Related papers: Kernel Density Estimation through Density Constrai…
Discrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location-scale mixture of Gaussian kernels is the golden standard, both having nice…
We propose a method to efficiently construct data-dependent kernels which can make use of large quantities of (unlabeled) data. Our construction makes an approximation in the standard construction of semi-supervised kernels in Sindhwani et…
We consider the problem of clustering a sample of probability distributions from a random distribution on $\mathbb R^p$. Our proposed partitioning method makes use of a symmetric, positive-definite kernel $k$ and its associated reproducing…
In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the…
When nonlinear measures are estimated from sampled temporal signals with finite-length, a radius parameter must be carefully selected to avoid a poor estimation. These measures are generally derived from the correlation integral which…
We study nonparametric estimation of density functions for undirected dyadic random variables (i.e., random variables defined for all n\overset{def}{\equiv}\tbinom{N}{2} unordered pairs of agents/nodes in a weighted network of order N).…
We present a unified framework for quantum sensitivity sampling, extending the advantages of quantum computing to a broad class of classical approximation problems. Our unified framework provides a streamlined approach for constructing…
Machine-learning models based on a point-cloud representation of a physical object are ubiquitous in scientific applications and particularly well-suited to the atomic-scale description of molecules and materials. Among the many different…
Kernel selection plays a central role in determining the performance of Gaussian Process (GP) models, as the chosen kernel determines both the inductive biases and prior support of functions under the GP prior. This work addresses the…
We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…
DBSCAN is a popular density-based clustering algorithm. It computes the $\epsilon$-neighborhood graph of a dataset and uses the connected components of the high-degree nodes to decide the clusters. However, the full neighborhood graph may…
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…
Kernel based methods including Gaussian process regression (GPR) and generally kernel ridge regression (KRR) have been finding increasing use in computational chemistry, including the fitting of potential energy surfaces and density…
While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel…
Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…
Measuring similarity between two objects is the core operation in existing clustering algorithms in grouping similar objects into clusters. This paper introduces a new similarity measure called point-set kernel which computes the similarity…
The sample complexity of estimating or maximising an unknown function in a reproducing kernel Hilbert space is known to be linked to both the effective dimension and the information gain associated with the kernel. While the information…
Nearest neighbor (NN) problem is an important scientific problem. The NN query, to find the closest one to a given query point among a set of points, is widely used in applications such as density estimation, pattern classification,…
Score-based causal discovery methods can effectively identify causal relationships by evaluating candidate graphs and selecting the one with the highest score. One popular class of scores is kernel-based generalized score functions, which…
Motivated by the problem of fast processing of attention matrices, we study fast algorithms for computing matrix-vector products for asymmetric Gaussian Kernel matrices $K\in \mathbb{R}^{n\times n}$. $K$'s columns are indexed by a set of…