Arnold-Liouville systems cannot be bi-Hamiltonian generically.
problem The bi-Hamiltonian structure of Arnold-Liouville systems.
method Proving that a specific class of smooth functions is a meagre subset for the Fréchet topology, which implies Arnold-Liouville systems cannot be bi-Hamiltonian.
result Generically, Arnold-Liouville systems cannot be bi-Hamiltonian.
Paper explores learning patterns in binary sequences, finding no method consistently outperforms others.
problem Learning patterns in infinite binary sequences.
method Various learning methods are compared, finding no method consistently outperforms others.
result No learning method consistently outperforms others in predicting binary sequences.
Proves spectral simplicity of Hodge Laplacian and curl operator along metric families.
problem Simplicity of Hodge Laplacian and curl operator eigenvalues along metric families.
method Generalized Teytel's method to compute meagre codimension of metrics with specific eigenvalue multiplicities.
result Simplicity of Hodge Laplacian and curl operator is not a meagre codimension 2 property.
The paper shows that the Gauss map of minimal surfaces is open and meagre in the space of holomorphic maps.
problem Characterizing the set of minimal surfaces with a specific Gauss map.
method Analyzing the spaces of conformal minimal immersions and holomorphic maps, and using topological properties.
result The Gauss map assignment is an open map, and the set of minimal surfaces satisfying the Osserman curvature estimate is meagre.
NeuralChaos efficiently approximates complex stochastic processes.
problem Representing and computing square-integrable predictable processes over time.
method Introduces NeuralChaos, a neural operator architecture for Rd-valued predictable processes. result NeuralChaos achieves best N-term chaoslet approximation rates and is dense in HT2(Rd). The paper proves rigidity of length identities for simple closed curves on hyperbolic surfaces.
problem Characterizing hyperbolic surfaces by their simple length spectra.
method Proving rigidity of length identities over Teichmüller spaces.
result Simple length spectra can be used as moduli for generic hyperbolic surfaces.
Neural networks improve loss reserving with case estimates and transaction data.
problem Improving loss reserving accuracy using neural networks.
method Comparison of feed-forward and recurrent neural networks trained on case estimates and transaction data.
result Case estimates significantly improve predictions, but memory-equipped neural networks offer minimal additional benefit.
A hybrid physics-ML model predicts FO water flux with high accuracy and uncertainty quantification.
problem Challenges in accurately modeling Forward Osmosis water flux due to complex internal mass transfer phenomena.
method Robust Hybrid Physics-ML framework using Gaussian Process Regression (GPR) for uncertainty-aware Jw prediction.
result Achieved a state-of-the-art MAPE of 0.26% and R2 of 0.999 on independent test data.
DEceit constructs effective universal pixel-restricted perturbations for deep image classifiers.
problem Creating effective universal pixel-restricted perturbations for deep neural networks.
method DEceit algorithm for black-box feedback, targeting 10% of pixels in images.
result Perturbing only 10% of pixels achieves high Fooling Rate and visual similarity.
New proof shows incremental flow models are essential for universal generation.
problem Understanding the universality of flow-based models in generating natural maps.
method Topological-dynamical argument and algebraic properties of flows.
result Incremental generation is necessary and sufficient for universal flow-based generation.
We define regular points of an extremal subset in an Alexandrov space and study their basic properties. We show that a neighborhood of a regular point in an extremal subset is almost isometric to an open subset in Euclidean space and that the set of regular points in an extremal subset has full measure and is dense in …
The paper defines quasi-convex subsets in spaces with lower curvature bound.
problem Understanding the geometry of spaces with lower curvature bound.
method Introducing and exploring quasi-convex subsets in Alexandrov spaces.
result Quasi-convex subsets are a fundamental concept for comparing Riemannian and Alexandrov spaces.
To find efficient screening methods for high dimensional linear regression models, this paper studies the relationship between model fitting and screening performance. Under a sparsity assumption, we show that a subset that includes the true submodel always yields smaller residual sum of squares (i.e., has better model…
Study on extremal subsets in geodesically complete spaces with curvature constraints.
problem Characterizing extremal subsets in GCBA spaces.
method Introduced and analyzed extremal subsets in GCBA spaces, proving their properties.
result Set of topological singularities forms an extremal subset under additional assumptions.
SOAK assesses data subset similarity for better model training.
problem Estimating similarity between data subsets for accurate predictions.
method Same/Other/All K-fold cross-validation method.
result SOAK estimates similarity of learnable/predictable patterns in data subsets.
One-pass algorithm finds small subset for ℓp subspace approximation with additive error.
problem Finding a small subset of data points for ℓp subspace approximation. method One-pass subset selection with additive approximation guarantee for p∈[1,∞). result First one-pass algorithm with additive error for ℓp subspace approximation. Let T be the group of smooth concordance classes of topologically slice knots, and {0}⊂⋯⊂Tn+1⊂Tn⊂⋯⊂T0⊂T be the bipolar filtration. In this paper, we show that a proper collection of the knots employed by H…
In each Menger manifold M we construct: (i) a closed nowhere dense subset M0 which is homeomorphic to M and is universal nowhere dense in the sense that for each nowhere dense set A⊂M there is a homeomorphism h of M such that h(A)⊂M0; (ii) a meager Fσ-set Σ0⊂M which is univers…
Bayesian approach selects subsets of variables for interpretable prediction and identifies key factors in educational outcomes.
problem Challenges in subset selection for stability, regularization, and inference.
method Bayesian perspective on subset selection, deriving optimal subsets and variable importance metrics.
result Better prediction, interval estimation, and variable selection compared to competing methods.
This paper improves volatility forecasting using dynamic subset selection in genetic programming.
problem Improving accuracy of implied volatility forecasting.
method Dynamic training-subset selection methods applied to genetic programming.
result Dynamic subset selection improves predictive accuracy of genetic programming models.
Study fractal dimension for motion without crossing a subset.
problem Fractal dimension of a subset X in R^n for motion without crossing.
method Analyzes fractal dimension of subset X in R^n.
result Determines conditions for motion without crossing a subset.
Proposes a neural framework to select subsets efficiently across different models.
problem Lack of generalizability in subset selection methods for unseen architectures.
method Introduces a trainable subset selection framework, SubSelNet, that uses attention-based neural gadgets and subset samplers.
result SubSelNet generalizes across architectures and outperforms existing methods.
Bayesian method selects subsets for LMMs with structured dependence.
problem Subset selection challenge in LMMs with structured dependence.
method Bayesian decision analysis with Mahalanobis loss function.
result Optimal linear coefficients for subsets and cardinality constraints.
In each manifold M modeled on a finite or infinite dimensional cube [0,1]n we construct a meager Fσ-subset X⊂M which is universal meager in the sense that for each meager subset A⊂M there is a homeomorphism h:M→M such that h(A)⊂X. We also prove that any two universal meager Fσ…
In this paper, we study extremal subsets in Alexandrov spaces with dimension n, curvature ≥κ, and diameter ≤D. We show that the following three quantities are uniformly bounded above in terms of n, κ, and D: (1) the number of extremal subsets in an Alexandrov space; (2) the Betti numbers of an extremal…
Quantum states associated with subsets of product manifolds are separable.
problem Characterizing quantum states associated with subsets of product manifolds.
method Using holomorphic sections of quantum line bundles and restriction maps.
result Quantum states associated with finite unions of products are separable.
Many machine learning tasks require sampling a subset of items from a collection based on a parameterized distribution. The Gumbel-softmax trick can be used to sample a single item, and allows for low-variance reparameterized gradients with respect to the parameters of the underlying distribution. However, stochastic o…
Every countable compact subset of sphere is tame.
problem Characterizing compact subsets of spheres.
method Proving homeomorphic complements imply homeomorphic subsets.
result Wild subspaces like Antoine contain Cantor sets.
New MCMC algorithm reduces subset selection passes to 2 for optimal k-dimensional subspace approximation.
problem Subset selection for k-dimensional subspace approximation with ε-approximation. method MCMC sampling algorithm reducing passes to 2 for p=2 case, poly(k/ε) size subset. result Subset selection of nearly optimal size in 2 passes, (1+ε) approximation. We consider combinatorial online learning with subset choices when only relative feedback information from subsets is available, instead of bandit or semi-bandit feedback which is absolute. Specifically, we study two regret minimisation problems over subsets of a finite ground set [n], with subset-wise relative prefe…
Score function estimators improve k-subset sampling efficiency.
problem Efficiently sampling k-subsets in machine learning tasks. method Revisit score function estimators, using discrete Fourier transform and control variates.
result Efficient and unbiased gradient estimates for k-subset sampling. The kth finite subset space of a topological space X is the space exp_k X of non-empty finite subsets of X of size at most k, topologised as a quotient of X^k. The construction is a homotopy functor and may be regarded as a union of configuration spaces of distinct unordered points in X. We show that the finite subset …
On R^n endowed with a riemannian metric of bounded nonpositive curvature, the weakly convex closed subsets are topologically trivial. The stability of such subsets under intersection characterizes the euclidean spaces.
In each manifold M modeled on a finite or infinite dimensional cube [0,1]n we construct a closed nowhere dense subset S⊂M (called a spongy set) which is a universal nowhere dense set in M in the sense that for each nowhere dense subset A⊂M there is a homeomorphism h:M→M such that $h(A)\sub…
New algorithm finds best subset in high-dimensional data models.
problem Finding the best subset of predictors in high-dimensional data models.
method Proposes a scalable algorithm using a generalized information criterion.
result Directly proves consistency and oracle property for the best-subset selection.
For any pseudoconvex Runge domain Ω⊂C2 we prove that every closed discrete subset in Ω is contained in a properly embedded complex curve in Ω with any prescribed topology (possibly infinite).
The current article stems from our study on the asymptotic behavior of holomorphic isometric embeddings of the Poincaré disk into bounded symmetric domains. As a first result we prove that any holomorphic curve exiting the boundary of a bounded symmetric domain Ω must necessarily be asymptotically totally geodesic. A…
B Wilking has recently shown that one can associate a Ricci flow invariant cone of curvature operators C(S), which are nonnegative in a suitable sense, to every $Ad_{SO(n,\C)}$ invariant subset $S \subset {\bf so}(n,\C)$. For curvature operators of a Kähler manifold of complex dimension n, one considers $Ad_{GL(n,\…
Flat subsets in Euclidean buildings are contained within apartments.
problem Understanding the structure of flat subsets in Euclidean buildings.
method Proving containment within apartments.
result Convex flat subsets are contained in apartments.
Curvature of 2D subsets preserved in their space.
problem Understanding curvature of subsets in 2D spaces.
method Analyzing subsets with vanishing first homology.
result Closed subsets inherit curvature bounds from ambient spaces.
Optimizes kernel discrepancies by selecting subsets efficiently.
problem Improving kernel discrepancies for QMC methods.
method Introduces a novel subset selection algorithm for kernel discrepancies.
result Efficiently generates low-discrepancy samples from various distributions.
Defines weak geodesics on specific subsets of manifolds.
problem Characterizing geodesics on prox-regular subsets of Riemannian manifolds.
method Defining weak geodesics as continuous curves with weak regularities, and characterizing them as viscosity critical points of the energy functional.
result Characterizes weak geodesics on prox-regular subsets of Riemannian manifolds.
Composite likelihood inference of fractional Gaussian processes with sequentially optimal subset selection
problem Estimating parameters in time series
method Composite likelihood method
result The method reduces computational cost
The paper develops an algorithm to select a subset of training data for efficient regression models.
problem Designing an efficient algorithm for selecting a subset of training data to train regression models quickly without sacrificing accuracy.
method The paper tackles this problem by formulating it as a minimization of training loss with respect to both trainable parameters and subset of training data, subject to error bounds on the validation set. They use a novel problem formulation and represent it with simplified constraints using the dual of the original training problem. They then develop SELCON, an efficient majorization-minimization algorithm for data subset selection, which admits an approximation guarantee.
result The experiments show that SELCON trades off accuracy and efficiency more effectively than the current state-of-the-art.
Study efficient algorithms for identifying minimum interventional sets to learn causal relationships.
problem Identify the smallest set of interventions to learn causal relationships between a subset of edges.
method Develop algorithms for subset verification and search problems under assumptions of faithfulness, causal sufficiency, and ideal interventions.
result For subset verification, an efficient algorithm is provided to compute a minimum sized interventional set.
New suboptimal algorithm for best subset selection in high-dimensional data.
problem Nonconvex and computationally challenging best subset selection in linear regression.
method Introducing a new suboptimal algorithm and comparing it with other popular methods.
result The new procedure is a competitive suboptimal algorithm for high-dimensional data.
Efficiently selects predictors in sparse regression without approximations.
problem High computational cost in subset selection for sparse regression.
method Conditional uncorrelation formula and efficient non-approximate method.
result Significant reduction in computational complexity for subset selection.
We introduce and study the space of \emph{subset currents} on the free group FN. A subset current on FN is a positive FN-invariant locally finite Borel measure on the space CN of all closed subsets of ∂FN consisting of at least two points. While ordinary geodesic currents generalize con…