Related papers: Accelerating Regression Tasks with Quantum Algorit…
In this paper we analyze boosting algorithms in linear regression from a new perspective: that of modern first-order methods in convex optimization. We show that classic boosting algorithms in linear regression, namely the incremental…
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
Multiple linear regression assumes an imperative role in supervised machine learning. In 2009, Harrow et al. [Phys. Rev. Lett. 103, 150502 (2009)] showed that their HHL algorithm can be used to sample the solution of a linear system…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
Convolutional neural network is a crucial tool for machine learning, especially in the field of computer vision. Its unique structure and characteristics provide significant advantages in feature extraction. However, with the exponential…
Reinforcement learning studies how an agent should interact with an environment to maximize its cumulative reward. A standard way to study this question abstractly is to ask how many samples an agent needs from the environment to learn an…
In the past decade, the field of quantum machine learning has drawn significant attention due to the prospect of bringing genuine computational advantages to now widespread algorithmic methods. However, not all domains of machine learning…
Recent works on quantum algorithms for solving semidefinite optimization (SDO) problems have leveraged a quantum-mechanical interpretation of positive semidefinite matrices to develop methods that obtain quantum speedups with respect to the…
Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…
We propose fast and practical quantum-inspired classical algorithms for solving linear systems. Specifically, given sampling and query access to a matrix $A\in\mathbb{R}^{m\times n}$ and a vector $b\in\mathbb{R}^m$, we propose classical…
By analyzing accelerated proximal gradient methods under a local quadratic growth condition, we show that restarting these algorithms at any frequency gives a globally linearly convergent algorithm. This result was previously known only for…
This paper introduces a quantum framework for addressing reinforcement learning (RL) tasks, grounded in the quantum principles and leveraging a fully quantum model of the classical Markov decision process (MDP). By employing quantum…
Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…
Quantum computing algorithms have been shown to produce performant quantum kernels for machine-learning classification problems. Here, we examine the performance of quantum kernels for regression problems of practical interest. For an…
The new model of quantum computation is proposed, for which an effective algorithm of solving any task in NP is described. The work is based and inspired be the Grover's algorithm for solving NP-tasks with quadratic speedup compared to the…
Topological invariants of a dataset, such as the number of holes that survive from one length scale to another (persistent Betti numbers) can be used to analyze and classify data in machine learning applications. We present an improved…
With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between…
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…
Time series prediction is essential for human activities in diverse areas. A common approach to this task is to harness Recurrent Neural Networks (RNNs). However, while their predictions are quite accurate, their learning process is complex…
High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective…