Related papers: Quantum Algorithms for Prediction Based on Ridge R…
The random feature (RF) approach is a well-established and efficient tool for scalable kernel methods, but existing literature has primarily focused on kernel ridge regression with random features (KRR-RF), which has limitations in handling…
We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the…
Quantum control optimization algorithms are routinely used to generate optimal quantum gates or efficient quantum state transfers. However, there are two main challenges in designing efficient optimization algorithms, namely overcoming the…
Quantum computing has the potential to outperform classical computers and is expected to play an active role in various fields. In quantum machine learning, a quantum computer has been found useful for enhanced feature representation and…
Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as…
We consider $L^2$-regularized linear (ridge) regression over a finite data sample $X$ with bounded covariance and linear prediction targets $y$ with additive isotropic noise of finite variance. We present an iterative procedure to compute…
Solving linear systems is often the computational bottleneck in real-life problems. Iterative solvers are the only option due to the complexity of direct algorithms or because the system matrix is not explicitly known. Here, we develop a…
We propose an $L_{2}$-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template $\gamma$, which is constrained to belong to a class of piecewise…
Quantum Phase Estimation is a crucial component of several front-running quantum algorithms. Improving the efficiency and accuracy of QPE is currently a very active field of research. In this work, we present a hybrid quantum-classical…
Machine learning employs dynamical algorithms that mimic the human capacity to learn, where the reinforcement learning ones are among the most similar to humans in this respect. On the other hand, adaptability is an essential aspect to…
We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that computes the gradient of a multi-variate real-valued function $f:\mathbb{R}^d\rightarrow \mathbb{R}$ by evaluating it…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not…
Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…
In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…
We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge…
In this paper, a quantum algorithm based on gaussian process regression model is proposed. The proposed quantum algorithm consists of three sub-algorithms. One is the first quantum subalgorithm to efficiently generate mean predictor. The…
Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the…