Related papers: Parsimonious Mahalanobis Kernel for the Classifica…
High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
Differential network is an important tool to capture the changes of conditional correlations under two sample cases. In this paper, we introduce a fast iterative algorithm to recover the differential network for high-dimensional data. The…
While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…
Kernel mean embedding is a useful tool to represent and compare probability measures. Despite its usefulness, kernel mean embedding considers infinite-dimensional features, which are challenging to handle in the context of differentially…
To witness quantum advantages in practical settings, substantial efforts are required not only at the hardware level but also on theoretical research to reduce the computational cost of a given protocol. Quantum computation has the…
Quantum kernel methods are a promising method in quantum machine learning thanks to the guarantees connected to them. Their accessibility for analytic considerations also opens up the possibility of prescreening datasets based on their…
We present several generative and predictive algorithms based on the RKHS (reproducing kernel Hilbert spaces) methodology, which, most importantly, are scale up efficiently with large datasets or high-dimensional data. It is well recognized…
Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…
Most machine learning methods require tuning of hyper-parameters. For kernel ridge regression with the Gaussian kernel, the hyper-parameter is the bandwidth. The bandwidth specifies the length scale of the kernel and has to be carefully…
In recent years, the crucial importance of metrics in machine learning algorithms has led to an increasing interest for optimizing distance and similarity functions. Most of the state of the art focus on learning Mahalanobis distances…
Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size…
There are schemes for realizing different types of kernels by quantum states of light. It is particularly interesting to realize the Gaussian kernel due to its wider applicability. A multimode coherent state can generate the Gaussian kernel…
Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this…
Crucial to many measurements at the LHC is the use of correlated multi-dimensional information to distinguish rare processes from large backgrounds, which is complicated by the poor modeling of many of the crucial backgrounds in Monte Carlo…
We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or…
Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…
The goal of supervised feature selection is to find a subset of input features that are responsible for predicting output values. The least absolute shrinkage and selection operator (Lasso) allows computationally efficient feature selection…
In the classical Gaussian SVM classification we use the feature space projection transforming points to normal distributions with fixed covariance matrices (identity in the standard RBF and the covariance of the whole dataset in Mahalanobis…
Gaussian processes provide a flexible, non-parametric framework for the approximation of functions in high-dimensional spaces. The covariance kernel is the main engine of Gaussian processes, incorporating correlations that underpin the…