Related papers: Least quantile regression via modern optimization
The selection of best variables is a challenging problem in supervised and unsupervised learning, especially in high dimensional contexts where the number of variables is usually much larger than the number of observations. In this paper,…
In our work, we consider the linear least squares problem for $m\times n$-systems of linear equations $Ax = b$, $m\geq n$, such that the matrix $A$ and right-hand side vector $b$ can vary within an interval $m\times n$-matrix and an…
Variational quantum algorithms offer fascinating prospects for the solution of combinatorial optimization problems using digital quantum computers. However, the achievable performance in such algorithms and the role of quantum correlations…
Cell-Free Massive multiple-input multiple-output (MIMO) systems are investigated with the support of a reconfigurable intelligent surface (RIS). The RIS phase shifts are designed for improved channel estimation in the presence of spatial…
The quantum approximate optimization algorithm (QAOA) has numerous promising applications in solving the combinatorial optimization problems on near-term Noisy Intermediate Scalable Quantum (NISQ) devices. QAOA has a quantum-classical…
Solving combinatorial optimization problems on near-term quantum devices has gained a lot of attraction in recent years. Currently, most works have focused on single-objective problems, whereas many real-world applications need to consider…
Feasible path algorithms have been widely used for process optimisation due to its good convergence. The sequential quadratic programming (SQP) algorithm is usually used to drive the feasible path algorithms towards optimality. However,…
The quantum approximate optimisation algorithm (QAOA) is a hybrid quantum-classical algorithm used to approximately solve combinatorial optimisation problems. It involves multiple iterations of a parameterised ansatz comprising a problem…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…
It is known that the estimating equations for quantile regression (QR) can be solved using an EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent…
Multi-objective optimization (MOO) is a well-studied problem for several important recommendation problems. While multiple approaches have been proposed, in this work, we focus on using constrained optimization formulations (e.g., quadratic…
We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first…
The least squares of depth-trimmed (LST) residuals regression, proposed and studied in Zuo and Zuo (2023), serves as a robust alternative to the classic least squares (LS) regression as well as a strong competitor to the renowned robust…
The quantum approximate optimization algorithm (QAOA) has become a cornerstone of contemporary quantum applications development. Here we show that the \emph{density} of problem constraints versus problem variables acts as a performance…
We analyze the performance of a linear-equality-constrained least-squares (CLS) algorithm and its relaxed version, called rCLS, that is obtained via the method of weighting. The rCLS algorithm solves an unconstrained least-squares problem…
The current boom of learned query optimizers (LQO) can be explained not only by the general continuous improvement of deep learning (DL) methods but also by the straightforward formulation of a query optimization problem (QOP) as a machine…
Searching for numerical methods that combine facility and efficiency, while remaining accurate and versatile, is critical. Often, irregular geometries challenge traditional methods that rely on structured or body-fitted meshes. Meshless…
We propose a machine learning based approach to accelerate quantum approximate optimization algorithm (QAOA) implementation which is a promising quantum-classical hybrid algorithm to prove the so-called quantum supremacy. In QAOA, a…
Quantum annealers can solve QUBO problems efficiently but struggle with continuous optimization tasks like regression due to their discrete nature. We introduce Quadratic Continuous Quantum Optimization (QCQO), an anytime algorithm that…
We present an efficient algorithm for the least squares parameter fitting optimized for component separation in multi-frequency CMB experiments. We sidestep some of the problems associated with non-linear optimization by taking advantage of…