Related papers: A Parallel Method for Large Scale Convex Regressio…
This paper introduces a new type of regression methodology named as Convex-Area-Wise Linear Regression(CALR), which separates given datasets by disjoint convex areas and fits different linear regression models for different areas. This…
Stochastic convex optimization problems with nonlinear functional constraints are ubiquitous in signal processing applications including constrained least-squares, set-membership adaptive filtering, and trajectory optimization under…
We propose a first-order method for convex optimization, where instead of being restricted to the gradient from a single parameter, gradients from multiple parameters can be used during each step of gradient descent. This setup is…
Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…
Many control policies used in various applications determine the input or action by solving a convex optimization problem that depends on the current state and some parameters. Common examples of such convex optimization control policies…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
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.…
In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
Convex quadratic programming (QP) is an important class of optimization problem with wide applications in practice. The classic QP solvers are based on either simplex or barrier method, both of which suffer from the scalability issue…
This study considers the control problem with signal temporal logic (STL) specifications. Prior works have adopted smoothing techniques to address this problem within a feasible time frame and solve the problem by applying sequential…
First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…
The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…
Quantile regression is a powerful tool capable of offering a richer view of the data as compared to least-squares regression. Quantile regression is typically performed individually on a few quantiles or a grid of quantiles without…
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
Stochastic convex optimization, where the objective is the expectation of a random convex function, is an important and widely used method with numerous applications in machine learning, statistics, operations research and other areas. We…
This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank…