Variational reduction simplifies Lagrangian systems with scaling symmetries.
problem Simplifying Lagrangian systems with scaling symmetries.
method Defining a variational reduction procedure for homogenous Lagrangian systems.
result Reconstructing trajectories from critical points of reduced variational principle.
New neural network method simplifies high-dimensional data.
problem Scalability issues in nonlinear sufficient dimension reduction.
method Stochastic neural network with adaptive gradient algorithm.
result Proposed method outperforms existing methods on large-scale data.
New method scales features for better clustering.
problem Irregular features disrupt classification.
method Spectral clustering with modified feature scales.
result Outperforms existing methods in experiments.
Reduces symplectic Hamiltonian systems to contact systems, realizing Poincaré's dream.
problem Scaling symmetries in Hamiltonian systems.
method Contact reduction of symplectic Hamiltonian systems.
result Generically possible reduction to contact Hamiltonian systems, reducing inputs needed.
The paper discusses reducing Hamiltonian systems by scaling and standard symmetries, leading to Kirillov Hamiltonian systems.
problem Reduction of symplectic Hamiltonian systems by scaling and standard symmetries.
method Proof of Kirillov Hamiltonian systems and equivalence of reductions.
result Equivalent Kirillov Hamiltonian systems from different reduction orders.
New method scales features for better supervised dimensionality reduction.
problem Irregularities and uncertainties in high-dimensional data.
method Formulate an eigenvalue problem to modify feature scales.
result Improves clustering and classification accuracy for both toy and real-world problems.
FibeRed reduces complex data dimensions while preserving topology.
problem Hard embedding of topologically complex datasets in low-dimensional Euclidean space.
method Modeling datasets with vector bundles, reducing fibers while preserving topology.
result FibeRed learns topologically faithful embeddings in lower dimensions than existing methods.
SRP efficiently learns class-aware embeddings for large datasets.
problem High computational complexity in supervised dimensionality reduction for large datasets.
method Supervised random projections (SRP) for direct class-aware embedding learning.
result SRP achieves 1-2 orders of magnitude better computational performance.
The hyperbolic plane is derived from a three-body problem in Euclidean space.
problem Constructing the hyperbolic plane from a three-body problem.
method Scale plus symmetry reduction of a three-body problem in Euclidean plane using Jacobi-Maupertuis metric.
result The hyperbolic plane and its geodesic flow are derived from a three-body problem.
MBS reduces CNN model size with minimal accuracy loss.
problem Reducing CNN model size while maintaining accuracy.
method Adaptive macroblock scaling based on effective flops.
result Significant model size reduction across various CNN architectures.
Paper proposes PPMM for fast estimation of large-scale OTM.
problem Estimation of large-scale optimal transport maps (OTM) is challenging due to the curse of dimensionality.
method Combines projection pursuit regression and sufficient dimension reduction to adaptively select projection directions.
result PPMM consistently estimates the most informative projection direction and weakly converges to the target OTM.
This paper investigates the hedging effectiveness of a dynamic moving window OLS hedging model, formed using wavelet decomposed time-series. The wavelet transform is applied to calculate the appropriate dynamic minimum-variance hedge ratio for various hedging horizons for a number of assets. The effectiveness of the dy…
Paper proposes conditional multidimensional scaling for better data reduction.
problem Mapping high-dimensional data to low-dimensional space with known features.
method Developed a broad class of methods called conditional multidimensional scaling (MDS) with an optimization algorithm.
result Conditional MDS improves estimation quality and simplifies visualization and knowledge discovery.
New DR method uses Gromov-Wasserstein distance for high-dimensional data.
problem Analyzing relationships between high-dimensional objects.
method Optimal transportation theory and Gromov-Wasserstein distance.
result Robust and efficient solution for complex high-dimensional datasets.
In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification. Previous theoretical results on randomized reduction methods hinge on strong assumptio…
Automates PDE model reduction with time-scale separation.
problem Computational expense in solving high-dimensional PDEs.
method Combines autoencoder and time-continuous model for latent dynamics.
result Automatically learns independent temporal scales in complex systems.
Efficient distributed SGD method improves training speed and robustness.
problem Scaling up stochastic optimization for large-scale data.
method Combining adaptivity and variance reduction techniques for distributed SGD.
result Achieves linear speedup, constant memory, and logarithmic communication rounds.
A new DR method for HSI classification improves accuracy with limited samples.
problem Challenges in DR for HSI classification with limited training samples.
method Graph-based spatial and spectral regularized local scaling cut (SSRLSC).
result Improved classification accuracy compared to spectral-only methods.
A new method, tree-SNE, solves the scale problem in t-SNE.
problem Clustering and visualizing high-dimensional data, especially MNIST digits.
method Revisits t-SNE idea to create a 2+1 dimensional embedding with a scale parameter.
result The optimal embedding depends continuously on the scale parameter for all initial conditions.
New method for constructing contact Lie systems on various spaces.
problem Constructing contact Lie systems on Riemannian and Lorentzian spaces.
method Adaptation of scaling symmetries to Lie-Hamilton systems, leading to contact Lie systems.
result Curvature-dependent reductions of contact Lie systems on Cayley-Klein spaces.
We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP_\infty by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.
A new method, k-SVRG, speeds up large-scale optimization.
problem Efficiently solving large-scale optimization problems with variance reduction.
method k-SVRG, which uses available memory and minimizes stalling phases.
result Proves linear convergence on strongly convex problems and convergence to stationary points on non-convex problems.
New theorem connects diverse machine learning algorithms using Bregman divergences.
problem Design and analysis of machine learning algorithms.
method Scaled Bregman theorem involving Bregman divergences.
result Allows re-writing certain distortions as scaled Bregman divergences.
New algorithm reduces robust optimization scale for better constraint satisfaction.
problem Finding robust solutions to optimization problems with unknown constraints.
method Empirical domain reduction to determine robustness scale.
result Our algorithm's scale is less affected by parameter dimensionality.
TriMap improves data visualization by preserving global structure better than existing methods.
problem Visualizing high-dimensional data with preserved global structure.
method TriMap uses triplet constraints for dimensionality reduction.
result TriMap outperforms other methods in terms of runtime and quality of embedding.
AutoScale improves LLM pre-training by adjusting data mixtures at different scales.
problem Data mixtures that work well at small scales may not perform as well at larger scales.
method AutoScale uses a two-stage approach: fitting a model to predict loss under different compositions and extrapolating optimal compositions to larger scales.
result AutoScale accelerates convergence and improves downstream performance.
BRIEF reduces CNN models by 32.3% on ImageNet, removing redundant channels.
problem Redundant neural channels in CNN models.
method Backward reduction algorithm based on information flow analysis.
result Significant model reduction (32.3%) on ResNet-34 in ImageNet scale.
Unified framework for DR and clustering using Gromov-Wasserstein.
problem Capturing structure in high-dimensional datasets.
method Distributional reduction framework using Gromov-Wasserstein.
result Unified approach recovers DR and clustering as special cases.
A new approach to group fairness treats it as a bargaining problem.
problem Fairness in deploying predictors across subpopulations.
method Interpreting fairness as a bargaining problem and proposing relative improvement.
result Relative improvement provides axiomatic justification and finite-sample convergence guarantees.
Nonlinear dimensionality reduction embeddings computed from datasets do not provide a mechanism to compute the inverse map. In this paper, we address the problem of computing a stable inverse map to such a general bi-Lipschitz map. Our approach relies on radial basis functions (RBFs) to interpolate the inverse map ever…
New algorithm for context bandits with continuous actions.
problem Efficient decision-making with unknown action structures.
method Reduction-style algorithm combining supervised learning.
result Proven to work in general and validated with experiments.
A new method reduces both features and samples for sparse SVMs efficiently.
problem Sparse SVMs struggle with large-scale problems due to high computational cost.
method Simultaneously identifies and removes inactive features and samples.
result Significant computational savings without loss of accuracy.
Novel SAAG variants reduce variance in large-scale learning.
problem Reduction of variance in noisy gradient approximations for large-scale machine learning.
method Proposed SAAG-III and IV variants with SBAS for step size determination.
result Proved linear convergence of SAAG-IV for all smoothness and strong-convexity combinations.
Proposes STRON method for large-scale machine learning problems.
problem Large-scale machine learning problems.
method Stochastic Trust Region Inexact Newton (STRON) method using CG to solve trust region subproblem with progressive subsampling.
result Empirical results show efficacy of STRON method.
The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In this paper we develop an approach for dimension reduction that exploits the assumpt…
We give a description of local and global moves on a class of locally planar trivalent graphs and we show that it contains λ-Scale calculus, therefore in particular untyped lambda calculus. Surprisingly, the beta reduction rule comes from a local "sewing" transformation of trivalent locally planar graphs.
Proposes a parametric t-SNE without perplexity tuning.
problem Non-parametric t-SNE's perplexity parameter limits DR quality.
method Multi-scale parametric t-SNE with deep neural network.
result Produces reliable embeddings with competitive neighborhood preservation.
New stochastic CG algorithm with variance reduction converges faster and is more efficient.
problem Optimization of linear and nonlinear problems, especially in machine learning.
method Stochastic Conjugate Gradient (CG) algorithm with variance reduction.
result The algorithm converges faster and is more efficient than existing methods.
eDCF estimates intrinsic dimension using local connectivity.
problem Challenges in estimating intrinsic dimension due to scale dependence.
method eDCF: a novel, scalable, and parallelizable method based on Connectivity Factor (CF).
result eDCF consistently matches leading estimators with comparable MAE and higher exact intrinsic dimension match rates.
This work improves understanding of dimension reduction algorithms and their probabilistic embeddings.
problem Improving theoretical understanding of non-linear dimension reduction algorithms.
method Analytical investigation of a generalized multidimensional scaling optimization problem.
result Probabilistic formulation of the problem leads to deterministic embeddings, contrary to standard implementations.
This research improves HC classification speed and memory usage with feature selection.
problem Large-scale HC datasets with high-dimensional features.
method Filter-based feature selection methods for dimensionality reduction.
result Up to 3x speed-up and 45% less memory usage on massive datasets.
We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local quadratic discriminant analysis classifier, and thus acts locally to each training po…
FPP creates interpretable 2D embeddings for high-dimensional data.
problem Discovering interpretable relationships in high-dimensional data.
method Function preserving projections (FPP) for scalable linear embeddings.
result FPP reveals non-linear patterns of user-selected response functions.
The study reveals how synaptic correlations promote dimension reduction in neural networks.
problem Understanding how synaptic correlations affect neural correlations and dimension reduction in deep neural networks.
method A simplified model of dimension reduction considering pairwise correlations among synapses, using mathematical self-consistency for both binary and continuous synapses.
result Weakly-correlated synapses encourage dimension reduction compared to orthogonal synapses, and they also slow down the decorrelation process.
A new model reduces the cost of simulating fluid flow through porous materials.
problem High computational cost of simulating fluid flow through porous materials.
method Proposes a fully probabilistic, Darcy-type reduced-order model.
result The model significantly accelerates uncertainty quantification tasks.
Paper analyzes classical multidimensional scaling for cluster recovery.
problem Cluster recovery from noisy data.
method Classical multidimensional scaling followed by distance-based clustering.
result Scaling conditions for high probability cluster recovery.
A new method reduces variance in distributed SGD for faster training.
problem High variance and poor scalability of SGD in distributed settings.
method CentralVR: Uses error corrections to reduce variance and scales linearly with workers.
result CentralVR achieves provably linear convergence and strong scaling up to hundreds of cores.
Paper presents a hierarchical learning strategy for sparse data representation.
problem Sparse representation of multivariate datasets.
method Hierarchical approximation spaces at finer scales, stability and convergence analysis.
result Efficient data reconstruction and error minimization in prediction.