In this paper, we firstly give a brief introduction of expectation maximization (EM) algorithm, and then discuss the initial value sensitivity of expectation maximization algorithm. Subsequently, we give a short proof of EM's convergence. Then, we implement experiments with the expectation maximization algorithm (We im…
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48 results for “Expectation-Maximization Algorithm”
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 injected noise speeds up the average convergence of the EM algorithm to a local…
We propose a modified expectation-maximization algorithm by introducing the concept of quantum annealing, which we call the deterministic quantum annealing expectation-maximization (DQAEM) algorithm. The expectation-maximization (EM) algorithm is an established algorithm to compute maximum likelihood estimates and appl…
Fast convergence of the Expectation Maximization algorithm under a logarithmic Sobolev inequalitystat.ML
New framework improves EM algorithm convergence under log-Sobolev inequality.
problem Improving convergence of the EM algorithm.
method Extending gradient flow techniques to EM algorithm, using free energy representation.
result Exponential convergence of EM algorithm under log-Sobolev inequality.
Clustering algorithms are a cornerstone of machine learning applications. Recently, a quantum algorithm for clustering based on the k-means algorithm has been proposed by Kerenidis, Landman, Luongo and Prakash. Based on their work, we propose a quantum expectation-maximization (EM) algorithm for Gaussian mixture models…
Establishes geometric convergence of iterative optimization algorithms.
problem Analyzes convergence of iterative optimization algorithms under general assumptions.
method General framework for iterative optimization algorithms, proving asymptotic geometric convergence and providing convergence rates.
result Asymptotic geometric convergence of iterative optimization algorithms with exact rate.
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 configurations and fails to find the global optimum. On the other hand, in the field …
We show that a large class of Estimation of Distribution Algorithms, including, but not limited to, Covariance Matrix Adaption, can be written as a Monte Carlo Expectation-Maximization algorithm, and as exact EM in the limit of infinite samples. Because EM sits on a rigorous statistical foundation and has been thorough…
This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum likelihood estimates from corrupted or incomplete data. The convergence speed-up is an e…
Markov Observation Modelsstat.ML
Expands Hidden Markov Model to include Markov chain observations.
problem Handling Markov chain observations in Hidden Markov Models.
method Developed Expectation-Maximization algorithm and Viterbi algorithm analogs.
result Estimates transition probabilities for hidden states and observations.
New method estimates Gaussian copulas with missing data using EM algorithm.
problem Estimating Gaussian copulas with missing data and prior assumptions.
method Rigorous application of the Expectation Maximization (EM) algorithm for marginal distributions and dependence structure.
result Joint distribution learned is closer to the underlying distribution.
EM algorithm speeds up convergence in federated learning with heterogenous data.
problem Understanding convergence rates of federated learning algorithms under data heterogeneity.
method Characterized convergence rate of EM algorithm for FMLR model under various regimes.
result EM algorithm converges to ground truth with SNR ≥ √K in all regimes.
We present a family of expectation-maximization (EM) algorithms for binary and negative-binomial logistic regression, drawing a sharp connection with the variational-Bayes algorithm of Jaakkola and Jordan (2000). Indeed, our results allow a version of this variational-Bayes approach to be re-interpreted as a true EM al…
Differentially Private (Gradient) Expectation Maximization Algorithm with Statistical Guaranteescs.LG
New DP EM algorithm with statistical guarantees for mixture models.
problem Preserving privacy in EM algorithms for mixture models.
method Proposed a DP EM algorithm with statistical guarantees.
result Near optimal estimation error for GMM in DP model.
A new EM algorithm improves inference from large datasets.
problem Efficient inference in latent variable models with large datasets.
method Introduces SPIDER-EM, a novel EM algorithm using SPIDER estimator.
result Finite-time complexity bounds for smooth non-convex likelihood.
Improves EM algorithm for better local optima in mixture models.
problem EM algorithm's sensitivity to initialization and bad local optima.
method Big Learning principle applied to upgrade EM algorithm.
result BigLearn-EM delivers optimal solution with high probability.
DiEM trains diffusion models from noisy data using EM.
problem Training diffusion models requires clean data, which is often unavailable.
method DiEM uses expectation-maximization algorithm to train diffusion models from incomplete and noisy observations.
result DiEM leads to proper diffusion models suitable for downstream tasks.
New algorithm robustly estimates sparse models in high dimensions with corrupted data.
problem Estimating latent variable models with arbitrarily corrupted samples in high dimensional space.
method Trimmed (Gradient) Expectation Maximization with trimming gradients and hard thresholding steps.
result The algorithm converges to near optimal statistical rate geometrically under certain conditions.
Paper shows DMS as an EM algorithm with improved convergence.
problem Improving the convergence of DMS algorithm.
method Shows DMS as a generalized EM algorithm and provides new proofs.
result Demonstrates global convergence and linear convergence of DMS.
The paper uses Gaussian mixture models for Bayesian networks and proposes an optimization algorithm.
problem Modeling nodes in Bayesian networks with complex distributions.
method Gaussian mixture models combined with double iteration algorithm.
result The double iteration algorithm optimizes Gaussian mixture models effectively.
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) algorithm in the context of Gaussian mixture models, where the maximization step in t…
In this paper we develop an Expectation Maximization(EM) algorithm to estimate the parameter of a Yule-Simon distribution. The Yule-Simon distribution exhibits the "rich get richer" effect whereby an 80-20 type of rule tends to dominate. These distributions are ubiquitous in industrial settings. The EM algorithm presen…
We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of transformations. The data is a point cloud in with arbitrary dimension .…
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estima…
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 data clustering and density estimation in statistics, control systems, and machine…
DCEM algorithm reduces bias in machine learning models trained on selective labels.
problem Bias in machine learning models trained on selective labels.
method Disparate Censorship Expectation-Maximization (DCEM) algorithm.
result DCEM improves bias mitigation without sacrificing discriminative performance.
Paper proposes a faster SPIDER-EM variant for large-scale nonconvex optimization.
problem High computational cost of EM algorithm in large-scale learning.
method Extension of SPIDER-EM for nonconvex finite-sum optimization problems.
result Achieves state-of-the-art complexity bounds and linear convergence under certain conditions.
Robust state-space radio interferometric imaging using Stochastic Approximation Expectation Maximization
problem Improving state-space radio interferometric imaging in the presence of heavy-tailed noise
method Stochastic Approximation Expectation Maximization
result Significant improvement in reconstruction fidelity and robustness to radio-frequency interference
Federated learning is viewed as a hierarchical latent variable model for new algorithm development.
problem Training models privately across multiple clients while maintaining privacy and efficiency.
method Viewing federated learning as a hierarchical latent variable model and applying Expectation-Maximization (EM) algorithm.
result Proposes FedSparse, a federated learning algorithm that promotes sparsity and reduces communication and inference costs.
Learning with hidden variables is a central challenge in probabilistic graphical models that has important implications for many real-life problems. The classical approach is using the Expectation Maximization (EM) algorithm. This algorithm, however, can get trapped in local maxima. In this paper we explore a new appro…
ROME improves algorithmic fairness by learning latent group structure robustly.
problem Latent subgroup disparities and distribution shifts in machine learning models.
method ROME uses an Expectation-Maximization algorithm for linear models and a neural Mixture-of-Experts for nonlinear settings.
result ROME significantly improves fairness compared to standard methods while maintaining average performance.
SEMF predicts prediction intervals for ML models using latent variables.
problem Uncertainty quantification in ML models, especially for diverse data distributions.
method Supervised Expectation-Maximization Framework (SEMF) extending EM algorithm for latent variable modeling.
result SEMF produces narrower prediction intervals with desired coverage probability.
NoMoPy models noise as HMM/FHMM in Python.
problem Modeling noise in data.
method Approximate and exact EM algorithms, cross-validation, confidence region estimation.
result Validated on example problems.
Hybridization of Expectation-Maximization and K-Means Algorithms for Better Clustering Performancecs.LG
The present work proposes hybridization of Expectation-Maximization (EM) and K-Means techniques as an attempt to speed-up the clustering process. Though both K-Means and EM techniques look into different areas, K-means can be viewed as an approximate way to obtain maximum likelihood estimates for the means. Along with …
DO-EM framework for quantum models improves generative tasks.
problem Lack of Expectation-Maximization framework for density operators.
method Demonstrated inequality for density operators, derived DO-EM framework.
result DO-EM framework outperforms probabilistic models in generative tasks.
Paper proves EM algorithm convergence for mixtures of discrete and continuous parameters.
problem Nontrivial convergence analysis for EM algorithms with mixed-integer parameters.
method Introduces conditions for EM convergence in mixed-integer optimization.
result Proves convergence of EM-based sparse Bayesian learning algorithm.
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find stationary points of the likelihood objective, and these points may be far from…
This work uses a scalable approach to identify partially observed nonlinear systems.
problem Offline identification of partially observed nonlinear systems.
method Certainty-equivalent expectation-maximization (CEEM) as block coordinate-ascent.
result The CEEM approach can identify high-dimensional systems reliably and efficiently.
The iterative nature of the expectation maximization (EM) algorithm presents a challenge for privacy-preserving estimation, as each iteration increases the amount of noise needed. We propose a practical private EM algorithm that overcomes this challenge using two innovations: (1) a novel moment perturbation formulation…
sEM uses optimal transport to improve EM algorithm for better convergence and avoiding local optima.
problem Improving the EM algorithm for better convergence and avoiding local optima.
method sEM uses entropic optimal transport to compute responsibilities in the expectation step, leading to better global convergence guarantees and avoiding local optima.
result sEM learns cell labels significantly better than other approaches, improving convergence and avoiding local optima.
Stochastic EM with biased MCMC improves inference stability.
problem Intractable E-step in EM algorithm.
method Stochastic approximation with biased MCMC.
result ULA is more stable and sometimes faster than MALA.
New algorithms learn staged trees from incomplete data.
problem Handling missing data in staged tree learning.
method Characterized likelihood and pseudo-likelihoods for missing data, implemented structural expectation-maximization algorithm.
result It is feasible to account for different missingness patterns when learning staged trees.
Decentralized EM Algorithm for Gaussian Mixtures under Data Heterogeneity and Partial Labelingstat.ML
New algorithms improve Gaussian mixture model estimation in DFL with heterogeneous data.
problem Bias in EM algorithm for Gaussian mixtures in DFL with heterogeneous data.
method MNEM and semi-MNEM algorithms integrating historical and partially labeled data.
result MNEM and semi-MNEM achieve asymptotic efficiency and improved convergence.
Probabilistic approach to Boolean matrix factorization can provide solutions robustagainst noise and missing values with linear computational complexity. However,the assumption about latent factors can be problematic in real world applications.This study proposed a new probabilistic algorithm free of assumptions of lat…
Finite mixture models are among the most popular statistical models used in different data science disciplines. Despite their broad applicability, inference under these models typically leads to computationally challenging non-convex problems. While the Expectation-Maximization (EM) algorithm is the most popular approa…
Semi-supervised EM improves convergence rate with labeled samples.
problem Improving convergence rate in EM algorithm with labeled and unlabeled data.
method Analysis of semi-supervised EM algorithm for Gaussian mixture models.
result Labeled samples significantly improve the convergence rate for the EM algorithm.
We propose two neural network based mixture models in this article. The proposed mixture models are explicit in nature. The explicit models have analytical forms with the advantages of computing likelihood and efficiency of generating samples. Computation of likelihood is an important aspect of our models. Expectation-…
Bayesian scores improve structure learning in probabilistic circuits.
problem Improper structure learning in probabilistic circuits based on heuristics.
method Developed Bayesian structure scores for deterministic PCs, using them in a greedy cutset algorithm.
result Effective protection against overfitting and fast, almost hyper-parameter-free structure learner.