are achieved.
Study examines how machine learning attribution methods reflect risk in finance.
problem Ensuring machine learning attribution methods accurately reflect underlying risks in finance.
method Examined Shapley value and Integrated Gradients, and derived axioms from asset pricing domain knowledge.
result Neither Shapley value nor Integrated Gradients can satisfy all axioms for reflecting risks accurately.
Constructs flows on quotients of Lie groups for Anosov subgroups.
problem Understanding dynamics on quotients of Lie groups by Anosov subgroups.
method Utilizes geometric structures and Lie group theory to construct and analyze flows.
result Establishes that all refraction flows arise from this construction.
Mathematical proofs for Shapley explanations clarify their properties.
problem Clarify the essential axioms and properties of Shapley values in machine learning.
method Mathematical rigor and axiomatic characterization.
result The symmetry axiom is essential for Shapley values, contradicting Lundberg and Lee's claim.
Paper proposes financial schemes that exploit the Axiom of Choice for quick gains.
problem Financial quick gains through non-degenerate price paths.
method Trading schemes based on the Axiom of Choice, considering continuous and positive price paths.
result Schemes can lead to infinite wealth under certain conditions, but are impractical due to the Axiom of Choice.
New sampling methods improve Shapley values for explaining machine learning predictions.
problem Computational limitations in calculating Shapley values for complex models.
method Asymptotic normality results and paired-sampling approximations (KernelSHAP and PermutationSHAP).
result Paired-sampling PermutationSHAP provides exact results for interactions of maximal order two and has the additive recovery property.
New risk-averse estimators uniquely characterize MAP and Wallace-Freeman estimators.
problem Formalizing and characterizing Bayesian point estimators.
method Formulated axioms for inference, showing unique characterizations of MAP and Wallace-Freeman estimators.
result Axioms uniquely characterize MAP and Wallace-Freeman estimators for different types of estimation problems.
A new diversification measure DQ derived from risk measures addresses limitations of existing indices.
problem Limitations of existing diversification indices in capturing tail heaviness and common shocks.
method DQs are defined based on a parametric family of risk measures, satisfying six axioms of diversification.
result DQs can properly capture tail heaviness and common shocks, improving portfolio selection.
The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidence index is an extension of the concept to topological (Nielsen) coincidence theory. We demonstrate that three natural axioms are su…
A new axiom for Finsler geometry leads to constant flag curvature.
problem Understanding Finslerian manifolds and their properties.
method Proposing and proving an axiom of spheres.
result Finslerian manifolds satisfying the axiom of spheres have constant flag curvature.
The purpose of this note is introduce a new axiom (called the Descent Axiom) in the theory of r-spin cohomological field theories. This axiom explains the origin of gravitational descendants in this theory. Furthermore, the Descent Axiom immediately implies the Vanishing Axiom, explicating the latter (which has no a …
New approach solves St. Petersburg paradox using randomness.
problem St. Petersburg paradox in game theory.
method Using Von Mises' axiom of randomness to determine cognitive strategies.
result Cognitive strategies can generate results not random, resolving paradox.
ASVs incorporate causal knowledge into AI explainability.
problem AI explainability and fairness in models.
method Introduces Asymmetric Shapley values (ASVs) to incorporate causal structure.
result ASVs improve model explanations, detect unfair discrimination, and support feature selection.
Paper defines spatial risk measures for analyzing extreme events.
problem Risk assessment of extreme environmental events.
method Introduces spatial risk measures and axioms, investigates conditions for asymptotic spatial homogeneity.
result Conditions for spatial risk measures to satisfy asymptotic spatial homogeneity are provided.
Criterions for constancy of the holomorphic sectional curvature and the antiholomorphic sectional curvature are proved for almost Hermitian manifolds. It is shown, that an almost Hermitian manifold satisfying the axiom of antiholomorphic planes or the axiom of antiholomorphic spheres is a real or a complex space form.
Study examines explainable machine learning for monotonic models, finding Integrated gradients better for strong monotonicity.
problem Applying explainable machine learning to science-informed models.
method Proposed axioms for monotonicity, tested Shapley value and Integrated gradients methods.
result Integrated gradients provides better explanations for strong monotonicity.
New models for B-type topological theories using complex functions.
problem Constructing open-closed topological field theories for non-compact Calabi-Yau manifolds.
method Differential models using cochain level data, including Dolbeault algebras and categories.
result Most axioms satisfied on cohomology, conjecture remaining axioms hold.
A Morse complex for Axiom A flows on smooth manifolds.
problem Constructing a finite-dimensional cohomological complex for Axiom A flows.
method Defining anisotropic Sobolev spaces and spectral projectors.
result The cohomology of the constructed complex is isomorphic to De Rham cohomology.
Paper proposes a new method to evaluate joint risk under uncertainty.
problem Evaluating joint risk of multiple insurance risks under dependence uncertainty.
method Axiomatic approach to scalar and vector-valued distortion joint risk measures.
result Established a new scalar distortion joint risk measure with positive homogeneity.
The axiom of θ-holomorphic 2-planes is introduced. It is proved, that if an almost Hermitian manifold satisfies this axiom for a fixed θ, 0< θ< π/2, then it is a real space form.
Treating a conjecture, P^#P != NP, on the separation of complexity classes as an axiom, an implication is found in three manifold topology with little obvious connection to complexity theory. This is reminiscent of Harvey Friedman's work on finitistic interpretations of large cardinal axioms.
It is known, that if a 2m-dimensional Kahler manifold satisfies the axiom of holomorphic 2n-spheres (1<n<m) or the axiom of antiholomorphic n-spheres (2<n), it is of constant holomorphic sectional curvature. In this paper the same result is obtained under weaker assumptions.
The notion of Courant algebroid was introduced by Liu, Weinstein and Xu in 1997. Its definition consists of five axioms and an assumption for a derivation. It is shown that two of the axioms and the assumption for the derivation follow from the rest of the axioms.
New model outperforms traditional choice models in predicting human choices.
problem Need for choice models that don't assume traditional axioms.
method Introduces Pairwise Choice Markov Chain (PCMC) model.
result Significantly outperforms Multinomial Logit (MNL) model in prediction tasks.
We studied the axiom of anti-invariant 2-spheres and the axiom of co-holomorphic (2n+1)-spheres. We proved that a nearly Kählerian manifold satisfying the axiom of anti-invariant 2-spheres is a space of constant holomorphic sectional curvature. We also showed that an almost Hermitian manifold M of dimension $2m\geq…
New axioms justify ES without NRC, linking it to mean-ES portfolio selection.
problem Economic axioms for portfolio risk assessment and mean-ES portfolio selection.
method Introducing concentration aversion as an alternative to NRC, establishing axiomatic foundations.
result Concentration aversion uniquely characterizes the family of ES and provides new formulas.
Open problem: Establishing bounds for Cayley-table completion to discover discrete algorithmic axioms.
problem Discovering discrete algorithmic axioms missing in deep learning.
method Cayley-table completion as a testbed for algorithmic complexity minimization.
result Formal exact recovery bounds for Cayley-table completion.
The famous theorems of Cartan, related to the axiom of r-planes, and Leung-Nomizu about the axiom of r-spheres were extended to Kähler geometry by several authors. In this paper we replace the strong notions of totally geodesic submanifolds (r-planes) and extrinsic spheres (r-spheres) by a wider class of specia…
Solves clustering contradictions by high-dimensional embedding with wide gaps.
problem Kleinberg's clustering axioms are contradictory.
method Embedding in high-dimensional space with wide gaps between clusters.
result Handles clustering contradictions by design.
It is proved, that if an almost Hermitian manifold satisfies the axiom of coholomorphic spheres, it is conformal flat.
We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.
The second author previously discussed how classical complexity separation conjectures, we call them "axioms", have implications in three manifold topology: polynomial length stings of operations which preserve certain Jones polynomial evaluations cannot produce exponential simplifications of link diagrams. In this pap…
Caratheodory's axiom limits arbitrage in resource-limited systems.
problem Non-arbitrage constraints in resource-limited financial systems.
method Preserving Caratheodory's axiom in resource-limited systems.
result Exponential family is the necessary geometric structure for both thermodynamics and finance.
Introduces joint Shapley values to measure feature importance in models.
problem Measuring the importance of feature sets in machine learning models.
method Extends Shapley's axioms to measure a set of features' average contribution to a model's prediction.
result Joint Shapley values provide unique insights and are more consistent with local intuitions.
The paper establishes axioms for AMMs to ensure fair pricing and fee structures.
problem Ensuring fair and efficient pricing in decentralized finance (DeFi) AMMs.
method Formulating axioms on utility functions to characterize swap sizes and pricing oracles.
result Most existing AMMs satisfy the proposed axioms, and a new AMM is proposed with desirable properties.
New clustering method avoids problematic properties of existing algorithms.
problem Existing clustering algorithms cannot satisfy all natural clustering properties.
method Developed Morse Clustering using Morse Theory to satisfy Kleinberg's axioms with a new property, Monotonic Consistency.
result Morse Clustering satisfies Kleinberg's original axioms with Consistency replaced by Monotonic Consistency.
This paper presents an axiomatic scheme for interest rate models in discrete time. We take a pricing kernel approach, which builds in the arbitrage-free property and provides a link to equilibrium economics. We require that the pricing kernel be consistent with a pair of axioms, one giving the inter-temporal relations …
We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local Reidemeister trace in coincidence theory.
We introduce a new method to explain Gaussian processes using Shapley values.
problem Explaining the uncertainty in Gaussian process models.
method Extending Shapley values to stochastic cooperative games for Gaussian processes.
result Our method generates explanations that are random variables and satisfy favorable axioms.
Using properties of the determinant line bundle for a family of elliptic boundary value problems, we explain how the Fock space functor defines an axiomatic quantum field theory which formally models the Fermionic path integral. The 'sewing axiom' of the theory arises as an algebraic pasting law for the determinant of …
Defines Alexandrov spaces via axioms, focusing on curvature bounds.
problem Understanding Alexandrov spaces with curvature constraints.
method Formalizes spaces via axioms, distinguishing between curvature above and below.
result Comprehensive structure theory of Alexandrov spaces with curvature bounds.
A new method to explain black box models using Shapley values.
problem Quantifying the impact of individual input variables in black box functions.
method Cohort Shapley measure based on cooperative game theory, using similarity cohorts.
result Introduces a new squared cohort Shapley value for variable importance.
We shall give an axiomatic construction of Wess-Zumino-Witten actions valued in (G=SU(N)), (N\geq 3). It is realized as a functor ({WZ}) from the category of conformally flat four-dimensional manifolds to the category of line bundles with connection that satisfies, besides the axioms of a topological field theory, the …
New axioms for singquandles simplify applications and reveal algebraic aspects.
problem Axiomatizing singular knots and links.
method Presented new axioms for singquandles, simplified existing ones, and reformulated for affine singquandles.
result Simplified applications and revealed new algebraic aspects of singquandles.