Related papers: Sufficient Dimension Reduction via Inverse Conditi…
A new dimension reduction (DR) method for data sets is proposed by autonomous deforming of data manifolds. The deformation is guided by the proposed deforming vector field, which is defined by two kinds of virtual interactions between data…
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…
Since their initial introduction, score-based diffusion models (SDMs) have been successfully applied to solve a variety of linear inverse problems in finite-dimensional vector spaces due to their ability to efficiently approximate the…
In this paper, we present a dimension reduction method to reduce the dimension of parameter space and state space and efficiently solve inverse problems. To this end, proper orthogonal decomposition (POD) and radial basis function (RBF) are…
Time series forecasting is vital across many domains, yet existing models struggle with fixed-length inputs and inadequate multi-scale modeling. We propose MR-CDM, a framework combining hierarchical multi-resolution trend decomposition, an…
Sliced inverse regression (SIR) is a popular sufficient dimension reduction method that identifies a few linear transformations of the covariates without losing regression information with the response. In high-dimensional settings, SIR can…
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…
This paper studies high-dimensional regression with two-way structured data. To estimate the high-dimensional coefficient vector, we propose the generalized matrix decomposition regression (GMDR) to efficiently leverage any auxiliary…
Solving high-dimensional PDE-governed inverse problems is often challenging due to complex non-Gaussian posterior distributions, expensive forward model evaluations, and misspecified prior information. To address these issues, we propose a…
Variable screening has been a useful research area that deals with ultrahigh-dimensional data. When there exist both marginally and jointly dependent predictors to the response, existing methods such as conditional screening or iterative…
Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…
Data dimension reduction (DDR) is all about mapping data from high dimensions to low dimensions, various techniques of DDR are being used for image dimension reduction like Random Projections, Principal Component Analysis (PCA), the…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
The method of dimensionality reduction (MDR) is extended for the axisymmetric frictionless unilateral Hertz-type contact problem for a viscoelastic half-space and an arbitrary axisymmetric rigid indenter under the assumption that an…
Learning-based isosurface extraction methods have recently emerged as a robust and efficient alternative to axiomatic techniques. However, the vast majority of such approaches rely on supervised training with axiomatically computed ground…
Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…
This paper examines the implications of using the Scale-Invariant Signal-to-Distortion Ratio (SI-SDR) as both evaluation and training objective in supervised speech separation, when the training references contain noise, as is the case with…
Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…
Inverse problems involving systems of partial differential equations (PDEs) with many measurements or experiments can be very expensive to solve numerically. In a recent paper we examined dimensionality reduction methods, both stochastic…
Fr\'echet regression has received considerable attention to model metric-space valued responses that are complex and non-Euclidean data, such as probability distributions and vectors on the unit sphere. However, existing Fr\'echet…