Related papers: Linear Regression by Quantum Amplitude Estimation …
The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequently in applications such as quantum control and…
Linear regression is fundamental to statistical analysis and machine learning, but its application to large-scale datasets necessitates distributed computing. The problem also arises in quantum computing, where handling extensive data…
We introduce a quantum linear system solving algorithm based on the Kaczmarz method, a widely used workhorse for large linear systems and least-squares problems that updates the solution by enforcing one equation at a time. Its simplicity…
Quantile regression is a statistical method for estimating conditional quantiles of a response variable. In addition, for mean estimation, it is well known that quantile regression is more robust to outliers than $l_2$-based methods. By…
Recently, there has been a surge of interest for quantum computation for its ability to exponentially speed up algorithms, including machine learning algorithms. However, Tang suggested that the exponential speed up can also be done on a…
We investigate the nonlinear regression problem under L2 loss (square loss) functions. Traditional nonlinear regression models often result in non-convex optimization problems with respect to the parameter set. We show that a convex…
Recently, linear regression models incorporating an optimal transport (OT) loss have been explored for applications such as supervised unmixing of spectra, music transcription, and mass spectrometry. However, these task-specific approaches…
$\ell_1$-penalized quantile regression is widely used for analyzing high-dimensional data with heterogeneity. It is now recognized that the $\ell_1$-penalty introduces non-negligible estimation bias, while a proper use of concave…
Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…
We propose a quantum algorithm based on ridge regression model, which get the optimal fitting parameters w and a regularization hyperparameter {\alpha} by analysing the training dataset. The algorithm consists of two subalgorithms. One is…
This paper considers the projection-free sparse convex optimization problem for the vector domain and the matrix domain, which covers a large number of important applications in machine learning and data science. For the vector domain…
The performance of quantum neural network models depends strongly on architectural decisions, including circuit depth, placement of parametrized operations, and data-encoding strategies. Selecting an effective architecture is challenging…
In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…
Logistic regression, the Support Vector Machine (SVM), and least squares are well-studied methods in the statistical and computer science community, with various practical applications. High-dimensional data arriving on a real-time basis…
Convex regression (CR) problem deals with fitting a convex function to a finite number of observations. It has many applications in various disciplines, such as statistics, economics, operations research, and electrical engineering.…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
Machine Learning algorithms are extensively used in an increasing number of systems, applications, technologies, and products, both in industry and in society as a whole. They enable computing devices to learn from previous experience and…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
Logistic regression is a widely used statistical model to describe the relationship between a binary response variable and predictor variables in data sets. It is often used in machine learning to identify important predictor variables.…