Related papers: Fast and Extensible Online Multivariate Kernel Den…
We introduce Kernel Density Discrimination GAN (KDD GAN), a novel method for generative adversarial learning. KDD GAN formulates the training as a likelihood ratio optimization problem where the data distributions are written explicitly via…
The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…
In this abstract paper, we introduce a new kernel learning method by a nonparametric density estimator. The estimator consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected…
Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…
This work presents a fast and scalable algorithm for incremental learning of Gaussian mixture models. By performing rank-one updates on its precision matrices and determinants, its asymptotic time complexity is of \BigO{NKD^2} for $N$ data…
Sequential quantile estimation refers to incorporating observations into quantile estimates in an incremental fashion thus furnishing an online estimate of one or more quantiles at any given point in time. Sequential quantile estimation is…
Sparse-dense linear algebra is crucial in many domains, but challenging to handle efficiently on CPUs, GPUs, and accelerators alike; multiplications with sparse formats like CSR and CSF require indirect memory lookups. In this work, we…
Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their…
An incremental/online state dynamic learning method is proposed for identification of the nonlinear Gaussian state space models. The method embeds the stochastic variational sparse Gaussian process as the probabilistic state dynamic model…
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an…
Detecting abrupt changes in real-time data streams from scientific simulations presents a challenging task, demanding the deployment of accurate and efficient algorithms. Identifying change points in live data stream involves continuous…
Predictive hotspot mapping plays a critical role in hotspot policing. Existing methods such as the popular kernel density estimation (KDE) do not consider the temporal dimension of crime. Building upon recent works in related fields, this…
This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact…
Recent contributions to kernel smoothing show that the performance of cross-validated bandwidth selectors improve significantly from indirectness. Indirect crossvalidation first estimates the classical cross-validated bandwidth from a more…
On-line estimation plays an important role in process control and monitoring. Obtaining a theoretical solution to the simultaneous state-parameter estimation problem for non-linear stochastic systems involves solving complex…
Gaussian Processes (GPs), as a nonparametric learning method, offer flexible modeling capabilities and calibrated uncertainty quantification for function approximations. Additionally, GPs support online learning by efficiently incorporating…
A number of problems in probability and statistics can be addressed using the multivariate normal (Gaussian) distribution. In the one-dimensional case, computing the probability for a given mean and variance simply requires the evaluation…
Kernel density estimators (KDEs) are ubiquitous tools for nonparametric estimation of probability density functions (PDFs), when data are obtained from unknown data generating processes. The KDEs that are typically available in software…
Deep neural networks are increasingly being used for the analysis of medical images. However, most works neglect the uncertainty in the model's prediction. We propose an uncertainty-aware deep kernel learning model which permits the…
Dot-product attention mechanism plays a crucial role in modern deep architectures (e.g., Transformer) for sequence modeling, however, na\"ive exact computation of this model incurs quadratic time and memory complexities in sequence length,…