Related papers: The Kernel Density Integral Transformation

Dynamic convolution enhances model capacity by adaptively combining multiple kernels, yet faces critical trade-offs: prior works either (1) incur significant parameter overhead by scaling kernel numbers linearly, (2) compromise inference…

Kernel density estimation (KDE) stands out as a challenging task in machine learning. The problem is defined in the following way: given a kernel function $f(x,y)$ and a set of points $\{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$, we…

The kernel trick in supervised learning signifies transformations of an inner product by a feature map, which then restructures training data in a larger Hilbert space according to an endowed inner product. A quantum feature map corresponds…

Recent work on background subtraction has shown developments on two major fronts. In one, there has been increasing sophistication of probabilistic models, from mixtures of Gaussians at each pixel [7], to kernel density estimates at each…

Kernel principal component analysis (kPCA) is a widely studied method to construct a low-dimensional data representation after a nonlinear transformation. The prevailing method to reconstruct the original input signal from kPCA -- an…

Kernel machines have sustained continuous progress in the field of quantum chemistry. In particular, they have proven to be successful in the low-data regime of force field reconstruction. This is because many equivariances and invariances…

The nonnegative matrix factorization (NMF) is widely used in signal and image processing, including bio-informatics, blind source separation and hyperspectral image analysis in remote sensing. A great challenge arises when dealing with a…

Kernel density estimation on a finite interval poses an outstanding challenge because of the well-recognized bias at the boundaries of the interval. Motivated by an application in cancer research, we consider a boundary constraint linking…

Large pre-trained transformers have revolutionized artificial intelligence across various domains, and fine-tuning remains the dominant approach for adapting these models to downstream tasks due to the cost of training from scratch.…

Deep Learning has demonstrated a significant improvement against traditional machine learning approaches in different domains such as image and speech recognition. Their success on benchmark datasets is transferred to the real-world through…

We introduce kernel thinning, a new procedure for compressing a distribution $\mathbb{P}$ more effectively than i.i.d. sampling or standard thinning. Given a suitable reproducing kernel $\mathbf{k}_{\star}$ and $O(n^2)$ time, kernel…

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern…

In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…

Collaborative analysis of decentralized confidential datasets is important, but direct sharing of original datasets is often restricted by privacy and institutional constraints. Data collaboration (DC) analysis transforms each dataset into…

We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely…

Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…

The primary hyperparameter in kernel regression (KR) is the choice of kernel. In most theoretical studies of KR, one assumes the kernel is fixed before seeing the training data. Under this assumption, it is known that the optimal kernel is…

Diffusion Transformers (DiT) have become the dominant methods in image and video generation yet still suffer substantial computational costs. As an effective approach for DiT acceleration, feature caching methods are designed to cache the…

Both feature selection and hyperparameter tuning are key tasks in machine learning. Hyperparameter tuning is often useful to increase model performance, while feature selection is undertaken to attain sparse models. Sparsity may yield…

In data science, individual observations are often assumed to come independently from an underlying probability space. Kernel matrices formed from large sets of such observations arise frequently, for example during classification tasks. It…