arXiv research

Paper improves efficiency in matrix computations for Gaussian processes.

Method for computing Khovanov homology of tangles.

Study star products on Poisson manifolds compatible with reduction.

Efficiently transforms Gaussian data to simulate various target distributions.

In the present paper we study naturally reductive homogeneous $(α,β)$-metric spaces. Under some conditions, we give some necessary and sufficient conditions for a homogeneous $(α,β)$-metric space to be naturally reductive. Then we show that for such spaces the two definitions of naturally reductive homogeneous Finsler …

We consider a family of tight contact structures on the three-dimensional torus and we compute the relative Contact Homology by using the variational theory of critical points at infinity. We will also show some algebraic equivariant homology reductions.

Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as symmetric generalized eigendecomposition problems. In this paper we outline how t…

Affective computing has become a very important research area in human-machine interaction. However, affects are subjective, subtle, and uncertain. So, it is very difficult to obtain a large number of labeled training samples, compared with the number of possible features we could extract. Thus, dimensionality reductio…

Ensemble learning has had many successes in supervised learning, but it has been rare in unsupervised learning and dimensionality reduction. This study explores dimensionality reduction ensembles, using principal component analysis and manifold learning techniques to capture linear, nonlinear, local, and global feature…

Unified neural network for linear and nonlinear dimension reduction.

Derive bihamiltonian structure for rational reduction of 2D-Toda hierarchy

Proposes a faster Isomap algorithm by reducing eigenvalue decomposition complexity.

New insights link diverse statistical problems via secret leakage planted clique.

Computes the component group of real reductive groups.

This work compares data reduction criteria for online Gaussian Processes.

Adapts DR objectives for both sample and feature size reduction.

Introduces a reduction system for Artin-Tits groups, improving algorithms and proving periodicity results.

We propose a greedy mixture reduction algorithm which is capable of pruning mixture components as well as merging them based on the Kullback-Leibler divergence (KLD). The algorithm is distinct from the well-known Runnalls' KLD based method since it is not restricted to merging operations. The capability of pruning (in …

Supervised dimensionality reduction strategies have been of great interest. However, current supervised dimensionality reduction approaches are difficult to scale for situations characterized by large datasets given the high computational complexities associated with such methods. While stochastic approximation strateg…

A method constructs a stochastic surrogate from dimensionality reduction results for high-dimensional uncertainty quantification.

Ant colonies and boosting algorithms both reduce bias and variance through adaptive mechanisms.

Paper proposes a method to estimate variance reduction in DNN training using importance sampling.

This paper puts the theory of quasi-Hamiltonian reduction in the framework of shifted symplectic structures developed by Pantev, Toën, Vaquié and Vezzosi. We compute the symplectic structures on mapping stacks and show how the AKSZ topological field theory defined by Calaque allows one to neatly package the constructio…

Dimensionality reduction is an important step in processing the hyperspectral images (HSI) to overcome the curse of dimensionality problem. Linear dimensionality reduction methods such as Independent component analysis (ICA) and Linear discriminant analysis (LDA) are commonly employed to reduce the dimensionality of HS…

DFR reduces the computational cost of sparse-group lasso and adaptive sparse-group lasso.

Dimension reduction of multivariate data supervised by auxiliary information is considered. A series of basis for dimension reduction is obtained as minimizers of a novel criterion. The proposed method is akin to continuum regression, and the resulting basis is called continuum directions. With a presence of binary sup…

We obtain new invariant Einstein metrics on the compact Lie groups $SO(n)$ ($n \geq 7$) which are not naturally reductive. This is achieved by imposing certain symmetry assumptions in the set of all left-invariant metrics on $SO(n)$ and by computing the Ricci tensor for such metrics. The Einstein metrics are obtained a…

In this paper we show that for the purposes of dimensionality reduction certain class of structured random matrices behave similarly to random Gaussian matrices. This class includes several matrices for which matrix-vector multiply can be computed in log-linear time, providing efficient dimensionality reduction of gene…

In this work, we revisit fast dimension reduction approaches, as with random projections and random sampling. Our goal is to summarize the data to decrease computational costs and memory footprint of subsequent analysis. Such dimension reduction can be very efficient when the signals of interest have a strong structure…

Unified model for reducing dimensions and clustering high-dimensional data.

Effective dimensionality reduction improves accuracy and reduces costs in estimating option Greeks.

The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the computational burden of the principal support vector machines method constrains …

This thesis explores fast algorithms for large matrices and data augmentation to improve model efficiency.

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…

In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation…

Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important. Here, we construct a mean-field framework to understand how compact representation…

Communication on heterogeneous edge networks is a fundamental bottleneck in Federated Learning (FL), restricting both model capacity and user participation. To address this issue, we introduce two novel strategies to reduce communication costs: (1) the use of lossy compression on the global model sent server-to-client;…

Stochastic gradient Markov Chain Monte Carlo (SG-MCMC) has been developed as a flexible family of scalable Bayesian sampling algorithms. However, there has been little theoretical analysis of the impact of minibatch size to the algorithm's convergence rate. In this paper, we prove that under a limited computational bud…

We propose a reduction for non-convex optimization that can (1) turn an stationary-point finding algorithm into an local-minimum finding one, and (2) replace the Hessian-vector product computations with only gradient computations. It works both in the stochastic and the deterministic settings, without hurting the algor…

Variance reduction (VR) methods boost the performance of stochastic gradient descent (SGD) by enabling the use of larger, constant stepsizes and preserving linear convergence rates. However, current variance reduced SGD methods require either high memory usage or an exact gradient computation (using the entire dataset)…

In the past decade, sparse principal component analysis has emerged as an archetypal problem for illustrating statistical-computational tradeoffs. This trend has largely been driven by a line of research aiming to characterize the average-case complexity of sparse PCA through reductions from the planted clique (PC) con…

In online advertising, display ads are increasingly being placed based on real-time auctions where the advertiser who wins gets to serve the ad. This is called real-time bidding (RTB). In RTB, auctions have very tight time constraints on the order of 100ms. Therefore mechanisms for bidding intelligently such as clickth…

Efficiently reduces rank of non-negative matrices with quadratic time complexity.

Paper proposes efficient BNN inference flow to reduce computation and memory costs.

U-statistics improve gradient estimation in importance-weighted variational inference.

We consider supervised dimension reduction problems, namely to identify a low dimensional projection of the predictors $\-x$ which can retain the statistical relationship between $\-x$ and the response variable $y$. We follow the idea of the sliced inverse regression (SIR) and the sliced average variance estimation (SA…

We determine the holonomy of generalized Killing spinor covariant derivatives of the form $D= \nabla + Ω$ on pseudo-Riemannian reductive homogeneous spaces in a purely algebraic and algorithmic way, where $Ω: TM \rightarrow Λ^*(TM)$ is a left-invariant homomorphism. This is essentially an application of the theory of i…

UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a practical scalable algorithm that applies to real world data. The UMAP algorithm is c…