Related papers: A Constructive Approach to the Estimation of Dimen…
Two methods are proposed for high-dimensional shape-constrained regression and classification. These methods reshape pre-trained prediction rules to satisfy shape constraints like monotonicity and convexity. The first method can be applied…
We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels…
Sufficient dimension reduction (SDR) is a popular class of regression methods which aim to find a small number of linear combinations of covariates that capture all the information of the responses i.e., a central subspace. The majority of…
Compressive spectral imaging (CSI) has emerged as an alternative spectral image acquisition technology, which reduces the number of measurements at the cost of requiring a recovery process. In general, the reconstruction methods are based…
Relative location prediction in computed tomography (CT) scan images is a challenging problem. In this paper, a regression model based on one-dimensional convolutional neural networks is proposed to determine the relative location of a CT…
We propose a direct, regression-based approach to 2D human pose estimation from single images. We formulate the problem as a sequence prediction task, which we solve using a Transformer network. This network directly learns a regression…
Beginning with a discussion of R. A. Fisher's early written remarks that relate to dimension reduction, this article revisits principal components as a reductive method in regression, develops several model-based extensions and ends with…
Model reduction is essential for real-time simulation of deformable objects. Linear techniques such as PCA provide structured and predictable behavior, but their limited expressiveness restricts accuracy under large or nonlinear…
Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the…
Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC…
In our work, we propose a novel formulation for supervised dimensionality reduction based on a nonlinear dependency criterion called Statistical Distance Correlation, Szekely et. al. (2007). We propose an objective which is free of…
The central subspace of a pair of random variables $(y,x) \in \mathbb{R}^{p+1}$ is the minimal subspace $\mathcal{S}$ such that $y \perp \hspace{-2mm} \perp x\mid P_{\mathcal{S}}x$. In this paper, we consider the minimax rate of estimating…
We provide two novel adaptive-rate compressive sensing (CS) strategies for sparse, time-varying signals using side information. Our first method utilizes extra cross-validation measurements, and the second one exploits extra low-resolution…
Sufficient dimension reduction (SDR) provides a framework for reducing the predictor space dimension in regression problems. We consider SDR in the context of deterministic functions of several variables such as those arising in computer…
Application of the minimum distance method to the linear regression model for estimating regression parameters is a difficult and time-consuming process due to the complexity of its distance function, and hence, it is computationally…
We propose an extreme dimension reduction method extending the Extreme-PLS approach to the case where the covariate lies in a possibly infinite-dimensional Hilbert space. The ideas are partly borrowed from both Partial Least-Squares and…
Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…
In traditional multivariate data analysis, dimension reduction and regression have been treated as distinct endeavors. Established techniques such as principal component regression (PCR) and partial least squares (PLS) regression…
For crowded scenes, the accuracy of object-based computer vision methods declines when the images are low-resolution and objects have severe occlusions. Taking counting methods for example, almost all the recent state-of-the-art counting…
Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical…