The Pinned AUC metric hides unintended bias when class distributions vary.
problem Unintended bias in classification models.
method Examines the Pinned AUC metric and its limitations.
result Pinned AUC can obscure different types of unintended bias.
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48 results for “Pinned AUC”
Unified Pin-SVM improves accuracy over existing Pin-SVM model.
problem Difficulty in Pin-SVM model for .
method Unified Pin-SVM model that solves a QPP for .
result Significant improvement in accuracy over existing Pin-SVM model.
User response prediction is a crucial component for personalized information retrieval and filtering scenarios, such as recommender system and web search. The data in user response prediction is mostly in a multi-field categorical format and transformed into sparse representations via one-hot encoding. Due to the spars…
The paper studies -structures on non-oriented 4-manifolds via Lefschetz fibrations.
problem Understanding -structures on non-oriented 4-manifolds and Lefschetz fibrations.
method Extending work on orientable settings, the paper uses Lefschetz fibrations to analyze -structures on non-orientable 4-manifolds and vector bundles.
result The paper provides existence results of and -structures on closed non-orientable 4-manifolds and Lefschetz fibrations over the 2-sphere.
Classifies stability of flat-core -elasticae pinned at boundaries.
problem Stability of flat-core -elasticae under pinned boundary conditions.
method Classification based on previous work for all and .
result Completes the classification of stable pinned -elasticae in .
Study pin manifolds using Clifford linear Dirac operator and KO-theory.
problem Index theory on Pin manifolds.
method Clifford linear Dirac operator and differential KO-theory.
result Systematic treatment of index theory on Pin manifolds.
Two Pin(2)-equivariant Floer homologies are shown to be equivalent.
problem Equivalence of Pin(2)-equivariant Floer homologies.
method Comparison of definitions by Lin and Manolescu.
result Pin(2)-equivariant monopole Floer homology is isomorphic to Seiberg-Witten Floer homology.
Bauer-Furuta invariantsmath.DG
Established a stable cohomotopy refinement for Pin(2) monopole invariants.
problem Refining monopole invariants for Pin(2) structures.
method Adapted Bauer-Furuta's Seiberg-Witten refinement method to Pin(2) monopole invariants.
result Connected sum formula for the refined invariants.
The paper explores properties of Pin structures on surfaces and their cobordism.
problem Understanding Pin structures on compact surfaces and their cobordism.
method Analyzes Pin structures on surfaces and their cobordism, providing a construction for dimensions up to two.
result Pin structures on surfaces differ by a diffeomorphism if and only if they are cobordant, but this does not extend to higher dimensions.
Study on a pinning model with random walk increments, showing convergence to a critical disordered pinning measure.
problem Understanding the critical behavior of a disordered pinning model.
method Analyzing a disordered pinning model induced by a random walk with specific moment conditions, showing convergence to a limiting measure.
result Convergence of point-to-point partition functions to the critical disordered pinning measure in the critical window.
The pinning ideal of multiloops is shown to be NP-complete.
problem Computing the pinning number of multiloops is NP-complete.
method Adapted algorithms from curve intersection and taut loop characterization to prove NP-completeness.
result The pinning number problem is NP-complete for multiloops in the sphere.
Monograph compares curve signs in intrinsic and Pin-dependent definitions.
problem Comparing curve signs in intrinsic and Pin-dependent definitions.
method Intrinsic perspective on Spin- and Pin-structures, detailed constructions of orientations, explicit comparison.
result Explicit comparison between curve signs in intrinsic and Pin-dependent definitions.
Complex pinning problem simplified for simple multiloops.
problem Complexity of pinning simple multiloops in fixed surfaces.
method Analysis of pinning problem in simple multiloops.
result Pinning problem in simple multiloops is P when 3 strands or fewer, NP-complete when 20 strands or more.
In this remark, we show how the monopole Frøyshov invariant, as well as the analogues of the Involutive Heegaard Floer correction terms , are related to the -equivariant Floer homology . We show that the only interesting correction terms of a $\mathrm{Pin}…
We give definitions of moduli spaces of framed, r-Spin and Pin surfaces. We apply earlier work of the author to show that each of these moduli spaces exhibits homological stability, and we identify the stable integral homology with that of certain infinite loop spaces in each case. We further show that these moduli spa…
We give necessary and sufficient conditions for the existence of pin+, pin- and spin structures on Riemannian manifolds with holonomy group . For any n>3 (resp. n>5) we give examples of pairs of compact manifolds (resp. compact orientable manifolds) M_1, M_2, non homeomorphic to each other, that are Laplace isos…
Paper extends Brownian bridge with random length and pinning point for financial modeling.
problem Modeling financial information flow with uncertainty in pinning point.
method Introduced an extension of Brownian bridge with random length and pinning point, derived formulae for conditional expectations.
result The extended Brownian bridge fails to be Markovian if pinning point distribution is absolutely continuous.
The paper finds curves minimizing elastic energy pinned at endpoints.
problem Finding curves that minimize elastic energy with fixed endpoints.
method Applying the shooting method to identify and classify critical points.
result Critical points consist of wavelike elasticae, and minimizers have no loops or interior inflection points.
The topological condition for the existence of a structure on the product of two Riemannian manifolds is derived and applied to construct examples of manifolds having the weaker Lipschitz structure, but no structure. An example of a five-dimensional manifold with this property is given; it is pointed ou…
Spaces of positive and tropical points described as Teichmüller and lamination spaces with pinnings.
problem Describing spaces of positive and tropical points in moduli space with pinnings.
method Topological description of Teichmüller and lamination spaces with pinnings.
result Formulae relating functions on Teichmüller space with pinnings and topological description of tropicalized amalgamation map.
PIN models feature interactions using a neural network that mimics decision trees.
problem Modeling feature interactions in tabular data for predictive modeling.
method Tree-like Pairwise Interaction Network (PIN) architecture that captures pairwise feature interactions through a shared feed-forward neural network.
result PIN outperforms traditional and modern neural networks benchmarks in predictive accuracy.
A correspondence between different -type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.
In previous work, we introduced a natural -structure on the -monopole Floer chain complex of a closed, oriented three-manifold , and showed that it is non-formal in the simplest case in which is the three-sphere . In this paper, we provide explicit descriptions of seve…
New equations use Pin(2) symmetry to study spinor and connection solutions.
problem Study of spinor and connection solutions on 4-manifolds.
method Define and analyze Seiberg-Witten-like equations with Rarita-Schwinger operators.
result Moduli space of solutions is non-compact and non-empty under certain conditions.
Pinned planar p-elasticaemath.DG
Classifies pinned -elasticae and finds unique optimality exponents.
problem Classifying and understanding -elasticae under pinned boundary conditions.
method Classification and analysis of -elasticae, proving uniqueness and existence.
result Discovery of a unique exponent for full optimality.
We study the behavior of -monopole Floer homology under connected sums. After constructing a (partially defined) -module structure on the -monopole Floer chain complex of a three manifold (in the spirit of Baldwin and Bloom's monopole category), we identify up to …
The study explores psc-metrics on non-spin manifolds with pin^\pm or spin^c structures.
problem Existence of psc-metrics on non-spin manifolds with specific structures.
method Analysis of Dirac operators and index theory on pin^\pm or spin^c manifolds.
result The index of a Dirac operator controls the existence of psc-metrics on certain manifolds.
Research provides obstructions to Stein fillings of certain rational homology spheres.
problem Obstructing Stein fillings of specific rational homology spheres.
method Uses Pin(2)-monopole Floer homology.
result Provides obstructions to the intersection forms of Stein fillings.
We compute the Pin(2)-equivariant monopole Floer homology for the class of plumbed 3-manifolds with at most one "bad" vertex (in the sense of Ozsvath and Szabo). We show that for these manifolds, the Pin(2)-equivariant monopole Floer homology can be calculated in terms of the Heegaard Floer/monopole Floer lattice compl…
This study analyzes a non-orientable spacetime model in 1+1D quantum gravity.
problem Analyzing a non-orientable spacetime model in 1+1D quantum gravity.
method Formulated a Jackiw-Teitelboim gravity toy model on the Möbius band, computed Stiefel-Whitney classes, and analyzed the Dirac operator.
result Half-integer momentum quantization, spectral symmetry, vanishing mod-2 index, and η_D(0) = 0 follow.
Unoriented 3d TFTshep-th
This paper generalizes two facts about oriented 3d TFTs to the unoriented case. On one hand, it is known that oriented 3d TFTs having a topological boundary condition admit a state-sum construction known as the Turaev-Viro construction. This is related to the string-net construction of fermionic phases of matter. We sh…
New methods prove weak homotopy inequivalence for manifold symmetries.
problem Understanding symmetries of smooth 4-manifolds.
method Using Pin(-2)-monopole equations.
result New examples of 4-manifolds where symmetries are not fully represented.
There are eight possible Pin groups that can be used to describe the transformation behaviour of fermions under parity and time reversal. We show that only two of these are compatible with general relativity, in the sense that the configuration space of fermions coupled to gravity transforms appropriately under the spa…
Two quandles from Coxeter groups studied, showing similarities in automorphism groups.
problem Understanding quandles from Coxeter groups and their automorphism groups.
method Defined two families of quandles from Coxeter quandles and Pin groups, analyzed their automorphism groups.
result Similarity in inner automorphism groups of the two quandles.
We establish a mod 2 index theorem for real vector bundles over 8k+2 dimensional compact pin manifolds. The analytic index is the reduced invariant of (twisted) Dirac operators and the topological index is defined through -theory. Our main result extends the mod 2 index theorem of Atiyan and Singer to non-o…
We investigate the -monopole invariants of symplectic -manifolds and Kähler surfaces with real structures. We prove the nonvanishing theorem for real symplectic -manifolds which is an analogue of Taubes' nonvanishing theorem of the Seiberg-Witten invariants for symplectic -manifolds. Further…
In studying the "11/8-Conjecture" on the Geography Problem in 4-dimensional topology, Furuta proposed a question on the existence of Pin(2)-equivariant stable maps between certain representation spheres. In this paper, we present a complete solution to this problem by analyzing the Pin(2)-equivariant Mahowald invariant…
We compute the Yamabe invariants for a new infinite class of closed -dimensional manifolds by using a "twisted" version of the Seiberg-Witten equations, the -monopole equations. The same technique also provides a new obstruction to the existence of Einstein metrics or long-time solutions of the no…
-monopole invariantsmath.GT
We introduce a diffeomorphism invariant of -manifolds, the -monopole invariant, defined by using the -monopole equations. We compute the invariants of several -manifolds, and prove gluing formulae. By using the invariants, we construct exotic smooth structures on the connecte…
Maximizing the area under the receiver operating characteristic curve (AUC) is a standard approach to imbalanced classification. So far, various supervised AUC optimization methods have been developed and they are also extended to semi-supervised scenarios to cope with small sample problems. However, existing semi-supe…
Improves AUC for disadvantaged groups by adding features.
problem Reducing cross-group differences in AUC for classification models.
method Feature augmentation to improve AUC for disadvantaged groups.
result Significantly improves AUC for disadvantaged groups.
Paper proposes a new algorithm to minimize AUC disparities in machine learning models.
problem Minimizing unfairness in AUC scores for machine learning models.
method Proposes a minimax learning and bias mitigation framework for AUC optimization.
result Proves the convergence of the proposed algorithm to minimize group-level AUC.
We prove the existence of an exact triangle for the Pin(2)-monopole Floer homology groups of three manifolds related by specific Dehn surgeries on a given knot. Unlike the counterpart in usual monopole Floer homology, only two of the three maps are those induced by the corresponding elementary cobordism. We use this tr…
This paper surveys AUC maximization for big data and AI.
problem Assessing classifier performance for imbalanced data.
method Maximizing AUC score directly.
result No comprehensive survey of AUC maximization exists.
Modified AUC improves CNN training by considering model confidence.
problem Improving binary classifier performance metrics.
method Proposes a modified AUC metric that incorporates model confidence into BCE loss for CNN training.
result Demonstrates improved performance on three datasets: MNIST, prostate MRI, and brain MRI.
Discounted optimal stopping of a Brownian bridge, with application to American options under pinningq-fin.CP
Optimizes American option exercise timing with discounted Brownian bridge model.
problem Optimizing American option exercise timing under special market conditions.
method Modeling terminal price as a Brownian bridge with future information disclosure and discount factor inclusion.
result Characterization and numerical computation of optimal stopping boundary with discount factor.
New classification for some unorientable 4-manifolds using modified surgery theory.
problem Classifying stable diffeomorphism classes of unorientable 4-manifolds.
method Modified surgery theory applied to unorientable 4-manifolds with specific fundamental groups.
result Found nine stable diffeomorphism classes for pin manifolds, one for pin, and four for neither, under certain conditions.
New algorithm optimizes AUC for sparse high-dimensional data in online learning.
problem Optimizing AUC for imbalanced classification with high-dimensional sparse data.
method Proposes extsc{FTRL-AUC} algorithm with reduced per-iteration cost and sparsity.
result Significantly improves AUC scores and model sparsity in real-world datasets.