Related papers: Mixed Precision Rayleigh Quotient Iteration for To…
We address the Least Quantile of Squares (LQS) (and in particular the Least Median of Squares) regression problem using modern optimization methods. We propose a Mixed Integer Optimization (MIO) formulation of the LQS problem which allows…
We consider a setting in which it is desired to find an optimal complex vector $\mathbf{x}\in\mathbb{C}^N$ that satisfies $\mathcal{A}(\mathbf{x}) \approx \mathbf{b}$ in a least-squares sense, where $\mathbf{b} \in \mathbb{C}^M$ is a data…
With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…
Quantization is essential for Neural Network (NN) compression, reducing model size and computational demands by using lower bit-width data types, though aggressive reduction often hampers accuracy. Mixed Precision (MP) mitigates this…
The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses…
In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…
We address the problem of solving a system of linear equations via the Quantum Singular Value Transformation (QSVT). One drawback of the QSVT algorithm is that it requires huge quantum resources if we want to achieve an acceptable accuracy.…
We consider the solution of full column-rank least squares problems by means of normal equations that are preconditioned, symmetrically or non-symmetrically, with a randomized preconditioner. With an effective preconditioner, the solutions…
Using lower precision in algorithms can be beneficial in terms of reducing both computation and communication costs. Motivated by this, we aim to further the state-of-the-art in developing and analyzing mixed precision variants of iterative…
Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive…
Certain optimization problems in communication systems, such as limited-feedback constant-envelope beamforming or noncoherent $M$-ary phase-shift keying ($M$PSK) sequence detection, result in the maximization of a fixed-rank positive…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…
Given a linear regression setting, Iterative Least Trimmed Squares (ILTS) involves alternating between (a) selecting the subset of samples with lowest current loss, and (b) re-fitting the linear model only on that subset. Both steps are…
LIDAR 3D object detection is one of the important tasks for autonomous vehicles. Ensuring that this task operates in real-time is crucial. Toward this, model quantization can be used to accelerate the runtime. However, directly applying…
We investigate iterative methods with randomized preconditioners for solving overdetermined least-squares problems, where the preconditioners are based on a random embedding of the data matrix. We consider two distinct approaches: the…