Related papers: Density Operator Expectation Maximization
Although the expectation maximisation (EM) algorithm was introduced in 1970, it remains somewhat inaccessible to machine learning practitioners due to its obscure notation, terse proofs and lack of concrete links to modern machine learning…
Operator learning based on neural operators has emerged as a promising paradigm for the data-driven approximation of operators, mapping between infinite-dimensional Banach spaces. Despite significant empirical progress, our theoretical…
Maximum likelihood estimation (MLE) is one of the most important methods in machine learning, and the expectation-maximization (EM) algorithm is often used to obtain maximum likelihood estimates. However, EM heavily depends on initial…
In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here we propose a theory of quantum…
Expectation maximization (EM) is a technique for estimating maximum-likelihood parameters of a latent variable model given observed data by alternating between taking expectations of sufficient statistics, and maximizing the expected log…
The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed…
The performance of ensemble-based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are…
We present a general method for fitting finite mixture models (FMM). Learning in a mixture model consists of finding the most likely cluster assignment for each data-point, as well as finding the parameters of the clusters themselves. In…
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)…
This short study reformulates the statistical Bayesian learning problem using a quantum mechanics framework. Density operators representing ensembles of pure states of sample wave functions are used in place probability densities. We show…
The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…
Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing maximum likelihood estimate when dealing with Gaussian Mixture Model (GMM). When the sample size is smaller than the data dimension, this could lead…
This paper introduces \textbf{Measure Learning}, a paradigm for modeling ambiguity via non-linear expectations. We define Neural Expectation Operators as solutions to Backward Stochastic Differential Equations (BSDEs) whose drivers are…
Processing high-volume, streaming data is increasingly common in modern statistics and machine learning, where batch-mode algorithms are often impractical because they require repeated passes over the full dataset. This has motivated…
We study the optimization landscape of the log-likelihood function and the convergence of the Expectation-Maximization (EM) algorithm in latent Gaussian tree models, i.e. tree-structured Gaussian graphical models whose leaf nodes are…
We study the expectation-maximization (EM) algorithm for general latent-variable models under (i) distributional misspecification and (ii) nonidentifiability induced by a group action. We formulate EM on the quotient parameter space and…
In this paper, we propose a dynamical systems perspective of the Expectation-Maximization (EM) algorithm. More precisely, we can analyze the EM algorithm as a nonlinear state-space dynamical system. The EM algorithm is widely adopted for…
Self-attention mechanism has been widely used for various tasks. It is designed to compute the representation of each position by a weighted sum of the features at all positions. Thus, it can capture long-range relations for computer vision…
In this paper, we will discuss how to generalize nonparametric density estimators to MLE parametric estimators. Basing on the Parzen window theory and using the advantages of probability amplitude of quantum theory, we model a nonlinear…
We present a new statistical learning paradigm for Boltzmann machines based on a new inference principle we have proposed: the latent maximum entropy principle (LME). LME is different both from Jaynes maximum entropy principle and from…