Related papers: An improved quantum algorithm for ridge regression
Deep neural networks excel in high-dimensional problems, outperforming models such as kernel methods, which suffer from the curse of dimensionality. However, the theoretical foundations of this success remain poorly understood. We follow…
The Kernel Polynomial Method (KPM) is one of the fast diagonalization methods used for simulations of quantum systems in research fields of condensed matter physics and chemistry. The algorithm has a difficulty to be parallelized on a…
Kernel method has been developed as one of the standard approaches for nonlinear learning, which however, does not scale to large data set due to its quadratic complexity in the number of samples. A number of kernel approximation methods…
Reinforcement learning (RL) provides a principled framework for decision-making in partially observable environments, which can be modeled as Markov decision processes and compactly represented through dynamic decision Bayesian networks.…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
While quantum reinforcement learning (RL) has attracted a surge of attention recently, its theoretical understanding is limited. In particular, it remains elusive how to design provably efficient quantum RL algorithms that can address the…
This paper presents a regularized recursive identification algorithm with simultaneous on-line estimation of both the model parameters and the algorithms hyperparameters. A new kernel is proposed to facilitate the algorithm development. The…
We present memory-efficient and scalable algorithms for kernel methods used in machine learning. Using hierarchical matrix approximations for the kernel matrix the memory requirements, the number of floating point operations, and the…
Leverage score sampling is crucial to the design of randomized algorithms for large-scale matrix problems, while the computation of leverage scores is a bottleneck of many applications. In this paper, we propose a quantum algorithm to…
The generalization performance of kernel ridge regression (KRR) exhibits a multi-phased pattern that crucially depends on the scaling relationship between the sample size $n$ and the underlying dimension $d$. This phenomenon is due to the…
In this paper we combine the k-means and/or k-means type algorithms with a hill climbing algorithm in stages to solve the joint stratification and sample allocation problem. This is a combinatorial optimisation problem in which we search…
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…
Random feature mapping (RFM) is a popular method for speeding up kernel methods at the cost of losing a little accuracy. We study kernel ridge regression with random feature mapping (RFM-KRR) and establish novel out-of-sample error upper…
High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…
The application of quantum computation to accelerate machine learning algorithms is one of the most promising areas of research in quantum algorithms. In this paper, we explore the power of quantum learning algorithms in solving an…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…
In this paper, we present the Parallel Quantum Rapidly-Exploring Random Tree (Pq-RRT) algorithm, a parallel version of the Quantum Rapidly-Exploring Random Trees (q-RRT) algorithm. Parallel Quantum RRT is a parallel quantum algorithm…
Ridge leverage scores provide a balance between low-rank approximation and regularization, and are ubiquitous in randomized linear algebra and machine learning. Deterministic algorithms are also of interest in the moderately big data…
This paper introduces algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. We adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert…