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.
PSMM method optimizes matrix sufficient dimension reduction.
Unified neural network for linear and nonlinear dimension reduction.
POTD estimates SDR subspace using optimal transport for binary response.
New neural network method simplifies high-dimensional data.
Enhances SDR via Hellinger correlation for better data dependency understanding.
The purpose of sufficient dimension reduction (SDR) is to find the low-dimensional subspace of input features that is sufficient for predicting output values. In this paper, we propose a novel distribution-free SDR method called sufficient component analysis (SCA), which is computationally more efficient than existing …
This paper reviews SDR methods for multivariate response regression.
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…
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 …
GenSDR tackles SDR by leveraging generative models to fully recover lower-dimensional structures.
Survey of SDR methods for high-dimensional regression and embedding.
Develops a nonparametric graphical model for conditional independence.
New method for reducing dimensions of distributional data.
A dimension allowing in particular to state necessary and sufficient conditions of the Morse-Sard Theorem for real valued functions is introduced.
Two novel methods estimate multiple FDR directions for binary categorical responses.
Listing has recently extended results of Kozameh, Newman and Tod for four-dimensional spacetimes and presented a set of necessary and sufficient conditions for a metric to be locally conformally equivalent to an Einstein metric in all semi-Riemannian spaces of dimension n>3 -- subject to a non-degeneracy restriction on…
R package psvmSDR simplifies SDR computation for machine learning.
Sufficient dimension reduction (SDR) using distance covariance (DCOV) was recently proposed as an approach to dimension-reduction problems. Compared with other SDR methods, it is model-free without estimating link function and does not require any particular distributions on predictors (see Sheng and Yin, 2013, 2016). …
Reduces IB problem to a simpler, lower-dimensional problem.
Study online multiclass classification under bandit feedback, extending previous results.
Paper introduces a nonparametric functional graphical model for random functions.
Neural networks simplify SDR in regression tasks.
Characterizes statistical complexity of realizable regression in PAC and online learning.
MSRL learns a representation maximizing mutual info with response variables.
Easy conditions found for simplifying complex systems.
SMAVE optimizes SDR by projecting onto a low-dimensional subspace on a Riemannian manifold.
We examine algebraic conditions for the sectional positivity of the Riemann curvature operator. We describe sufficient conditions for dimension , and complete characterization for a dense open subset of the space of operators in dimension . We also briefly examine higher-dimentional curvature operators.
Modified relative universality for unbiasedness and consistency in dimension reduction.
We consider sufficient conditions of local removability of coincidences of maps f,g:N->M, where M,N are manifolds with dimensions dimN>dimM. The coincidence index is the only obstruction to the removability for maps with fibers either acyclic or homeomorphic to spheres of certain dimensions. We also address the normali…
Unified framework for fair representation learning in machine learning.
In this short note, we give a sufficient condition for almost smooth compact metric measure spaces to satisfy the Bakry-Émery condition . The sufficient condition is satisfied for the glued space of any two (not necessary same dimensional) closed pointed Riemannian manifolds at their base points. This tells …
We extend the validity of a Gromov's dimension comparison estimate for topological hypersurfaces to sufficiently large classes of rectifiable sets, arising from Sobolev mappings. Our tools are a suitably weak exterior differentiation for pullback differential forms and a new low rank property for Sobolev mappings.
We classify manifolds of small dimension that admit both, a Riemannian metric of non-negative scalar curvature, and a -- a priori different -- metric for which all wedge products of harmonic forms are harmonic. For manifolds whose first Betti numbers are sufficiently large, this classification extends to higher dimensi…
Paper improves SDR estimation speed and conditions.
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of the signal space, a geometric parameter independent of the specific signal and m…
Proposes a method to estimate personalized treatments from high-dimensional data.
We define the second Paneitz-Branson operator on a compact Einsteinian manifold of dimension and we give sufficient conditions that make it attained.
We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper is devoted to the study of when these metric dimensions of a metric space are locally given by the …
Proposes a deep learning method for effective data representation.
We prove a vanishing result for critical points of the supersymmetric nonlinear sigma model on complete non-compact Riemannian manifolds of positive Ricci curvature that admit an Euclidean type Sobolev inequality, assuming that the dimension of the domain is bigger than two and that a certain energy is sufficiently sma…
Two methods preserve tensor structure for reduced dimensionality in tensor regression.
We construct explicit compact supersymmetric solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic string equations in dimension five. We present a quadratic condition on the curvature which is necessary and sufficient the heterotic supersymmetry and the anomaly cancellation t…
FlowSDR learns a low-dimensional projection preserving the response's conditional distribution.
We introduce and study the conical curvature-dimension condition, , for graphs. We show that provides necessary and sufficient conditions for the underlying graph to satisfy a sharp global Poincaré inequality which in turn translates to a sharp lower bound for the first eigenvalues of these graphs.…
We construct explicit compact solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic string equations in dimensions seven and eight. We present a quadratic condition on the curvature which is necessary and sufficient the heterotic supersymmetry and the anomaly cancellation to i…
Given a semi-Riemannian manifold, we give necessary and sufficient conditions for a Riemannian submanifold of arbitrary co-dimension to be umbilical along normal directions. We do that by using the so-called \emph{total shear tensor}, i.e., the trace-free part of the second fundamental form. We define the \emph{shear s…
It was proved by H. Whitney in 1933 that it is possible to mark a point in all curves in a continuous way. The main result of this paper extends the Whitney theorem to dimensions 2 and 3. Namely, we prove that it is possible to choose a point continuously in all two-dimensional surfaces sufficiently close to a given su…
For spacetime dimensions, we derive sufficient conditions for the twisting function in a twisted product spacetime, such that there is a global foliation by spacelike CMC surfaces.