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The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…
In applications, a substantial number of problems can be formulated as non-linear least squares problems over smooth varieties. Unlike the usual least squares problem over a Euclidean space, the non-linear least squares problem over a…
We are interested in parallelizing the Least Angle Regression (LARS) algorithm for fitting linear regression models to high-dimensional data. We consider two parallel and communication avoiding versions of the basic LARS algorithm. The two…
This work provides simple algorithms for multi-class (and multi-label) prediction in settings where both the number of examples n and the data dimension d are relatively large. These robust and parameter free algorithms are essentially…
We present a novel quantum high-dimensional linear regression algorithm with an $\ell_1$-penalty based on the classical LARS (Least Angle Regression) pathwise algorithm. Similarly to available classical algorithms for Lasso, our quantum…
Time series forecasting presents unique challenges that limit the effectiveness of traditional machine learning algorithms. To address these limitations, various approaches have incorporated linear constraints into learning algorithms, such…
In modern data analysis, random sampling is an efficient and widely-used strategy to overcome the computational difficulties brought by large sample size. In previous studies, researchers conducted random sampling which is according to the…
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…
In this paper we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a…
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…
For reconstruction of low-rank matrices from undersampled measurements, we develop an iterative algorithm based on least-squares estimation. While the algorithm can be used for any low-rank matrix, it is also capable of exploiting a-priori…
We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior…
The adaptive Antoulas-Anderson (AAA) algorithm for rational approximation is a widely used method for the efficient construction of highly accurate rational approximations to given data. While AAA can often produce rational approximations…
Maximum Likelihood Estimation of continuous variable models can be very challenging in high dimensions, due to potentially complex probability distributions. The existence of multiple interdependencies among variables can make it very…
The attention mechanism is an important reason for the success of transformers. It relies on computing pairwise relations between tokens. To reduce the high computational cost of standard quadratic attention, linear attention has been…
In this paper we formulate and solve a robust least squares problem for a system of linear equations subject to quantization error in the data matrix. Ordinary least squares fails to consider uncertainty in the operator, modeling all noise…
We propose a new Iteratively Reweighted Least Squares (IRLS) algorithm for the problem of completing or denoising low-rank matrices that are structured, e.g., that possess a Hankel, Toeplitz or block-Hankel/Toeplitz structure. The algorithm…
Modeling and forecasting interval-valued time series (ITS) have attracted considerable attention due to their growing presence in various contexts. To the best of our knowledge, there have been no efforts to model large-scale ITS. In this…
Total least squares (TLS) methods have been widely used in data fitting. Compared with the least squares method, for TLS problem we takes into account not only the observation errors, but also the errors in the measurement matrix. This is…
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…