Related papers: Density Operator Expectation Maximization
We derive an expression for a density operator estimated via Bayesian quantum inference in the limit of an infinite number of measurements. This expression is derived under the assumption that the reconstructed system is in a pure state. In…
While many problems in machine learning focus on learning mappings between finite-dimensional spaces, scientific applications require approximating mappings between function spaces, i.e., operators. We study the problem of learning…
The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…
Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…
Mixture density networks are neural networks that produce Gaussian mixtures to represent continuous multimodal conditional densities. Standard training procedures involve maximum likelihood estimation using the negative log-likelihood (NLL)…
Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
The Expectation-Maximization (EM) algorithm is a popular choice for learning latent variable models. Variants of the EM have been initially introduced, using incremental updates to scale to large datasets, and using Monte Carlo (MC)…
We present a noise-injected version of the Expectation-Maximization (EM) algorithm: the Noisy Expectation Maximization (NEM) algorithm. The NEM algorithm uses noise to speed up the convergence of the EM algorithm. The NEM theorem shows that…
The connection between the Maximum Entropy (MaxEnt) formalism and Restricted Boltzmann Machines (RBMs) is natural, as both give rise to a Boltzmann-like distribution with constraints enforced by Lagrange multipliers, which corresponds to…
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…
Quantum machine learning (QML) requires powerful, flexible and efficiently trainable models to be successful in solving challenging problems. We introduce density quantum neural networks, a model family that prepares mixtures of trainable…
Mixture models serve as one fundamental tool with versatile applications. However, their training techniques, like the popular Expectation Maximization (EM) algorithm, are notoriously sensitive to parameter initialization and often suffer…
The expectation-maximization (EM) algorithm is an iterative method for finding maximum likelihood estimates when data are incomplete or are treated as being incomplete. The EM algorithm and its variants are commonly used for parameter…
The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the…
Learning probabilistic models that can estimate the density of a given set of samples, and generate samples from that density, is one of the fundamental challenges in unsupervised machine learning. We introduce a new generative model based…
Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…
We study estimation of large Dynamic Factor models implemented through the Expectation Maximization (EM) algorithm, jointly with the Kalman smoother. We prove that as both the cross-sectional dimension, $n$, and the sample size, $T$,…
The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step…
The performance of deep neural networks, such as Deep Belief Networks formed by Restricted Boltzmann Machines (RBMs), strongly depends on their training, which is the process of adjusting their parameters. This process can be posed as an…