arXiv research

We complete the reduction scheme in the whole LP category, introduced in [7] to perform Lagrangian reduction by stages. We answer affirmatively the open question of whether reduction can be done in the whole category and analyze the Noether theorem on LP-bundles, the relationship with Hamiltonian reduction by stages an…

Paper compares Lagrangian reduction methods for rigid body systems.

Proposes a new category of bundles for Lagrangian reduction in field theory.

The abstract discusses conditions for hyperkähler manifolds and Kähler reduction.

Survey of Lagrangian reduction for discrete mechanical systems.

This work extends reduction processes for nonholonomic discrete mechanical systems.

In many classification systems, sensing modalities have different acquisition costs. It is often {\it unnecessary} to use every modality to classify a majority of examples. We study a multi-stage system in a prediction time cost reduction setting, where the full data is available for training, but for a test example, m…

The Landau-Lifshitz equation is derived as the reduction of a geodesic flow on the group of maps into the rotation group. Passing the symmetries of spatial isotropy to the reduced space is an example of semidirect product reduction by stages.

Proposes a faster Isomap algorithm by reducing eigenvalue decomposition complexity.

We give a simple and effective two stage algorithm for approximating a point cloud $\mathcal{S}\subset\mathbb{R}^m$ by a simplicial complex $K$. The first stage is an iterative fitting procedure that generalizes k-means clustering, while the second stage involves deleting redundant simplices. A form of dimension reduct…

Study detects SLI in children from spontaneous narrative transcripts.

Automatic sleep staging is a challenging problem and state-of-the-art algorithms have not yet reached satisfactory performance to be used instead of manual scoring by a sleep technician. Much research has been done to find good feature representations that extract the useful information to correctly classify each epoch…

We propose a data-driven approach to solve multiscale elliptic PDEs with random coefficients based on the intrinsic low dimension structure of the underlying elliptic differential operators. Our method consists of offline and online stages. At the offline stage, a low dimension space and its basis are extracted from th…

This paper develops a generalized formulation of Lagrangian mechanics on fibered manifolds, together with a reduction theory for symmetries corresponding to Lie groupoid actions. As special cases, this theory includes not only Lagrangian reduction (including reduction by stages) for Lie group actions, but also classica…

In the monitoring of a complex electric grid, it is of paramount importance to provide operators with early warnings of anomalies detected on the network, along with a precise classification and diagnosis of the specific fault type. In this paper, we propose a novel multi-stage early warning system prototype for electr…

Adapts DR objectives for both sample and feature size reduction.

In this work we introduce a category of discrete Lagrange--Poincare systems LP_d and study some of its properties. In particular, we show that the discrete mechanical systems and the discrete mechanical systems obtained by the Lagrangian reduction of symmetric discrete mechanical systems are objects in LP_d. We introdu…

Hippo optimizes deep learning hyper-parameters by reducing redundant trials.

New approach proves existence of gravitating vortices on Riemann surfaces.

Within a supervised classification framework, labeled data are used to learn classifier parameters. Prior to that, it is generally required to perform dimensionality reduction via feature extraction. These preprocessing steps have motivated numerous research works aiming at recovering latent variables in an unsupervise…

Proposes a federated learning approach for industrial asset failure prediction.

Two-stage mechanism designs reduce regret in recommender systems with stochastic covariates.

We show that deliberately introducing a nested simulation stage can lead to significant variance reductions when comparing two stopping times by Monte Carlo. We derive the optimal number of nested simulations and prove that the algorithm is remarkably robust to misspecifications of this number. The method is applied to…

We introduce the bilinear bandit problem with low-rank structure in which an action takes the form of a pair of arms from two different entity types, and the reward is a bilinear function of the known feature vectors of the arms. The unknown in the problem is a $d_1$ by $d_2$ matrix $\mathbfΘ^*$ that defines the reward…

This paper reviews and compares supervised linear dimension-reduction techniques.

DML-IV improves IV regression for learning decision policies by reducing bias.

GDMaps reduces high-dimensional data to lower dimensions for better classification.

Symplectic reduction by abelian subgroups coincides under specific conditions.

Efficiently identifies promising hyperparameters for online learning models.

We study channel number reduction in combination with weight binarization (1-bit weight precision) to trim a convolutional neural network for a keyword spotting (classification) task. We adopt a group-wise splitting method based on the group Lasso penalty to achieve over 50% channel sparsity while maintaining the netwo…

This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order multisymplectic field theories with constraints, such as the incompressibility constr…

Theoretical analysis of t-SNE for visualizing clustered data.

New deep network derived from rate reduction principles, explaining features and efficiency.

In the paper, we study the stochastic alternating direction method of multipliers (ADMM) for the nonconvex optimizations, and propose three classes of the nonconvex stochastic ADMM with variance reduction, based on different reduced variance stochastic gradients. Specifically, the first class called the nonconvex stoch…

BasisVAE combines VAE and clustering for tabular data analysis.

A new deep neural network tackles nonlinear functional regression with improved dimensionality reduction.

We study stock market instability by using cross-correlations constructed from the return time series of 366 stocks traded on the Tokyo Stock Exchange from January 5, 1998 to December 30, 2013. To investigate the dynamical evolution of the cross-correlations, cross-correlation matrices are calculated with a rolling win…

We consider forecasting a single time series using a large number of predictors in the presence of a possible nonlinear forecast function. Assuming that the predictors affect the response through the latent factors, we propose to first conduct factor analysis and then apply sufficient dimension reduction on the estimat…

This paper tackles variance issues in GNN training by proposing a method to reduce both embedding and gradient variances.

CAG method predicts nonlinear solid mechanics responses in real-time with high accuracy and efficiency.

We study the problem of minimizing a strongly convex, smooth function when we have noisy estimates of its gradient. We propose a novel multistage accelerated algorithm that is universally optimal in the sense that it achieves the optimal rate both in the deterministic and stochastic case and operates without knowledge …

Sparse generalized eigenvalue problem (GEP) plays a pivotal role in a large family of high-dimensional statistical models, including sparse Fisher's discriminant analysis, canonical correlation analysis, and sufficient dimension reduction. Sparse GEP involves solving a non-convex optimization problem. Most existing met…

This paper develops a new theory for ensemble learning beyond variance reduction.

CoVAE improves VAEs by reducing training steps and improving quality.

Two-stage TMLE reduces bias and improves efficiency in CRTs.

An ensemble of neural networks is known to be more robust and accurate than an individual network, however usually with linearly-increased cost in both training and testing. In this work, we propose a two-stage method to learn Sparse Structured Ensembles (SSEs) for neural networks. In the first stage, we run SG-MCMC wi…

We generalize various symplectic reduction techniques to the context of the optimal momentum map. Our approach allows the construction of symplectic point and orbit reduced spaces purely within the Poisson category under hypotheses that do not necessarily imply the existence of a momentum map. We construct an orbit red…

Two-Timescale EM Methods improve EM for nonconvex models.