Movement primitives are an important policy class for real-world robotics. However, the high dimensionality of their parametrization makes the policy optimization expensive both in terms of samples and computation. Enabling an efficient representation of movement primitives facilitates the application of machine learni…
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
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48 results for “parameter space reduction”
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.
We introduce several new black-box reductions that significantly improve the design of adaptive and parameter-free online learning algorithms by simplifying analysis, improving regret guarantees, and sometimes even improving runtime. We reduce parameter-free online learning to online exp-concave optimization, we reduce…
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.
We study the Euler-Lagrange equations for a parameter dependent -invariant Lagrangian on a homogeneous -space. We consider the pullback of the parameter dependent Lagrangian to the Lie group , emphasizing the special invariance properties of the associated Euler-Poincaré equations with advected parameters.
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.
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.
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.
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.
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.
The classical result of describing harmonic maps from surfaces into symmetric spaces of reductive Lie groups states that the Maurer-Cartan form with an additional parameter, the so-called loop parameter, is integrable for all values of the loop parameter. As a matter of fact, the same result holds for -symmetric spa…
Rollings of reductive homogeneous spaces are studied using intrinsic curves.
problem Investigate rollings of reductive homogeneous spaces without slip and twist.
method An intrinsic point of view, considering rollings as curves in the configuration space tangent to a certain distribution.
result Explicit solutions for rollings of over are obtained for specific cases.
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…
The paper explores how to reduce classification tasks to optimization problems in Euclidean space.
problem Understanding the minimum dimension needed for reducing classification tasks to optimization problems.
method Developed a generalization of the Borsuk-Ulam Theorem to analyze the expressivity of reductions.
result The minimum Euclidean dimension required can be exponentially larger than the VC dimension, even for slightly non-trivial reductions.
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.
Survey of factor analysis, PCA, variational inference, and VAE.
problem Dimensionality reduction and generative modeling of data.
method Variational inference, factor analysis, probabilistic PCA, and VAE.
result Derivation and explanation of ELBO, EM, and closed-form solutions.
This paper contains a classification of smooth Kaluza--Klein reductions (by one-parameter subgroups) of the maximally supersymmetric anti de Sitter backgrounds of supergravity theories. We present a classification of one-parameter subgroups of isometries of anti de Sitter spaces, discuss the causal properties of their …
A new method reduces both input and output dimensions for better goal-oriented analysis.
problem Simultaneous reduction of input and output dimensions for more accurate analysis.
method Coupled input-output dimension reduction, optimizing gradient-based bounds.
result Determine most informative sensors and influential parameters efficiently.
The paper provides statistical guarantees for generative models using dimension reduction.
problem Improving the quality of generative models without increasing dimensionality.
method Modeling generative devices as smooth transformations of a lower-dimensional space and using integral probability metrics.
result Established a risk bound showing the impact of dimension reduction on generative model error.
DM uses semigroup property to tune diffusion time for better data analysis.
problem Difficulty in tuning diffusion time for optimal data analysis.
method Proposes a semigroup criterion to select diffusion time.
result Effective and robust method for picking diffusion time.
Given a reductive homogeneous space M=G/H endowed with a naturally reductive metric, we study the one-parameter family of connections joining the canonical and the Levi-Civita connection (t=0, 1/2). We show that the Dirac operator D^t corresponding to t=1/3 is the so-called ``cubic'' Dirac operator recently introduced …
Spatiotemporal sequence prediction is an important problem in deep learning. We study next-frame(s) video prediction using a deep-learning-based predictive coding framework that uses convolutional, long short-term memory (convLSTM) modules. We introduce a novel reduced-gate convolutional LSTM(rgcLSTM) architecture that…
Adapts POD basis for parametric ROMs using pGP.
problem Updating POD basis for accurate system behavior over parameter space.
method Formulates problem as supervised statistical learning, uses pGP to learn mapping between parameter space and Grassmann manifold.
result Proposes pGP for optimal estimation of POD basis parameters and quantifies uncertainty.
Direct contextual policy search methods learn to improve policy parameters and simultaneously generalize these parameters to different context or task variables. However, learning from high-dimensional context variables, such as camera images, is still a prominent problem in many real-world tasks. A naive application o…
A Fully Bayesian Gradient-Free Supervised Dimension Reduction Method using Gaussian Processesstat.ML
Gradient-free method reduces dimensionality without gradients for expensive models.
problem Reducing high-dimensional input spaces for expensive models without gradient information.
method Fully Bayesian, gradient-free approach using Gaussian processes.
result Improves active subspace recovery and probabilistic prediction accuracy with limited data.
A new method for classifying naturally reductive spaces is presented. This method relies on the structure theory of naturally reductive spaces developed in \cite{Storm2018a} and the new construction of naturally reductive spaces in \cite{Storm2018}. We obtain the classification of all naturally reductive spaces in dime…
A new construction of naturally reductive spaces is presented. This construction gives a large amount of new families of naturally reductive spaces. First the infinitesimal models of the new naturally reductive spaces are constructed. A concrete transitive group of isometries is given for the new spaces and also the na…
In the present paper we study naturally reductive homogeneous -metric spaces. Under some conditions, we give some necessary and sufficient conditions for a homogeneous -metric space to be naturally reductive. Then we show that for such spaces the two definitions of naturally reductive homogeneous Finsler …
RC flow learns molecular kinetics in low dimensions.
problem Discovering interpretable low-dimensional models of molecular kinetics.
method Normalizing flow for coordinate transformation and Brownian dynamics for kinetics approximation.
result Tractable and trainable model of reduced kinetics in continuous time and space.
Optimizes parameters in high-dimensional spaces for practical applications.
problem Tuning parameters for complex systems like electron accelerators.
method Bayesian optimization techniques applied to high-dimensional problems.
result Novel algorithm BORING for parameter optimization.
Study extends Kobayashi's method to non-reductive subgroups for homogeneous spaces.
problem Existence of compact Clifford-Klein forms in homogeneous spaces.
method Extend Kobayashi's method to non-reductive subgroups and compare Cartan projections and non-compact dimensions.
result Examples of homogeneous spaces without compact Clifford-Klein forms.
Simultaneously Learning Neighborship and Projection Matrix for Supervised Dimensionality Reductioncs.CV
Explicitly or implicitly, most of dimensionality reduction methods need to determine which samples are neighbors and the similarity between the neighbors in the original highdimensional space. The projection matrix is then learned on the assumption that the neighborhood information (e.g., the similarity) is known and f…
Approximation rates of quantum neural networks for periodic functions via Jackson's inequalityquant-ph
Quantum neural networks approximate periodic functions more efficiently.
problem Approximating periodic functions with quantum neural networks.
method Using Jackson's inequality to construct a QNN that approximates a trigonometric polynomial of the function.
result Quantum neural networks can achieve better approximation results with fewer parameters for smoother functions.
Typical dimensionality reduction methods focus on directly reducing the number of random variables while retaining maximal variations in the data. In this paper, we consider the dimensionality reduction in parameter spaces of binary multivariate distributions. We propose a general Confident-Information-First (CIF) prin…
Supervised linear feature extraction can be achieved by fitting a reduced rank multivariate model. This paper studies rank penalized and rank constrained vector generalized linear models. From the perspective of thresholding rules, we build a framework for fitting singular value penalized models and use it for feature …
Adaptive framework improves nonparametric dimensionality reduction.
problem Optimal hyper-parameter tuning for nonparametric dimensionality reduction.
method Adaptive framework using intrinsic dimension estimator and optimal local neighbourhood sizes.
result Significant improvements in various learning tasks through better low-dimensional visualizations.
Paper presents a novel hyperbolic neural network for efficient data representation.
problem Efficient representation of hierarchical data in hyperbolic space.
method Develops a fully hyperbolic neural network using projections and equivariant embeddings.
result Proves the proposed embedding is isometric and equivariant under Lorentz transformations.
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.
Random forests are among the most popular classification and regression methods used in industrial applications. To be effective, the parameters of random forests must be carefully tuned. This is usually done by choosing values that minimize the prediction error on a held out dataset. We argue that error reduction is o…
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)…
New method for analyzing complex data spaces.
problem Dimensionality reduction and learning data representations for continuous spaces.
method Manifold factorization based on spectral graph methods.
result Recovering factors yields meaningful lower-dimensional representations.
New findings on Codazzi tensors in homogeneous spaces.
problem Characterizing Codazzi tensor fields in reductive homogeneous spaces.
method Extending results from Lie groups to reductive homogeneous spaces, analyzing the curvature of canonical connections.
result Invariant Codazzi tensor fields on naturally reductive homogeneous spaces are parallel.
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.
This paper proposes BRIEF, a backward reduction algorithm that explores compact CNN-model designs from the information flow perspective. This algorithm can remove substantial non-zero weighting parameters (redundant neural channels) of a network by considering its dynamic behavior, which traditional model-compaction te…
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…
Study on rolling Stiefel manifolds with specific metrics.
problem Intrinsic and extrinsic rolling of Stiefel manifolds with -metrics.
method Investigation of intrinsic rolling of normal naturally reductive homogeneous spaces, derivation of ODEs for rolling, and explicit solutions.
result Explicit solutions for intrinsic and extrinsic rolling of Stiefel manifolds.
New method reduces version space for CNNs, improving active learning performance.
problem Sampling bias in active learning hinders optimal hypothesis finding in neural networks.
method Version space reduction through prior mass reduction and diameter reduction, proposing a new Gibbs-vote disagreement method.
result Diameter-based querying method reduces version space more effectively than prior mass reduction and other methods.