Related papers: Learning deep kernels for exponential family densi…
Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a…
Deep kernel learning aims at designing nonlinear combinations of multiple standard elementary kernels by training deep networks. This scheme has proven to be effective, but intractable when handling large-scale datasets especially when the…
We investigate penalized maximum log-likelihood estimation for exponential family distributions whose natural parameter resides in a reproducing kernel Hilbert space. Key to our approach is a novel technique, doubly dual embedding, that…
This paper investigates efficient deep neural networks (DNNs) to replace dense unstructured weight matrices with structured ones that possess desired properties. The challenge arises because the optimal weight matrix structure in popular…
A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…
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…
We propose a deep learning approach for discovering kernels tailored to identifying clusters over sample data. Our neural network produces sample embeddings that are motivated by--and are at least as expressive as--spectral clustering. Our…
We address the problem of learning of continuous exponential family distributions with unbounded support. While a lot of progress has been made on learning of Gaussian graphical models, we still lack scalable algorithms for reconstructing…
Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…
Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…
Deep learning's successes are often attributed to its ability to automatically discover new representations of the data, rather than relying on handcrafted features like other learning methods. We show, however, that deep networks learned…
Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of…
Kernel survival analysis models estimate individual survival distributions with the help of a kernel function, which measures the similarity between any two data points. Such a kernel function can be learned using deep kernel survival…
In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…
We study the expressive power of kernel methods and the algorithmic feasibility of multiple kernel learning for a special rich class of kernels. Specifically, we define \emph{Euclidean kernels}, a diverse class that includes most, if not…
We describe \textit{deep exponential families} (DEFs), a class of latent variable models that are inspired by the hidden structures used in deep neural networks. DEFs capture a hierarchy of dependencies between latent variables, and are…
In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…
Fisher's linear discriminant analysis is a classical method for classification, yet it is limited to capturing linear features only. Kernel discriminant analysis as an extension is known to successfully alleviate the limitation through a…