Subset LLDA improves scalability for large label sets in multi-label classification.
problem Scalability issues in Labeled Latent Dirichlet Allocation (LLDA) for large label sets.
method Subset LLDA, a simple variant of LLDA, addressing scalability issues.
result Subset LLDA outperforms LLDA and extreme multi-label classification algorithms on large label sets.
Study of regular points in extremal subsets of Alexandrov spaces.
problem Characterizing extremal subsets in Alexandrov spaces.
method Definition and analysis of regular points, properties of neighborhoods, and applications to convergence and fibration structures.
result Regular points have full measure and are dense in extremal subsets, with applications to convergence and fibration structures.
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…
Uniform bounds found for extremal subsets in specific Alexandrov spaces.
problem Bounding properties of extremal subsets in Alexandrov spaces with constraints on dimension, curvature, and diameter.
method Application of essential coverings introduced by Yamaguchi.
result Uniform upper bounds on the number, Betti numbers, and volume of extremal subsets.
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.
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.
Every discrete subset in a complex domain is in a complex curve.
problem Embedding discrete subsets in complex domains.
method Proving every closed discrete subset is in a complex curve with any topology.
result Closed discrete subsets are contained in complex curves with any topology.
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. 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.
Improves performance in various machine learning tasks by reparameterizing subset sampling.
problem Stochastic optimization involving subset sampling is not reparameterizable.
method Continuous relaxation of subset sampling to provide reparameterization gradients.
result Improves performance in instance-wise feature selection, deep stochastic k-nearest neighbors, and parametric t-SNE.
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.
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.
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.
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…
The study shows a new way to prove a fundamental group property.
problem Proving a specific property of a group of knots.
method Employing a collection of knots to demonstrate a fundamental group property.
result Proves a new fundamental group property.
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.
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. 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 …
Holomorphic curves exiting bounded symmetric domains are asymptotically totally geodesic.
problem Understanding the asymptotic behavior of holomorphic curves in bounded symmetric domains.
method Proof by contradiction and rescaling, using the Poincaré-Lelong equation.
result Holomorphic curves exiting a bounded symmetric domain are asymptotically totally geodesic.
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.
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.
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…
Kähler metrics with constant curvature extend smoothly to compact subsets.
problem Extending Kähler metrics with constant curvature to compact subsets.
method Using developing maps and the theory of Kähler metrics.
result Kähler metrics with constant holomorphic sectional curvature extend smoothly to the entire ball.
A metric is defined for the Chabauty space of closed subsets.
problem No specific problem stated; Chabauty space is abstract.
method Explicit metric definition for Chabauty space.
result A metric induces the Chabauty topology.
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,\…
New algorithms minimize regret in combinatorial online learning with relative feedback.
problem Minimizing regret in online learning with subset-wise relative preference feedback.
method Instance-dependent and order-optimal regret algorithms for two settings: bounded size subsets and fixed size subsets.
result Regret bounds of O(mnlnT) and O(knlnT) for respective settings. 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.
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.
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
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.
Two diversity models improve subset selection for image classification tasks.
problem Data scarcity and high costs in human labeling for supervised learning.
method Facility-Location and Disparity-Min models for training data subset selection and active learning.
result Subset selection improves accuracy by 2-3% with less training data.
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…
We prove that for a coarse space X the ideal S(X) of small subsets of X coincides with the ideal D<(X) of subsets A⊂X of asymptotic dimension asdim(A)<asdim(X) provided that X is coarsely equivalent to an Euclidean space Rn. Also we prove that for a locally compact Abelian group X, the equali…
LESS combines local predictors for subsets to learn from heterogeneous input-output pairs.
problem Learning from heterogeneous input-output pairs in populations with varied behavior.
method LESS algorithm: generates subsets, trains local predictors, combines them.
result LESS is highly competitive compared to state-of-the-art methods.
Detects anomalous inputs in neural networks using subset scanning.
problem Detecting adversarial noise and out-of-distribution samples in neural networks.
method Subset scanning applied to neural network activations using non-parametric scan statistics.
result Identifies the most anomalous subset of node activations in neural networks.
We generalize subset currents on hyperbolic groups to surfaces.
problem Generalizing subset currents to surfaces.
method Developed the theory of subset currents on π_1(Σ), proving they are a measure-theoretic completion of conjugacy classes of subgroups.
result The space of subset currents on Σ is a measure-theoretic completion of conjugacy classes of non-trivial subgroups, each geometrically corresponding to a convex core.
In a complete simply connected Riemannian manifold X of pinched negative curvature, we give a sharp criterion for a subset C to be the epsilon-neighbourhood of some convex subset of X, in terms of the extrinsic curvatures of the boundary of C.
An open subset U of a complex surface can be topologically perturbed to yield an open subset whose inherited complex structure is Stein, if and only if U is homeomorphic to the interior of a handlebody whose handles all have index equal or less than 2.