相关论文: Least-Squares Linear Dilation-Erosion Regressor Tr…
In this work, we develop a distributed least squares approximation (DLSA) method that is able to solve a large family of regression problems (e.g., linear regression, logistic regression, and Cox's model) on a distributed system. By…
We present linear prediction as a differentiable padding method. For each channel, a stochastic autoregressive linear model is fitted to the padding input by minimizing its noise terms in the least-squares sense. The padding is formed from…
A new generalized multilinear regression model, termed the Higher-Order Partial Least Squares (HOPLS), is introduced with the aim to predict a tensor (multiway array) $\tensor{Y}$ from a tensor $\tensor{X}$ through projecting the data onto…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
We introduce the first learning-based dense matching algorithm, termed Equirectangular Projection-Oriented Dense Kernelized Feature Matching (EDM), specifically designed for omnidirectional images. Equirectangular projection (ERP) images,…
Recent studies show that deep learning (DL) based MRI reconstruction outperforms conventional methods, such as parallel imaging and compressed sensing (CS), in multiple applications. Unlike CS that is typically implemented with…
We introduce a novel optimization algorithm for image recovery under learned sparse and low-rank constraints, which we parameterize as weighted extensions of the $\ell_p^p$-vector and $\mathcal S_p^p$ Schatten-matrix quasi-norms for…
We propose convex relaxations for convolutional neural nets with one hidden layer where the output weights are fixed. For convex activation functions such as rectified linear units, the relaxations are convex second order cone programs…
Dense pixel matching problems such as optical flow and disparity estimation are among the most challenging tasks in computer vision. Recently, several deep learning methods designed for these problems have been successful. A sufficiently…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…
The rapid growth of nature-inspired metaheuristics has exposed a persistent gap between metaphorical novelty and genuine algorithmic advancement. Motivated by the biophysics of chromatin loop extrusion -- a well-characterized genome-folding…
Exact inference in the linear regression model with spike and slab priors is often intractable. Expectation propagation (EP) can be used for approximate inference. However, the regular sequential form of EP (R-EP) may fail to converge in…
While traditional Deep Learning (DL) optimization methods treat all training samples equally, Distributionally Robust Optimization (DRO) adaptively assigns importance weights to different samples. However, a significant gap exists between…
Additive parameter updates, as used in gradient descent and its adaptive extensions, underpin most modern machine-learning optimization. Yet, such additive schemes often demand numerous iterations and intricate learning-rate schedules to…
This paper studies adaptive first-order least-squares finite element methods for second-order elliptic partial differential equations in non-divergence form. Unlike the classical finite element method which uses weak formulations of PDEs…
Convolutional neural networks (CNNs) have succeeded in many practical applications. However, their high computation and storage requirements often make them difficult to deploy on resource-constrained devices. In order to tackle this issue,…
Spatial relations between objects in an image have proved useful for structural object recognition. Structural constraints can act as regularization in neural network training, improving generalization capability with small datasets.…
This paper is concerned with numerical approximation of some two-dimensional Keller-Segel chemotaxis models, especially those generating pattern formations. The numerical resolution of such nonlinear parabolic-parabolic or…
Deep neural networks (DNNs) have been quite successful in solving many complex learning problems. However, DNNs tend to have a large number of learning parameters, leading to a large memory and computation requirement. In this paper, we…
We introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\mathbb{R}^{d}$ for each data point.…