Related papers: Kernel Density Matrices for Probabilistic Deep Lea…
Quantum computing promises to revolutionize machine learning, offering significant efficiency gains in tasks such as clustering and distance estimation. Additionally, it provides enhanced security through fundamental principles like the…
Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…
Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has…
Probabilistic deep learning is deep learning that accounts for uncertainty, both model uncertainty and data uncertainty. It is based on the use of probabilistic models and deep neural networks. We distinguish two approaches to probabilistic…
Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most…
Students in quantum mechanics class are taught that the wave function contains all knowable information about an isolated system. Later in the course, this view seems to be contradicted by the mysterious density matrix, which introduces a…
Density matrix embedding theory (DMET) is a quantum embedding theory for strongly correlated systems. From a computational perspective, one bottleneck in DMET is the optimization of the correlation potential to achieve self-consistency,…
Deep neural networks have established themselves as one of the most promising machine learning techniques. Training such models at large scales is often parallelized, giving rise to the concept of distributed deep learning. Distributed…
This paper introduces a new kernel-based classifier by viewing kernel matrices as generalized graphs and leveraging recent progress in graph embedding techniques. The proposed method facilitates fast and scalable kernel matrix embedding,…
Most supervised machine learning tasks are subject to irreducible prediction errors. Probabilistic predictive models address this limitation by providing probability distributions that represent a belief over plausible targets, rather than…
We introduce the loss kernel, an interpretability method for measuring similarity between data points according to a trained neural network. The kernel is the covariance matrix of per-sample losses computed under a distribution of…
Determining ground state energies of quantum systems by hybrid classical/quantum methods has emerged as a promising candidate application for near-term quantum computational resources. Short of large-scale fault-tolerant quantum computers,…
Empirical data can often be considered as samples from a set of probability distributions. Kernel methods have emerged as a natural approach for learning to classify these distributions. Although numerous kernels between distributions have…
Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to…
This paper presents a strategy for efficient quantum circuit design for density estimation. The strategy is based on a quantum-inspired algorithm for density estimation and a circuit optimisation routine based on memetic algorithms. The…
This paper proposes a probabilistic deep metric learning (PDML) framework for hyperspectral image classification, which aims to predict the category of each pixel for an image captured by hyperspectral sensors. The core problem for…
Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…
Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space…
In this paper, we will discuss how to generalize nonparametric density estimators to MLE parametric estimators. Basing on the Parzen window theory and using the advantages of probability amplitude of quantum theory, we model a nonlinear…
Deep learning models frequently make incorrect predictions with high confidence when presented with test examples that are not well represented in their training dataset. We propose a novel and straightforward approach to estimate…