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This paper introduces the Univariate Gaussian Mixture Model Neural Network (uGMM-NN), a novel neural architecture that embeds probabilistic reasoning directly into the computational units of deep networks. Unlike traditional neurons, which…
We propose an Gaussian Mixture Model (GMM) learning algorithm, based on our previous work of GMM expansion idea. The new algorithm brings more robustness and simplicity than classic Expectation Maximization (EM) algorithm. It also improves…
The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It…
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…
Multi-model ensemble analysis integrates information from multiple climate models into a unified projection. However, existing integration approaches based on model averaging can dilute fine-scale spatial information and incur bias from…
Single-channel deep speech enhancement approaches often estimate a single multiplicative mask to extract clean speech without a measure of its accuracy. Instead, in this work, we propose to quantify the uncertainty associated with clean…
Probability theory has become the predominant framework for quantifying uncertainty across scientific and engineering disciplines, with a particular focus on measurement and control systems. However, the widespread reliance on simple…
Probabilistic time series forecasting is crucial for quantifying future uncertainty, with significant applications in fields such as energy and finance. However, existing methods often rely on computationally expensive sampling or…
We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of $\mathbb{P}(\mathbf{y}|\mathbf{X}=x)$ in regression…
In domains with interdependent data, such as graphs, quantifying the epistemic uncertainty of a Graph Neural Network (GNN) is challenging as uncertainty can arise at different structural scales. Existing techniques neglect this issue or…
We consider maximum likelihood estimation for Gaussian Mixture Models (Gmms). This task is almost invariably solved (in theory and practice) via the Expectation Maximization (EM) algorithm. EM owes its success to various factors, of which…
This work focuses on optimizing the hybrid quantum noise model to improve the capacity of Gaussian quantum channels using Machine Learning (ML) generated clusters. The work specifically leverages Gaussian Mixture Model (GMM) and the…
Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing (local) maximum likelihood estimate (MLE). It can be used in an extensive range of problems, including the clustering of data based on the Gaussian…
We derive an asymptotic expansion for the log likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for…
Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…
The Expectation-Maximization (EM) algorithm is one of the most popular methods used to solve the problem of parametric distribution-based clustering in unsupervised learning. In this paper, we propose to analyze a generalized EM (GEM)…
In this work, we investigate Gaussian Mixture Models ({\it abbrv} GMM) and the related problem of non parametric maximum likelihood estimation ({\it abbrv} NPMLE) from the perspective of statistical mechanics. In particular, we establish…
Gaussian mixture models (GMMs) are ubiquitous in statistical learning, particularly for unsupervised problems. While full GMMs suffer from the overparameterization of their covariance matrices in high-dimensional spaces, spherical GMMs…
Contextual optimization enhances decision quality by leveraging side information to improve predictions of uncertain parameters. However, existing approaches face significant challenges when dealing with multimodal or mixtures of…
Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…