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arXiv research

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.

168,932 papers · 148 categories

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0.3%0.5%0.8%0.2% · Dec 201519922001200920172026
6 results for “Sigma-Algebra”
An elementary proof of representation of submodular function as an supremum of measures on σσ-algebra with totally ordered generating classmath.FA

An elementary proof shows submodular functions can be represented as measure suprema.

problem Representing submodular functions as supremum of measures.
method Elementary proof using standard extension theorem of measures.
result Submodular functions can be expressed as supremum of measures.
submodular functionssuprema of measurestotal ordermeasurable spacestandard extension theorem
2024-06-26abs ↗pdf ↗
On conditioning and consistency for nonlinear functionalsq-fin.MF

The paper defines and characterizes conditional nonlinear expectations.

problem Defining and characterizing conditional nonlinear expectations.
method Embedding in decision theory, using state-dependent preferences, and continuous utility representation.
result Consistent backward conditional projections are characterized by the Sure-Thing Principle.
conditional nonlinear expectationsconsistencydecision theorystate-dependent preferencesSure-Thing Principle
2024-01-17abs ↗pdf ↗
On the equivalence between graph isomorphism testing and function approximation with GNNscs.LG

Graph isomorphism can be tested using GNNs, proving their expressive power.

problem Testing graph isomorphism using Graph Neural Networks (GNNs).
method Equivalence between GNNs' function approximation and graph isomorphism testing, using sigma-algebra.
result Equivalence between graph isomorphism testing and GNN function approximation.
Graph Neural NetworksGraph IsomorphismFunction ApproximationSigma-AlgebraInvariant Graph Network
2019-05-29abs ↗pdf ↗
Machine Unlearning via Information Theoretic Regularizationcs.LG

Unified framework for removing unwanted information from machine learning models.

problem Removing undesirable features or data points from machine learning models while preserving utility.
method Information-theoretic regularization approach for data point and feature unlearning.
result Unified mathematical framework with provable guarantees for both data point and feature unlearning.
machine learningunlearninginformation theoryfeature selectiondata point removal
2025-02-08abs ↗pdf ↗