Related papers: LS-Net: Learning to Solve Nonlinear Least Squares …
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
We present a novel algorithm for self-supervised monocular depth completion. Our approach is based on training a neural network that requires only sparse depth measurements and corresponding monocular video sequences without dense depth…
Estimating 3D scene flow from a sequence of monocular images has been gaining increased attention due to the simple, economical capture setup. Owing to the severe ill-posedness of the problem, the accuracy of current methods has been…
As one of the recently proposed algorithms for sparse system identification, $l_0$ norm constraint Least Mean Square ($l_0$-LMS) algorithm modifies the cost function of the traditional method with a penalty of tap-weight sparsity. The…
Most systems and learning algorithms optimize average performance or average loss -- one reason being computational complexity. However, many objectives of practical interest are more complex than simply average loss. This arises, for…
This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much…
We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a $(\delta,\epsilon)$-stationary point from…
Many problems in computer vision and robotics can be phrased as non-linear least squares optimization problems represented by factor graphs, for example, simultaneous localization and mapping (SLAM), structure from motion (SfM), motion…
We study the total least squares (TLS) problem that generalizes least squares regression by allowing measurement errors in both dependent and independent variables. TLS is widely used in applied fields including computer vision, system…
There has been tremendous research progress in estimating the depth of a scene from a monocular camera image. Existing methods for single-image depth prediction are exclusively based on deep neural networks, and their training can be…
We propose an algorithm, called OEM (a.k.a. orthogonalizing EM), intended for var- ious least squares problems. The first step, named active orthogonization, orthogonalizes an arbi- trary regression matrix by elaborately adding more rows.…
Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra,…
In this work, we study the problem of non-blind image deconvolution and propose a novel recurrent network architecture that leads to very competitive restoration results of high image quality. Motivated by the computational efficiency and…
Extremum seeking (ES) optimization approach has been very popular due to its non-model based analysis and implementation. This approach has been mostly used with gradient based search algorithms. Since least squares (LS) algorithms are…
For three decades, carrier-phase observations have been used to obtain the most accurate location estimates using global navigation satellite systems (GNSS). These estimates are computed by minimizing a nonlinear mixed-integer least-squares…
Convolutional neural networks (CNN) have shown state-of-the-art results for low-level computer vision problems such as stereo and monocular disparity estimations, but still, have much room to further improve their performance in terms of…
In this paper, we study the problem of finding the least square solutions of over-determined linear algebraic equations over networks in a distributed manner. Each node has access to one of the linear equations and holds a dynamic state. We…
The success of deep neural networks hinges on our ability to accurately and efficiently optimize high-dimensional, non-convex functions. In this paper, we empirically investigate the loss functions of state-of-the-art networks, and how…
Deep learning approaches, known for their ability to model complex relationships and fast execution, are increasingly being applied to solve large optimization problems. However, existing methods often face challenges in simultaneously…