Related papers: Quantum Time Series Similarity Measures and Quantu…

Finding the failure scenarios of a system is a very complex problem in the field of Probabilistic Safety Assessment (PSA). In order to solve this problem we will use the Hidden Quantum Markov Models (HQMMs) to create a generative model.…

We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…

We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample…

Traditional hidden Markov models have been a useful tool to understand and model stochastic dynamic data; in the case of non-Gaussian data, models such as mixture of Gaussian hidden Markov models can be used. However, these suffer from the…

Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…

Motivated by applications to the study of stochastic processes, we introduce a new analysis of positive definite kernels $K$, their reproducing kernel Hilbert spaces (RKHS), and an associated family of feature spaces that may be chosen in…

Kernel approximation is widely used to scale up kernel SVM training and prediction. However, the memory and computation costs of kernel approximation models are still too high if we want to deploy them on memory-limited devices such as…

A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…

Kernel method in machine learning consists of encoding input data into a vector in a Hilbert space called the feature space and modeling the target function as a linear map on the feature space. Given a cost function, computing such an…

Kernel methods map data into high-dimensional spaces, enabling linear algorithms to learn nonlinear functions without explicitly storing the feature vectors. Quantum kernel methods promise efficient learning by encoding feature maps into…

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

Quantum computing leverages quantum effects to build algorithms that are faster then their classical variants. In machine learning, for a given model architecture, the speed of training the model is typically determined by the size of the…

At large scales, quantum systems may become advantageous over their classical counterparts at performing certain tasks. Developing tools to analyse these systems at the relevant scales, in a manner consistent with quantum mechanics, is…

Quantum machine learning is considered one of the current research fields with immense potential. In recent years, Havl\'i\v{c}ek et al. [Nature 567, 209-212 (2019)] have proposed a quantum machine learning algorithm with quantum-enhanced…

Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…

Statistical machine learning plays an important role in modern statistics and computer science. One main goal of statistical machine learning is to provide universally consistent algorithms, i.e., the estimator converges in probability or…

Computing the similarity between two DNA sequences is of vital importance in bioscience, yet it can be computationally expensive on classical hardware. For example, the edit distance with move operations (EDM), a DNA similarity measure of…

Quantum and classical machine learning have been naturally connected through kernel methods, which have also served as proof-of-concept for quantum advantage. Quantum embeddings encode classical data into quantum feature states, enabling…

Quantum machine learning is a growing research field that aims to perform machine learning tasks assisted by a quantum computer. Kernel-based quantum machine learning models are paradigmatic examples where the kernel involves quantum…

Quantum computers have the opportunity to be transformative for a variety of computational tasks. Recently, there have been proposals to use the unsimulatably of large quantum devices to perform regression, classification, and other machine…