Related papers: On a progressive and iterative approximation metho…
Variational inference consists in finding the best approximation of a target distribution within a certain family, where `best' means (typically) smallest Kullback-Leiber divergence. We show that, when the approximation family is…
We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distribution. By applying the principle of maximum entropy, the weight…
Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an…
Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.),…
Image smoothing is by reducing pixel-wise gradients to smooth out details. As existing methods always rely on gradients to determine smoothing manners, it is difficult to distinguish structures and details to handle distinctively due to the…
We propose a randomized first order optimization algorithm Gradient Projection Iterative Sketch (GPIS) and an accelerated variant for efficiently solving large scale constrained Least Squares (LS). We provide theoretical convergence…
Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, we propose a novel optimization algorithm for minimizing a convex objective which decomposes…
We propose a novel algorithm for the fitting of 3D human shape to images. Combining the accuracy and refinement capabilities of iterative gradient-based optimization techniques with the robustness of deep neural networks, we propose a…
Rational approximation appears in many contexts throughout science and engineering, playing a central role in linear systems theory, special function approximation, and many others. There are many existing methods for solving the rational…
We propose an iterative algorithm for low-rank matrix completion that can be interpreted as an iteratively reweighted least squares (IRLS) algorithm, a saddle-escaping smoothing Newton method or a variable metric proximal gradient method…
Latest least squares regression (LSR) methods mainly try to learn slack regression targets to replace strict zero-one labels. However, the difference of intra-class targets can also be highlighted when enlarging the distance between…
Accurately assessing the perceptual quality of face images is crucial, especially with the rapid progress in face restoration and generation. Traditional quality assessment methods often struggle with the unique characteristics of face…
A two-step method for solving planar Laplace problems via rational approximation is introduced. First complex rational approximations to the boundary data are determined by AAA approximation, either globally or locally near each corner or…
Fitting parametric models of human bodies, hands or faces to sparse input signals in an accurate, robust, and fast manner has the promise of significantly improving immersion in AR and VR scenarios. A common first step in systems that…
We analyze the problem of fitting a fonction en escalier or multi-step function to a curve in L^2 Hilbert space. We propose a two-stage optimization approach whereby the step positions are initially fixed, corresponding to a classic linear…
We introduce the ``Sequential Empirical Bayes Method'', an adaptive constrained-curve fitting procedure for extracting reliable priors. These are then used in standard augmented-chi-square fits on separate data. This better stabilizes fits…
In this paper, we propose a new way of remembering by introducing a memory influence mechanism for the least squares support vector machine (LSSVM). Without changing the equation constraints of the original LSSVM, this mechanism, allows an…
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…
Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with…
Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…