Framework uses dropout to efficiently explore Rashomon set for multiplicity estimation.
problem Efficiently measuring and mitigating conflicting model outputs in classification tasks.
method Dropout-based exploration of Rashomon set for multiplicity estimation.
result Framework outperforms baselines in multiplicity metric estimation with significant runtime speedup.
Paper proves Pareto efficient insurance for multiple entities.
problem Optimizing insurance for multiple policyholders and insurers.
method Sum-minimization characterization and pairwise implementability analysis.
result Characterization of Pareto efficient insurance arrangements.
Paper proposes a new method to compare classifiers across multiple datasets.
problem Comparing classifiers over multiple datasets with multiple criteria.
method Adopting decision theory, the paper introduces generalized stochastic dominance for ranking classifiers.
result Generalized stochastic dominance can be used to rank classifiers and statistically tested.
Proposes DEXP3.M for unknown delay in multi-arm bandit with multiple play.
problem Unknown delays in adversarial multi-armed bandit with multiple play.
method DEXP3.M algorithm addressing the challenge of associating feedback losses to arms.
result Regret bound is only slightly worse than single play setting.
Paper proposes S-BOMM for optimization with multiple models, focusing on consistency.
problem Optimization challenges with multiple models of varying fidelity and accuracy.
method Set-Based Optimization with Multiple Models (S-BOMM) focusing on model consistency.
result Empirical results show S-BOMM's effectiveness in identifying good solutions across multiple models.
We define a functor Q from the category of multiple conjugation biquandles to that of multiple conjugation quandles. We show that for any multiple conjugation biquandle X, there is a one-to-one correspondence between the set of X-colorings and that of Q(X)-colorings diagrammatically for any …
We consider the notion of multiple gap as a finite set of ideals that cannot be separated. We study the different types of such objects that can be found in the Boolean algebra of subsets of the natural numbers modulo finite sets.
New method identifies proxies for causal effects on multiple outcomes.
problem Estimating causal effects in scenarios with multiple outcomes and treatments.
method Causal discovery method leveraging multiple outcomes as proxies for each treatment effect.
result Parallel studies of multiple outcomes can assist in causal identification.
Study on geodesics proving index and intersection bounds, with examples of multiplicity.
problem Understanding the index and intersections of min-max geodesics on surfaces.
method Proof of tangent cone structure, construction of metrics with multiplicity.
result Upper bounds on index and intersections, examples of multiplicity.
Unified framework controls false discovery rate in bandit multiple testing.
problem Designing adaptive algorithms to identify true discoveries in multiple hypothesis testing.
method Unified modular framework using e-processes for FDR control in arbitrary settings.
result Unified framework ensures FDR control for dependent and simultaneous arm queries.
Variant of Seiberg-Witten equations for multiple-spinors connects to stability of holomorphic bundles.
problem Detecting stability of holomorphic vector bundles using Seiberg-Witten equations.
method Abelian gauge-theoretic variant of Seiberg-Witten equations for multiple-spinors.
result Constructs a numerical invariant related to φ−stability of SU(n)−holomorphic vector bundles. I construct multiplicies and orientations of tangent cones to any blow-up set Z for the Seiberg-Witten equation with multiple spinors. This is used to prove that Z determines a homology class, which is shown to be equal to the Poincaré dual of the first Chern class of the determinant line bundle. I also obtain a lo…
Integrates multiple datasets to solve open set crowdsourcing problems.
problem Crowdsourcing with unknown label space and unfamiliar tasks.
method Integrates multiple crowdsourced datasets, weights them based on category correlation, and uses open set transfer learning.
result Proves OSCrowd solves open set crowdsourcing problems and outperforms related solutions.
Simple greedy algorithms can excel in multi-objective bandits with multiple good arms.
problem Optimizing multiple objectives in bandits is traditionally harder.
method Introduced greedy algorithms that exploit multiple good arms for multiple objectives.
result Simple greedy algorithms achieve strong performance in multi-objective bandits.
We study the multiplicity sets of first order symbols associated with differential operators on two dimensional surfaces. This work is inspired by the phenomenon of conical refraction explained by the existence of singularities in the Fresnel hyper-surface for Maxwell's equations on an anisotropic crystal.
The paper extends the spacetime positive mass theorem to multiple time dimensions.
problem Proving the nonnegativity of mass in spacetimes with multiple time dimensions.
method Generalizing the spacetime positive mass theorem to include multiple time dimensions and showing mass nonnegativity through energy inequalities.
result Equality in the energy inequality implies a foliation by flat submanifolds.
rMCL improves on MCL by preserving diversity in predictions for regression problems.
problem Multimodal density estimation in regression settings with multiple targets.
method rMCL uses a learned scoring scheme based on Voronoi tessellations to maintain diversity among predictions.
result rMCL outperforms existing MCL variants in sound source localization tasks.
We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models can only utilize the sufficiently fine-grained auxiliary data sets on the same doma…
Study proves existence and convergence of discrete-time Kyle models with multiple insiders.
problem Existence and convergence of discrete-time Kyle models with multiple informed traders.
method Proves existence and convergence of discrete-time Kyle models with multiple informed traders using mathematical proofs.
result Equilibrium exists and converges to continuous-time equilibrium as the number of trading times increases.
Sharp generalization of boundary regularity for area minimizing currents with arbitrary multiplicity.
problem Boundary regularity of area minimizing currents with multiplicity.
method Sharp generalization of Allard's boundary regularity theorem to higher multiplicity settings.
result The set of density Q/2 singular boundary points of T is Hm−3-rectifiable. Enhances anomaly detection using multiple reference datasets.
problem Lack of performance with multiple reference datasets.
method Generalizes existing techniques CWoLa and SALAD for multiple reference datasets.
result Improved performance across various settings.
X-SHAP assesses multiplicative variable contributions in machine learning models.
problem Understanding multiplicative interactions in machine learning models.
method Model-agnostic method that extends SHAP to assess multiplicative contributions.
result X-SHAP proves useful in capturing multiplicative feature importance.
Approach generates multiple correct predictions from single supervision.
problem Single correct prediction from multiple possible alternatives.
method Develops an approach to generate multiple high-quality predictions.
result Can generate high-quality outputs different from observed.
It is shown that the singular set for the Yang-Mills flow on unstable holomorphic vector bundles over compact Kaehler manifolds is completely determined by the Harder-Narasimhan-Seshadri filtration of the initial holomorphic bundle. We assign a multiplicity to irreducible top dimensional components of the singular set …
A multiple instance dictionary learning method using functions of multiple instances (DL-FUMI) is proposed to address target detection and two-class classification problems with inaccurate training labels. Given inaccurate training labels, DL-FUMI learns a set of target dictionary atoms that describe the most distincti…
Localized sketching improves matrix multiplication and ridge regression complexity.
problem Efficiently approximate matrix multiplication and ridge regression with limited data availability.
method Localized sketching matrices for block diagonal structure, reducing sample complexity.
result Localized sketching achieves sample complexity matching global sketching methods.
We study diffeologies on locally convex spaces and their application to smooth multiplication of distributions.
problem Constructing smooth multiplication of distributions on locally convex spaces.
method Using diffeological colimits and wavefront-set criterion.
result Proving smooth multiplication of microlocally multipliable distributions.
Bayesian model compares ML algorithms on various datasets.
problem Comparing multiple machine learning algorithms across multiple datasets.
method Bayesian Bradley-Terry model, defining regions of practical equivalence (ROPE).
result Allows nuanced statements and ROPE definitions for algorithm comparison.
The paper strengthens a theorem on crossings under linear perturbations with Hausdorff measure estimates.
problem Understanding multiple-point crossings under linear perturbations.
method Establishes a transversality theorem with Hausdorff measure estimates for exceptional parameter sets.
result Explicit upper bounds on the Hausdorff dimension of the exceptional set.
The paper proves that most metrics satisfy a strong version of Arnold's conjecture for Laplace eigenvalues.
problem Understanding metrics that satisfy a strong version of Arnold's conjecture for Laplace eigenvalues.
method Using geometric characterizations and perturbation theory, the paper proves the conjecture for most metrics.
result The Strong Arnold Hypothesis is satisfied for all metrics except for a set of infinite codimension.
Generalizes quandle constructions and defines a multiplication that results in an abelian group.
problem Tackles the construction and multiplication of quandle structures.
method Defines a composition of quandle structures and proves conditions for it to form a quandle, then shows the resulting group is abelian.
result Multiplication of quandle structures results in an abelian group.
We consider a problem of grouping multiple graphs into several clusters using singular value thesholding and non-negative factorization. We derive a model selection information criterion to estimate the number of clusters. We demonstrate our approach using "Swimmer data set" as well as simulated data set, and compare i…
Study on geodesics in spacetime, proving properties of multiple maximizing paths.
problem Characterizing multiple maximizing geodesics in globally hyperbolic spacetimes.
method Analyzing topological properties of the locus of multiple maximizing geodesics.
result The set of multiple maximizing geodesics is locally contractible.
The study explores mapping degree sets and their properties for manifolds.
problem Understanding the structure and properties of mapping degree sets for manifolds.
method Analyzes the properties of mapping degree sets and their relationships with self-mapping degree sets.
result Not every multiplicative set containing 0,1 is a self-mapping degree set.
We determine the sample complexity of pure exploration bandit problems with multiple good answers. We derive a lower bound using a new game equilibrium argument. We show how continuity and convexity properties of single-answer problems ensures that the Track-and-Stop algorithm has asymptotically optimal sample complexi…
New method uses Multiple Choice Learning for speech separation.
problem Ambiguous task of assigning model predictions to ground truth signals.
method Uses Multiple Choice Learning (MCL) instead of Permutation Invariant Training (PIT).
result MCL matches PIT performance but is computationally advantageous.
Adapts manifold structure for better clustering performance.
problem Lack of consideration for local manifold structure in existing multiple kernel k-means methods.
method Adopts manifold adaptive kernel to integrate local manifold structure of kernels.
result Proposed method outperforms state-of-the-art methods.
Method constructs uniformly valid prediction sets across multiple distributions.
problem Uniformly valid prediction sets across multiple distributions.
method Max-p aggregation scheme and optimization programs.
result Optimal and efficient prediction sets for multiple distributions.
We introduce Bayesian multi-tensor factorization, a model that is the first Bayesian formulation for joint factorization of multiple matrices and tensors. The research problem generalizes the joint matrix-tensor factorization problem to arbitrary sets of tensors of any depth, including matrices, can be interpreted as u…
We investigate the adversarial bandit problem with multiple plays under semi-bandit feedback. We introduce a highly efficient algorithm that asymptotically achieves the performance of the best switching m-arm strategy with minimax optimal regret bounds. To construct our algorithm, we introduce a new expert advice alg…
We present a proof of the Riemannian Penrose inequality with charge in the context of asymptotically flat initial data sets for the Einstein-Maxwell equations, having possibly multiple black holes with no charged matter outside the horizon, and satisfying the relevant dominant energy condition. The proof is based on a …
The nonzero level sets in n-dimensional flat affine space of a translationally homogeneous function are improper affine spheres if and only if the Hessian determinant of the function is equal to a nonzero constant multiple of the nth power of the function. The exponentials of the characteristic polynomials of certa…
The paper develops a new formula for financial pricing under multiple interest rates and collateralization.
problem Financial pricing under multiple interest rates and collateralization.
method Derives a change of measure formula for recursive conditional expectations in a jump-diffusion setting.
result Generalizes the change of numéraire technique for multiple interest rates and collateralization.
New method improves transductive learning predictions with multiplicative oracle inequalities.
problem Improving transductive learning predictions with known covariates.
method Median of Level-Set Aggregation (MLSA) for transductive LOO prediction.
result Proved multiplicative oracle inequality for LOO error.
Screening is the problem of finding a superset of the set of non-zero entries in an unknown p-dimensional vector β* given n noisy observations. Naturally, we want this superset to be as small as possible. We propose a novel framework for screening, which we refer to as Multiple Grouping (MuG), that groups variables, pe…
Multiple sets of measurements on the same objects obtained from different platforms may reflect partially complementary information of the studied system. The integrative analysis of such data sets not only provides us with the opportunity of a deeper understanding of the studied system, but also introduces some new st…
Recent literature has demonstrated promising results for training Generative Adversarial Networks by employing a set of discriminators, in contrast to the traditional game involving one generator against a single adversary. Such methods perform single-objective optimization on some simple consolidation of the losses, e…
New algorithm for active learning in multiple matrix completion problems.
problem Simultaneous matrix completion with unknown ranks and varying sizes.
method MAlocate algorithm that adapts to unknown ranks and sizes.
result Minimax-optimal performance demonstrated with lower-bound analysis.