Bayesian method improves sparse CCA for multi-view data.
problem Integrative statistical analysis of multi-view high-dimensional data.
method Bayesian infinite factor model with graphical horseshoe prior or diagonal structure to encourage sparsity.
result The proposed Bayesian ScSCCA approach achieves robust estimation of sparse CCA.
GRASP simplifies Bayesian regression with grouped predictors using an adaptive NBP prior.
problem Regression with grouped predictors and adaptive shrinkage.
method Normal Beta Prime (NBP) prior with tunable hyperparameters for flexible sparsity control.
result Empirical validation of robust and versatile GRASP across various sparsity and signal-to-noise ratios.
PIE-PINN estimates elastic properties from noisy, low-res displacement data.
problem Estimating heterogeneous elastic properties from low-resolution, noisy data.
method Probabilistic Physics-Informed Neural Network (PIE-PINN) framework combining B-spline and hierarchical scale model.
result Robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data.
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.
Study of multiplicative connections in Lie groupoids.
problem Defining and understanding multiplicative connections in Lie groupoids.
method Definition and study of multiplicative connections satisfying compatibility with the groupoid structure.
result Identification of the obstruction to the existence of a multiplicative connection.
Study rectifying curves in 3D multiplicative Euclidean space.
problem Investigate rectifying curves in a non-Newtonian geometry setting.
method Apply multiplicative differential-geometric concepts to rectifying curves.
result Classify multiplicative rectifying curves using spherical curves.
The paper classifies symmetric triads with multiplicities and their applications.
problem Classifying symmetric triads with multiplicities and their applications.
method Developed the theory of symmetric triads with multiplicities, classified abstract triads, and determined corresponding triads for commutative compact triads.
result Classified symmetric triads with multiplicities and their applications.
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.
We define a concept which we call multiplicity. First, multiplicity of a morphism is defined. Then the multiplicity of an object over another object is defined to be the minimum of the multiplicities of all morphisms from one to another. Based on this multiplicity, we define a pseudo distance on the class of objects. W…
We introduce a multiple conjugation biquandle, and show that it is the universal algebra to define a semi-arc coloring invariant for handlebody-links. A multiple conjugation biquandle is a generalization of a multiple conjugation quandle. We extend the notion of n-parallel biquandle operations for any integer n, an…
Study finds methods to learn multiple solutions from single task in offline RL.
problem Learning multiple solutions from a single task in offline RL.
method Proposed algorithms for offline RL.
result Empirical results show learning of multiple solutions in offline RL.
Let (M,ω) be a connected symplectic manifold on which a connected Lie group G acts properly and in a Hamiltonian fashion with moment map $μ:M \lra \mf g^*$. Our purpose is investigate multiplicity-free actions, giving criteria to decide a multiplicity freenes of the action. As an application we give the complete cl…
MKLpy simplifies Multiple Kernel Learning in Python.
problem Learning optimal kernel functions from data.
method Python-based framework for Multiple Kernel Learning algorithms.
result Maximizes usability and simplifies development of novel solutions.
Recently neural networks and multiple instance learning are both attractive topics in Artificial Intelligence related research fields. Deep neural networks have achieved great success in supervised learning problems, and multiple instance learning as a typical weakly-supervised learning method is effective for many app…
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.
New infinite-dimensional representations with bounded multiplicity found for Lie groups.
problem Finding representations with bounded multiplicity for Lie groups.
method Proving existence of infinite-dimensional irreducible representations with bounded multiplicity property.
result Infinite-dimensional irreducible representations with bounded multiplicity found for non-compact semisimple Lie groups.
Classifies compact multiplicity free quasi-Hamiltonian manifolds.
problem Classifying compact, multiplicity free, quasi-Hamiltonian manifolds.
method Symplectic reductions and Lie group analysis.
result Recover old and find new examples of these structures.
Paper describes how to extend multiple conjugation quandles using maps.
problem Understanding affine extensions of multiple conjugation quandles.
method Introduces augmented MCQ Alexander pairs for affine extensions.
result Affine extensions of multiple conjugation quandles can be described by quadruples of maps.
New method constructs multiple group racks, differing from known constructions.
problem Define new invariants for spatial surfaces.
method Using a G-family of racks and a normal subgroup N of G.
result New method yields multiple group racks not derived from known methods.
Framework for generating multiple clusterings from multi-view data.
problem Challenges in finding optimal clustering criteria and handling incomplete multi-view data.
method DiMVMC framework that optimizes multiple decoder deep networks to complete data views and generate shared representations.
result DiMVMC outperforms state-of-the-art competitors in generating multiple clusterings with high diversity and quality.
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.
The paper introduces new measures to quantify variability in decision tree models due to observational multiplicity.
problem The variability in decision tree models due to observational multiplicity.
method Introduces leaf regret and structural regret to decompose observational multiplicity.
result Structural regret is the primary driver of observational multiplicity, accounting for over 15 times the variability of leaf regret in some datasets.
M3E2 neural network estimates multiple treatment effects.
problem Estimating effects of multiple treatments simultaneously.
method Multi-task learning neural network model for multiple treatments, continuous and binary.
result M3E2 outperforms baselines in synthetic datasets.
Log-Normal Multiplicative Dynamics improves low-precision training of neural networks.
problem Training large neural networks with low precision is unstable.
method Derive a Bayesian learning rule with log-normal posterior distributions and multiplicative updates.
result LMD achieves stable and accurate training for Vision Transformer and GPT-2.
In this paper we prove that the generic singularities of mean curvature flow of closed embedded surfaces in R3 modeled by closed self-shrinkers with multiplicity has multiplicity one. Together with the previous result by Colding-Minicozzi in [CM12], we conclude that the only generic singularity of mean curva…
Describes curves on surfaces with punctures and boundaries.
problem Representing multiple curves on surfaces with punctures and boundaries.
method Using geometric intersection numbers with embedded curves.
result Each multiple curve can be uniquely described.
Introduces Rashomon Capacity to measure predictive multiplicity in probabilistic classifiers.
problem Predictive multiplicity in classification models leading to unjustified decisions.
method Introduces Rashomon Capacity, a metric for probabilistic classifiers, and provides a rigorous derivation.
result Rashomon Capacity captures nuanced score variations and provides strategies for disclosing conflicting models.
Motivated by the study of a certain family of classical geometric problems we investigate the existence of multiplicative connections on proper Lie groupoids. We show that one can always deform a given connection which is only approximately multiplicative into a genuinely multiplicative connection. The proof of this fa…
Study ruled surfaces with finite multiplicity, focusing on their curves and singularities.
problem Understanding ruled surfaces with finite multiplicity.
method Analyzing striction curves and singularities of ruled surfaces.
result Geometric meanings of invariants related to ruled surfaces.
New example of surface flow converging to a plane with multiplicity 2.
problem Constructing mean curvature flows with specific convergence properties.
method Constructing a new example of a mean curvature flow in R3. result The flow converges to a plane with multiplicity 2 as time approaches infinity.
A (quasi-)Hamiltonian manifold is called multiplicity free if all of its symplectic reductions are 0-dimensional. In this paper, we classify multiplicity free Hamiltonian actions for (twisted) loop groups or, equivalently, multiplicity free (twisted) quasi-Hamiltonian manifolds for simply connected compact Lie groups. …
Multi-view clustering aims at integrating complementary information from multiple heterogeneous views to improve clustering results. Existing multi-view clustering solutions can only output a single clustering of the data. Due to their multiplicity, multi-view data, can have different groupings that are reasonable and …
Three counterexamples show higher eigenvalue multiplicities than conjectured.
problem Determining the maximum eigenvalue multiplicity for closed hyperbolic surfaces.
method Applying the twisted Selberg trace formula to induced representations of triangle groups.
result Found counterexamples with higher eigenvalue multiplicities than previously conjectured.
We introduce the notion of a conjugation-free geometric presentation for a fundamental group of a line arrangement's complement, and we show that the fundamental groups of the following family of arrangements have a conjugation-free geometric presentation: A real arrangement L, whose graph of multiple points is a union…
Polynomial algorithm for multiplication on one-hole torus skein algebra.
problem Complexity of multiplicative structure in skein algebra.
method Provided a polynomial algorithm for one-hole torus.
result Closed form formulas for multiplication of curves with low crossing number.
Proves C1,1 regularity for multiple membrane solutions.
problem Stationary C1,α solutions to the multiple membrane problem. method Uses C1,1-regularity estimate. result Proves C1,1 regularity for stationary solutions. Framework improves gradient estimation for faster training convergence.
problem Efficiently estimating noisy gradients in stochastic optimization.
method Dynamic adaptive importance sampling combining multiple distributions.
result Adaptively weighted multiple importance sampling yields superior gradient estimates.
On a Riemannian compact manifold, we give existence and multiplicity results for solutions of elliptic PDE by introducing isometry invariances. When the groups we used have finite orbits, we get multiplicity results for equations with the classical critical Sobolev exponent, for instance the Yamabe equation. When there…
Develops theory of weightings for Lie groupoids and algebroids.
problem Understanding differential geometry of weightings for Lie groupoids and algebroids.
method Extending work on weighted manifolds, defining weighted submanifolds, and developing theories of linear weightings and multiplicative weightings.
result Characterizes infinitesimally multiplicative weightings for Lie algebroids and classifies multiplicative weightings of Lie groupoids.
Multiplicative noise models are often used instead of additive noise models in cases in which the noise variance depends on the state. Furthermore, when Poisson distributions with relatively small counts are approximated with normal distributions, multiplicative noise approximations are straightforward to implement. Th…
Motivated by our attempt to recast Cartan's work on Lie pseudogroups in a more global and modern language, we are brought back to the question of understanding the linearization of multiplicative forms on groupoids and the corresponding integrability problem. From this point of view, the novelty of this paper is that w…
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix multiplication, that are robust to stragglers (i.e., machines that may perform slower …
Develops a method for solving optimal stopping problems with multiple exercise rights.
problem Optimal stopping with multiple exercise rights under model uncertainty.
method Pathwise duality approach based on robust martingale dual representation.
result Establishes upper and lower bounds that converge to the true solution.
Researchers create initial data for multiple collapsing boson stars.
problem Forming multiple trapped surfaces in spacetime.
method Constructed Cauchy initial data for EMKG system.
result Multiple trapped surfaces form in finite time.
The paper bounds eigenvalue multiplicities for hyperbolic surfaces using short geodesics.
problem Bounding the multiplicity of Laplacian eigenvalues for hyperbolic surfaces.
method Using the number of short closed geodesics and surface genus.
result Upper bounds on eigenvalue multiplicities, showing sublinear behavior under certain conditions.
Bayesian method corrects for model selection multiplicity in regression.
problem Model selection multiplicity in regression analysis.
method Developed a Bayesian prior distribution based on Holm procedure analogy.
result Adequate multiplicity correction requires sparsity not provided by recommended priors.
Algorithm calculates stable multiplicities in cohomology of configuration spaces.
problem Computing stable multiplicities of irreducible representations in cohomology.
method Developed an algorithm to compute stable multiplicities of families of irreducible representations.
result Computed stable multiplicities for all Young diagrams with 23 boxes up to degree 50.
Multiplicative random cascade model naturally reproduces the intermittency or multifractality, which is frequently shown among hierarchical complex systems such as turbulence and financial markets. As described herein, we investigate the validity of a multiplicative hierarchical random cascade model through an empirica…