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.
Efficiently reduces rank of non-negative matrices with quadratic time complexity.
Efficiently reduces tensor ranks using mean-field approximation.
T. Kobayashi conjectured in the 36th Geometry Symposium in Japan (1989) that a homogeneous space G/H of reductive type does not admit a compact Clifford-Klein form if rank G - rank K < rank H - rank K_H. We solve this conjecture affirmatively. We apply a cohomological obstruction to the existence of compact Clifford-Kl…
We study the Jacobi osculating rank of geodesics on naturally reductive homogeneous manifolds and we apply this theory to the 3-dimensional case. Here, each non-symmetric, simply connected naturally reductive 3-manifold can be given as a principal bundle over a surface of constant curvature, such that the curvature of …
Proposes a faster Isomap algorithm by reducing eigenvalue decomposition complexity.
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 …
We reduce variance in monetization metrics for ranking experiments.
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…
We show that the finiteness length of an -arithmetic subgroup in a noncommutative isotropic absolutely almost simple group over a global function field is one less than the sum of the local ranks of taken over the places in . This determines the finiteness properties for arithmetic subgroups in isotro…
The paper extends a theorem to number fields without infinite places.
New algorithms estimate matrix leverage scores using rank revealing and randomization.
PSMM method optimizes matrix sufficient dimension reduction.
Study evaluates feature ranking methods' faithfulness in ML models, improving with dimensionality reduction.
Paper presents a reduction-based framework for conservative bandits and RL with improved lower and upper bounds.
A trisymplectic structure on a complex 2n-manifold is a triple of holomorphic symplectic forms such that any linear combination of these forms has constant rank 2n, n or 0, and degenerate forms in belong to a non-degenerate quadric hypersurface. We show that a trisymplectic manifold is equipped with a holomorphic 3…
IRCUR accelerates RPCA by using CUR decomposition for efficient low rank estimation.
New method finds efficient low-rank neural networks during training.
The problem of low-rank approximation with convex constraints, which appears in data analysis, system identification, model order reduction, low-order controller design and low-complexity modelling is considered. Given a matrix, the objective is to find a low-rank approximation that meets rank and convex constraints, w…
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation matrix completion in various fields such as the financial market and the low-ra…
New method reduces variance in estimating PL model expectations.
We present Matrix Krasulina, an algorithm for online k-PCA, by generalizing the classic Krasulina's method (Krasulina, 1969) from vector to matrix case. We show, both theoretically and empirically, that the algorithm naturally adapts to data low-rankness and converges exponentially fast to the ground-truth principal su…
This paper gives a review and synthesis of methods of evaluating dimensionality reduction techniques. Particular attention is paid to rank-order neighborhood evaluation metrics. A framework is created for exploring dimensionality reduction quality through visualization. An associated toolkit is implemented in R. The to…
We show that polar actions of cohomogeneity two on simple compact Lie groups of higher rank, endowed with a biinvariant Riemannian metric, are hyperpolar. Combining this with a recent result of the second-named author, we are able to prove that polar actions induced by reductive algebraic subgroups in the isometry grou…
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor selection and rank reduction are the most popular strategies for obtaining lower-d…
New method solves matrix completion problems to certifiable optimality.
We consider locally conformal Kaehler geometry as an equivariant (homothetic) Kaehler geometry: a locally conformal Kaehler manifold is, up to equivalence, a pair (K,Γ) where K is a Kaehler manifold and Γa discrete Lie group of biholomorphic homotheties acting freely and properly discontinuously. We define a new invari…
A neural network approach for feature selection using mutual information.
SVD training reduces DNN rank and computation load without SVD per step.
Optimizes wide low-rank neural networks for reduced parameters and cost.
Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern high-dimensional data and interactions thereof can be modeled as lying approximat…
Develops precise expressions for random projections for better machine learning tasks.
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…
Consider an effective Hamiltonian torus action on a topologically twisted,generalized complex manifold of dimension . We prove that the and that the topological twisting survives Hamiltonian reduction. We then construct a large new class of such actions satisfying $rank(T) =…
We demonstrate that almost all non-parametric dimensionality reduction methods can be expressed by a simple procedure: regularized loss minimization plus singular value truncation. By distinguishing the role of the loss and regularizer in such a process, we recover a factored perspective that reveals some gaps in the c…
Low-rank approximations of data matrices are an important dimensionality reduction tool in machine learning and regression analysis. We consider the case of categorical variables, where it can be formulated as the problem of finding low-rank approximations to Boolean matrices. In this paper we give what is to the best …
The study proposes a method for risk reduction without relying on risk measurement.
Whereas most dimensionality reduction techniques (e.g. PCA, ICA, NMF) for multivariate data essentially rely on linear algebra to a certain extent, summarizing ranking data, viewed as realizations of a random permutation on a set of items indexed by , is a great statistical challenge, due to…
SRCA reduces high-dimensional data to lower dimensions while preserving geometric structures.
During the last decades, we have witnessed a surge of interests of learning a low-dimensional space with discriminative information from one single view. Even though most of them can achieve satisfactory performance in some certain situations, they fail to fully consider the information from multiple views which are hi…
New method detects low-dimensional manifolds within bounds.
New method compresses neural networks up to 14x with minimal performance loss.
Contact reductions explained through symplectic reductions.
New estimator GMIPS reduces variance in ranking policy evaluation.
We study isometric actions on Riemannian symmetric spaces of noncompact type which are induced by reductive algebraic subgroups of the isometry group. We show that for such an action there exists a corresponding isometric action on a dual compact symmetric space, which reflects many properties of the original action. F…
New algorithm for fair ranking in contextual bandits with concave rewards.
The paper explores how to reduce classification tasks to optimization problems in Euclidean space.
IMPACT optimizes LLM compression by focusing on activation importance, reducing model size up to 55.4%.
High-dimensional representations often have a lower dimensional underlying structure. This is particularly the case in many decision making settings. For example, when the representation of actions is generated from a deep neural network, it is reasonable to expect a low-rank structure whereas conventional structures l…