Related papers: Fast and Extensible Online Multivariate Kernel Den…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
Current tools for multivariate density estimation struggle when the density is concentrated near a nonlinear subspace or manifold. Most approaches require choice of a kernel, with the multivariate Gaussian by far the most commonly used.…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
Deep learning, especially convolutional neural networks, has triggered accelerated advancements in computer vision, bringing changes into our daily practice. Furthermore, the standardized deep learning modules (also known as backbone…
A framework of online adaptive statistical compressed sensing is introduced for signals following a mixture model. The scheme first uses non-adaptive measurements, from which an online decoding scheme estimates the model selection. As soon…
Large scale online kernel learning aims to build an efficient and scalable kernel-based predictive model incrementally from a sequence of potentially infinite data points. A current key approach focuses on ways to produce an approximate…
During the last few decades, online controlled experiments (also known as A/B tests) have been adopted as a golden standard for measuring business improvements in industry. In our company, there are more than a billion users participating…
The estimation of probability density functions is a fundamental problem in science and engineering. However, common methods such as kernel density estimation (KDE) have been demonstrated to lack robustness, while more complex methods have…
Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy…
A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically…
The performance of multivariate kernel density estimation (KDE) depends strongly on the choice of bandwidth matrix. The high computational cost required for its estimation provides a big motivation to develop fast and accurate methods. One…
Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…
Streaming data often exhibit heterogeneity due to heteroscedastic variances or inhomogeneous covariate effects. Online renewable quantile and expectile regression methods provide valuable tools for detecting such heteroscedasticity by…
Modelling of multivariate densities is a core component in many signal processing, pattern recognition and machine learning applications. The modelling is often done via Gaussian mixture models (GMMs), which use computationally expensive…
We consider bandwidth matrix selection for kernel density estimators (KDEs) of density level sets in $\mathbb{R}^d$, $d \ge 2$. We also consider estimation of highest density regions, which differs from estimating level sets in that one…
Combining Gaussian processes with the expressive power of deep neural networks is commonly done nowadays through deep kernel learning (DKL). Unfortunately, due to the kernel optimization process, this often results in losing their Bayesian…
Density estimation is a fundamental problem that arises in many areas of astronomy, with applications ranging from selecting quasars using color distributions to characterizing stellar abundances. Astronomical observations are inevitably…
We introduce a new method for high-dimensional, online changepoint detection in settings where a $p$-variate Gaussian data stream may undergo a change in mean. The procedure works by performing likelihood ratio tests against simple…
Deep networks are nowadays becoming popular in many computer vision and pattern recognition tasks. Among these networks, deep kernels are particularly interesting and effective, however, their computational complexity is a major issue…
Contemporary applications, such as recommendation systems and mobile health monitoring, require real-time processing and analysis of sequentially arriving high-dimensional tensor data. Traditional offline learning, involving the storage and…