Related papers: Generalized Minimum Error Entropy for Adaptive Fil…
Entropy is ubiquitous in machine learning, but it is in general intractable to compute the entropy of the distribution of an arbitrary continuous random variable. In this paper, we propose the amortized residual denoising autoencoder…
The Gaussian kernel is one of the most important kernels, applicable to many research fields, including scientific computing and data science. In this paper, we present asymptotic analysis of the Gaussian kernel matrix in high dimension…
We consider estimation of a deterministic unknown parameter vector in a linear model with non-Gaussian noise. In the Gaussian case, dimensionality reduction via a linear matched filter provides a simple low dimensional sufficient statistic…
Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…
An $\varepsilon$-coreset for a given set $D$ of $n$ points, is usually a small weighted set, such that querying the coreset \emph{provably} yields a $(1+\varepsilon)$-factor approximation to the original (full) dataset, for a given family…
Gaussian mixtures are widely used for approximating density functions in various applications such as density estimation, belief propagation, and Bayesian filtering. These applications often utilize Gaussian mixtures as initial…
This paper determines to within a single measurement the minimum number of measurements required to successfully reconstruct a signal drawn from a Gaussian mixture model in the low-noise regime. The method is to develop upper and lower…
Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the…
This work introduces a novel probabilistic deep learning technique called deep Gaussian mixture ensembles (DGMEs), which enables accurate quantification of both epistemic and aleatoric uncertainty. By assuming the data generating process…
We present simple, user-friendly bounds for the expected operator norm of a random kernel matrix under general conditions on the kernel function $k(\cdot,\cdot)$. Our approach uses decoupling results for U-statistics and the non-commutative…
Fitting a theoretical model to experimental data in a Bayesian manner using Markov chain Monte Carlo typically requires one to evaluate the model thousands (or millions) of times. When the model is a slow-to-compute physics simulation,…
Non-Gaussian noise and the uncertainty of noise distribution are the common factors that reduce accuracy in dynamic state estimation of power systems (PS). In addition, the optimal value of the free coefficients in the unscented Kalman…
Generalized estimating equations (GEE) are widely used to analyze longitudinal data; however, they are not appropriate for heteroscedastic data, because they only estimate regressor effects on the mean response{\textemdash}and therefore do…
We present a Gaussian kernel loss function and training algorithm for convolutional neural networks that can be directly applied to both distance metric learning and image classification problems. Our method treats all training features…
Recent progress in quantum computing is paving the way for the realization of early fault-tolerant quantum computers. To maximize the utility of these devices, it is important to develop quantum algorithms that match their capabilities and…
Expectation Maximization (EM) is the standard method to learn Gaussian mixtures. Yet its classic, centralized form is often infeasible, due to privacy concerns and computational and communication bottlenecks. Prior work dealt with data…
Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data…
The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…
Sparse adaptive channel estimation problem is one of the most important topics in broadband wireless communications systems due to its simplicity and robustness. So far many sparsity-aware channel estimation algorithms have been developed…
Generalization error predictors (GEPs) aim to predict model performance on unseen distributions by deriving dataset-level error estimates from sample-level scores. However, GEPs often utilize disparate mechanisms (e.g., regressors,…