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…
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48 results for “Stabilized Expectation-Maximization”
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…
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.
Hidden Markov Models analyze mobile health data to identify APNS states.
problem Subjective self-report measures of APNS lead to errors and biases.
method Exploratory hidden Markov factor models and Stabilized Expectation-Maximization algorithm.
result Identified homogeneous APNS states and dynamic transitions.
A new MFG framework for evolving clusters from Gaussian mixtures.
problem Evolutionary clustering of time-dependent Gaussian mixtures.
method Control-theoretic framework based on Mean Field Games (MFG) with coupled HJB and Fokker-Planck systems.
result MFG dynamics recover classical EM algorithm trajectories with mass conservation.
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…
The paper analyzes when credal sets stabilize under iterative updates in machine learning.
problem When do credal sets stabilize under iterative updates in machine learning?
method Fixed-point theorems for credal set updates.
result The paper provides the first analysis of credal set stability.
A new EM framework for goal-conditioned RL improves performance on sparse reward tasks.
problem Handling sparse rewards in goal-conditioned reinforcement learning.
method A graphical model framework with an EM algorithm that includes a learning-in-hindsight E-step and a supervised M-step.
result hEM significantly outperforms model-free baselines on goal-conditioned benchmarks with sparse rewards.
This paper uses dynamical systems to analyze and ensure convergence of the Bayesian EM algorithm.
problem Ensuring convergence of the Bayesian EM algorithm in incomplete-data scenarios.
method Applying Lyapunov stability theory to discrete-time dynamical systems.
result Conditions for convergence and potential for fast convergence of MAP-EM are established.
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…
Paper addresses online identification and clustering for mixed linear regression models.
problem Online identification and clustering of mixed linear regression models.
method Introduces two online identification algorithms based on the EM principle, proving global convergence without i.i.d. data assumptions.
result Global convergence of the proposed algorithms for mixed linear regression models.
We design iterative receiver schemes for a generic wireless communication system by treating channel estimation and information decoding as an inference problem in graphical models. We introduce a recently proposed inference framework that combines belief propagation (BP) and the mean field (MF) approximation and inclu…
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 …
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.
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.
In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This s…
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.
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…
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.
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.
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.
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…
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.
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.
Proposes a novel graph self-training method with EM regularization for semi-supervised node classification.
problem Handles noisy graph structures and feature spaces in semi-supervised node classification.
method Introduces an Expectation-Maximization (EM) regularization scheme for uncertainty-aware pseudo-label generation and model retraining.
result Significantly outperforms strong baselines by up to 2.5% in accuracy.
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.
New method for LLMs to learn reasoning by optimizing latent variables.
problem Teaching LLMs to generate logical justifications for answers.
method Formalized reasoning as latent variable model, derived FEM objective, designed sampling schemes.
result Prompt Posterior Sampling (PPS) outperforms other schemes in learning to reason.
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.
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.
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
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.
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.
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-…
Many real world tasks such as reasoning and physical interaction require identification and manipulation of conceptual entities. A first step towards solving these tasks is the automated discovery of distributed symbol-like representations. In this paper, we explicitly formalize this problem as inference in a spatial m…
Training deep generative models with maximum likelihood remains a challenge. The typical workaround is to use variational inference (VI) and maximize a lower bound to the log marginal likelihood of the data. Variational auto-encoders (VAEs) adopt this approach. They further amortize the cost of inference by using a rec…
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 .…
QEM uses parallel importance weighting for fast approximate Bayesian inference.
problem Bayesian inference challenges in large models with many observations and latent variables.
method Expectation Maximization (EM) with massively parallel importance weighting.
result QEM is faster and more scalable than RWS and VI.
This paper improves SNN training by using multiple sample compartments.
problem Training SNNs with single-sample estimators leads to inaccurate log-likelihood estimates.
method Proposes a GEM-based online learning algorithm that uses multiple independent spiking signals.
result Significant improvements in log-likelihood, accuracy, and calibration with multiple compartments.
New method improves weakly-supervised action localization.
problem Locating action segments in videos with limited labels.
method Explicitly models key instance assignment as hidden variable using EM framework.
result Achieves state-of-the-art performance on THUMOS14 and ActivityNet1.2 benchmarks.
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.
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.
Integrates VAEs into EM for deep clustering and generation.
problem Clustering and generating new samples from complex distributions.
method Combines VAEs and EM, updating model parameters and refining cluster assignments.
result Superior clustering performance on MNIST and FashionMNIST.
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.