New black-box reductions simplify online learning algorithms.
problem Designing adaptive and parameter-free online learning algorithms.
method Introducing black-box reductions to simplify analysis and improve regret guarantees.
result Improved regret bounds for parameter-free learning.
Paper reduces movement primitive dimensionality in parameter space.
problem High dimensionality of movement primitives makes policy optimization expensive.
method Investigates dimensionality reduction in parameter space, identifying principal movements.
result Dimensionality reduction in parameter space is more effective than in configuration space.
A new method reduces high-dimensional parameter spaces for faster numerical tasks.
problem Efficiently reducing high-dimensional parameter spaces for numerical tasks.
method Local Active Subspaces (LAS) combining active subspaces with clustering techniques.
result Significant speed-up in numerical tasks through efficient dimension reduction.
A method for policy search with high-dimensional context variables.
problem Learning from high-dimensional context variables like camera images is challenging.
method Model-based relative entropy stochastic search framework with integrated dimensionality reduction.
result The proposed method outperforms naive dimensionality reduction methods.
A new method reduces dimensionality for better likelihood-free parameter estimation.
problem Estimating parameters from data with no closed-form likelihood.
method Combines reconstruction map estimation with dimension-reduction techniques.
result The proposed method outperforms existing techniques in accuracy and efficiency.
New method reduces PDE model parameters by 30% with sparsity.
problem Redundant parameters in neural network projections.
method Bregman iterations for sparsity, POD compression, bias propagation.
result 30% fewer parameters with similar accuracy.
New framework optimizes random forest parameters for stability and cost.
problem Optimizing random forest parameters for industrial applications.
method Bayesian optimization framework considering error, stability, and cost.
result Parameter settings that balance error, stability, and cost.
Transformers reduce redundancy by focusing on invariant relational quantities.
problem Substantial internal redundancy in Transformer models due to coordinate-dependent representations and continuous symmetries.
method Reformulate representations, attention mechanisms, and optimization dynamics in terms of invariant relational quantities, eliminating redundant degrees of freedom by construction.
result Architectures that operate directly on relational structures, providing a principled geometric framework for reducing parameter redundancy and analyzing optimization.
Paper improves tree probability estimation using stochastic optimization and variance reduction.
problem Improving tree probability estimation in phylogenetic inference.
method Introduces computationally efficient methods for training SBNs and variance reduction for optimization.
result Methods outperform previous baseline methods in tree topology probability estimation and Bayesian phylogenetic inference.
Pruning neural networks can improve test accuracy even with significant parameter reduction.
problem The tradeoff between generalization and stability in neural network pruning.
method Analysis of pruning behavior over training, focusing on instability and its relation to generalization.
result Pruning's benefit to generalization increases with its instability.
The un-reduction procedure introduced previously in the context of Mechanics is extended to covariant Field Theory. The new covariant un-reduction procedure is applied to the problem of shape matching of images which depend on more than one independent variable (for instance, time and an additional labelling parameter)…
Efficient policy learning from observational data using weighted classification reductions.
problem Efficient policy evaluation does not necessarily lead to efficient estimation of policy parameters.
method Proposed an estimation approach based on generalized method of moments, efficient for policy parameters.
result Demonstrated empirical efficiency and regret benefits of a proposed method.
We study the Euler-Lagrange equations for a parameter dependent G-invariant Lagrangian on a homogeneous G-space. We consider the pullback of the parameter dependent Lagrangian to the Lie group G, emphasizing the special invariance properties of the associated Euler-Poincaré equations with advected parameters.
A new framework learns clustering and dimensionality reduction together.
problem Challenges in clustering high-dimensional data.
method Gradient-based manifold optimization for joint learning.
result Better performance compared to existing clustering algorithms.
Researchers find non-abelian symmetric gravitating vortices on a sphere.
problem Finding solutions to non-abelian gravitating vortex equations on a sphere.
method Dimensional reduction of Kähler-Yang-Mills-Higgs equations, reduction to ODEs, method of continuity.
result Existence and admissible volumes of solutions proved.
Typical dimensionality reduction (DR) methods are often data-oriented, focusing on directly reducing the number of random variables (features) while retaining the maximal variations in the high-dimensional data. In unsupervised situations, one of the main limitations of these methods lies in their dependency on the sca…
KD technique improves QDNN performance with reduced hyper-parameters.
problem Restoring performance loss in QDNNs due to quantization.
method Applied KD with reduced hyper-parameters, including a new coefficient reduction technique.
result Achieved 92.7% test accuracy on CIFAR-10 and 67.0% on CIFAR-100 with 2-bit weights.
PathCapsNet improves CapsNet by reducing parameters and enhancing performance.
problem Limitations of CapsNet, including excessive parameters and shallow architecture.
method Introducing a deep parallel multi-path version of CapsNet, incorporating depth, max-pooling, regularization, and new routing techniques.
result Better or comparable results to CapsNet with significantly reduced parameter count.
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.
Sliced Inverse Regression reduces parameter space for estimating complex financial models.
problem High-dimensional parameter space in stochastic differential equations.
method Sliced Inverse Regression for dimension reduction.
result Reduced computational costs in estimating parameters.
A new method reduces complexity and uncertainty in neural networks.
problem Uncertainty quantification in complex neural networks.
method Condensed Stein Variational Gradient Descent (cSVGD) method.
result Condensed SVGD provides uncertainty quantification on parameters.
TVR optimizes black-box simulators by targeting variance reduction over control and noise parameters.
problem Optimizing black-box simulators with uncertain parameters.
method Targeted Variance Reduction (TVR) method that optimizes (x,θ) jointly. result Improved robust optimization performance over state-of-the-art methods.
This work optimizes statistical inference with neural networks for high-energy physics data.
problem Optimal dimensionality reduction with minimal loss of information in the presence of systematic uncertainties.
method Neural network optimization based on binned Poisson likelihoods with nuisance parameters.
result Estimates of parameters of interest close to optimal.
Reduced CNN complexity for exoplanet detection without significant loss in accuracy.
problem Reducing the number of parameters in CNNs for time-series data.
method Two methods for complexity reduction in AstroNet: tactical reduction of layers and modification of input data.
result Non-substantial loss in accuracy with up to 85% reduction in training time.
A parsimonious model reduces over-parameterization in skewed matrix variate mixtures.
problem Over-parameterization in skewed matrix variate mixtures.
method Parsimonious family of 256 models using bilinear factor analyzers constrained over clusters, with AECM algorithm for estimation.
result Extensive simulations and real-world datasets (MNIST, Olivetti faces) demonstrate the method's effectiveness.
DCFNet decomposes CNN filters into learned coefficients with bases, reducing parameters and computation.
problem Reduction of model parameters and computation in CNNs.
method DCFNet decomposes convolutional filters into a truncated expansion with pre-fixed bases, learning only the coefficients.
result DCFNet maintains accuracy for image classification tasks with significantly fewer parameters, including with random bases.
A model order reduction framework reduces financial risk analysis models efficiently.
problem Simulating high-dimensional financial risk models.
method Adaptive greedy sampling based on POD and surrogate modeling.
result Reduced models provide significant speedup with excellent accuracy.
Efficiently transforms samples from various statistical models.
problem Approximately transforming samples from one statistical model to another without knowing the source model's parameters.
method Constructs computationally efficient procedures to reduce uniform, Erlang, and Laplace models to general target families.
result Establishes nonasymptotic reductions between canonical high-dimensional problems, such as mixtures of experts, phase retrieval, and signal denoising.
Method reduces complexity of spatial interaction networks.
problem Complex spatial interaction networks.
method Empirical Bayes approach with tree partitioning and generalized double Pareto prior.
result Compact vectorial representations and interpretable visualizations.
MMbeddings reduces categorical embeddings by treating them as latent effects, significantly decreasing parameters and mitigating overfitting.
problem Large cardinalities in categorical embeddings lead to high parameter counts and overfitting.
method MMbeddings treats embeddings as latent random effects in a variational autoencoder framework, reducing parameter count and mitigating overfitting.
result MMbeddings consistently outperforms traditional embeddings across various tasks, demonstrating its potential in machine learning applications.
The paper evaluates and compares dimensionality reduction quality metrics without tuning.
problem Evaluating the quality of nonlinear dimensionality reduction visualizations is challenging.
method Comparison of dimensionality reduction quality metrics on datasets with known ground truth manifolds.
result A few methods consistently perform well, with one proposed as a benchmark.
RCLA reduces noise in topological data analysis, preserving essential structure.
problem Noise in large datasets obscures topological features in persistent homology.
method Grid-based RCLA integrates data reduction and denoising with a threshold parameter.
result RCLA provides a theoretical guarantee and automatic parameter selection.
New analysis improves black-box k-PCA algorithms, reducing parameter loss.
problem Designing efficient k-PCA algorithms with black-box access to a 1-PCA oracle. method Black-box deflation methods, analyzing ePCA and cPCA approximations.
result Deflation methods suffer no asymptotic parameter loss for k-cPCA in feasible regimes. Bayesian neural networks improve uncertainty quantification in non-linear dimensionality reduction.
problem Current neural network models lack adequate uncertainty quantification.
method Deploy Markov chain Monte Carlo sampling algorithms for Bayesian inference in ANN models with latent variables.
result New research directions are needed due to fundamental challenges in neural networks with latent variables.
Wassmap reduces image complexity while preserving key features.
problem Global nonlinear dimensionality reduction in imaging.
method Wassmap uses Wasserstein space and pairwise distances to create isometric embeddings.
result Wassmap can recover parameters of image manifolds like translations and dilations.
Paper accelerates SAGA using sampled negative momentum.
problem Directly accelerating SAGA for optimization problems.
method Proposes SSNM for direct acceleration of SAGA.
result Achieves best known oracle complexity for strongly convex problems.
A method estimates and prunes neural network filters to reduce computation and improve accuracy.
problem Reduction of neural network parameters to save computation and energy.
method Estimates each neuron's contribution to loss using first and second-order Taylor expansions; iteratively removes less important neurons.
result High (>93%) correlation between estimated and true importance; 40% FLOPS reduction with 0.02% top-1 accuracy loss.
Classifies geodesic orbit spaces with abelian isotropy subgroups.
problem Characterizing and classifying geodesic orbit spaces with specific isotropy subgroups.
method Simplified study of geodesic orbit metrics on G/S by reducing to submanifolds and generalized flag manifolds, using properties of root systems.
result Geodesic orbit spaces of the form (G/S,g) are naturally reductive.
Study pseudo-Riemannian Sasaki metrics on solvable Lie groups.
problem Characterize and classify pseudo-Riemannian Sasaki solvmanifolds.
method Sasaki reduction and pseudo-Kähler quotient under Reeb vector field action.
result Classify pseudo-Riemannian Sasaki solvmanifolds in dimensions 5 and 7.
Unified approach for non-stationary linear bandits with dynamic regret.
problem Non-stationary linear bandits with round-specific feasible actions and drifting reward models.
method Unified misspecification-reduction viewpoint, restarting algorithms with misspecification-dependent regret guarantees.
result Optimal \(T^{2/3}P_T^{1/3}\) dynamic-regret dependence for both linear bandits and contextual linear bandits.
Study classifies metrics on anti-de Sitter spacetime with specific symmetries.
problem Classifying metrics with specific symmetries on anti-de Sitter spacetime.
method Used classification techniques for pseudo-Riemannian and almost contact metric structures.
result Obtained classifications of homogeneous structures on anti-de Sitter spacetime.
This paper concerns model reduction of dynamical systems using the nuclear norm of the Hankel matrix to make a trade-off between model fit and model complexity. This results in a convex optimization problem where this trade-off is determined by one crucial design parameter. The main contribution is a methodology to app…
We provide some insights in the study of branching problems of reductive groups, and a method of investigations into symmetry breaking operators. First, we give geometric criteria for finiteness property of linearly independent continuous (respectively, differential) operators that intertwine two induced representation…
Extended Siegel-Jacobi upper half-plane geometry studied with invariant metrics.
problem Characterizing the geometry of the extended Siegel-Jacobi upper half-plane.
method Parameterized using S-coordinates and expressed in terms of invariant metrics.
result Extended Siegel-Jacobi upper half-plane is a reductive, non-symmetric manifold.
A novel supervised visualization technique for data exploration.
problem Lack of supervised dimensionality reduction methods considering class labels.
method Random forest proximities and diffusion-based dimensionality reduction.
result Retains local and global structures in data, emphasizing important variables.
We consider active maximum a posteriori (MAP) inference problem for Hidden Markov Models (HMM), where, given an initial MAP estimate of the hidden sequence, we select to label certain states in the sequence to improve the estimation accuracy of the remaining states. We develop an analytical approach to this problem for…
Paper proposes a tensor data model for incomplete imaging data.
problem Prognostics models for incomplete imaging data.
method Supervised tensor dimension reduction with TTF supervision and optimization.
result Model effectively extracts low-dimensional features from incomplete data.
A new neural network architecture reduces parameters by 94% while maintaining performance.
problem Reduction of trainable parameters in neural networks.
method Spatially-coupled sparse construction to allocate trainable parameters efficiently.
result Performance comparable to traditional neural networks with 94% fewer parameters.