A fast Modal EM algorithm for Gaussian mixtures.
problem Clustering with Gaussian mixtures.
method Modal EM algorithm for Gaussian mixtures.
result High flexibility in various clustering contexts.
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48 results for “Modal EM algorithm”
Introduces geometric formulation of EM algorithm for robust inference and various applications.
problem Statistical inference with missing data or unobservables.
method Information geometric formulation of EM algorithm and its extensions.
result Outlier-robust inference algorithm and various applications in deep learning.
Optimal Biweight kernel and computationally efficient Epanechnikov kernel for modal linear regression.
problem Finding the best kernel for modal linear regression.
method Refined analysis of asymptotic statistical behavior and IRLS algorithm convergence.
result Biweight kernel minimizes asymptotic mean squared error, Epanechnikov kernel guarantees IRLS convergence.
This paper proposes an EM approach to reduce inference latency in NAR sequence generation.
problem High inference latency in NAR models due to multi-modality in sequence generation.
method A unified EM framework that jointly optimizes AR and NAR models, with iterative refinement.
result The proposed approach achieves competitive performance with existing NAR models and significantly reduces inference latency.
We define and discuss the first sparse coding algorithm based on closed-form EM updates and continuous latent variables. The underlying generative model consists of a standard `spike-and-slab' prior and a Gaussian noise model. Closed-form solutions for E- and M-step equations are derived by generalizing probabilistic P…
A new diffusion model improves cryo-EM structure sampling.
problem Gaussian prior in VAE fails to match approximate posterior in cryo-EM data.
method Train a diffusion model as an expressive, learnable prior in cryoDRGN framework.
result Samples accurately follow the data distribution, not the VAE prior.
SMM improves signal recovery from noisy data.
problem Estimating signals from noisy and scaled observations.
method Spiked mixture model (SMM) with EM algorithm.
result SMM outperforms GMM in signal recovery.
EGMM improves clustering by better handling uncertainty with evidential framework.
problem Clustering uncertainty and complexity in data.
method Proposes EGMM, a new model-based clustering algorithm using belief functions and EM algorithm.
result EGMM generates more informative evidential partitions and outperforms other algorithms.
The K-Mean and EM algorithms are popular in clustering and mixture modeling, due to their simplicity and ease of implementation. However, they have several significant limitations. Both coverage to a local optimum of their respective objective functions (ignoring the uncertainty in the model space), require the apriori…
New method clusters multimodal data with consistency.
problem Multimodal clustering with unaligned data.
method Conjugate mixture models and EM algorithm.
result Consistent multimodal clustering achieved.
The paper analyzes and proposes an algorithm for multi-modal nonlinear embeddings with theoretical performance bounds.
problem Generalizability of multi-modal nonlinear embeddings to unseen data.
method Theoretical analysis and a multi-modal nonlinear representation learning algorithm motivated by performance bounds.
result The proposed algorithm yields promising performance in multi-modal image classification and cross-modal image-text retrieval applications.
Bayesian networks (BN) are used in a big range of applications but they have one issue concerning parameter learning. In real application, training data are always incomplete or some nodes are hidden. To deal with this problem many learning parameter algorithms are suggested foreground EM, Gibbs sampling and RBE algori…
The EM algorithm is one of many important tools in the field of statistics. While often used for imputing missing data, its widespread applications include other common statistical tasks, such as clustering. In clustering, the EM algorithm assumes a parametric distribution for the clusters, whose parameters are estimat…
We study the statistical properties of an estimator derived by applying a gradient ascent method with multiple initializations to a multi-modal likelihood function. We derive the population quantity that is the target of this estimator and study the properties of confidence intervals (CIs) constructed from asymptotic n…
With the emergence of diverse data collection techniques, objects in real applications can be represented as multi-modal features. What's more, objects may have multiple semantic meanings. Multi-modal and Multi-label (MMML) problem becomes a universal phenomenon. The quality of data collected from different channels ar…
Generalising the idea of the classical EM algorithm that is widely used for computing maximum likelihood estimates, we propose an EM-Control (EM-C) algorithm for solving multi-period finite time horizon stochastic control problems. The new algorithm sequentially updates the control policies in each time period using Mo…
An EM Gradient Algorithm for Mixture Models with Components Derived from the Manly Transformationstat.ML
A new EM gradient algorithm for mixture models with skewed components.
problem Fitting mixture models with skewed components derived from the Manly transformation.
method Proposes an alternative EM gradient algorithm using Newton's method for better parameter updates.
result Shows improved convergence and parameter estimation compared to the Nelder-Mead optimization.
This study optimizes multi-modal learning thresholds and algorithms in high dimensions.
problem Optimizing multi-modal learning performance in high-dimensional data.
method Analytical quantification and derivation of AMP algorithm with state evolution analysis.
result Bayes-optimal performance and recovery thresholds derived for multi-modal data.
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.
Proposes a parametric modal regression method using the implicit function theorem.
problem Finding conditional modes for multi-modal conditional distributions.
method Uses the implicit function theorem to develop an objective function for learning a joint function over inputs and targets.
result Empirically demonstrates scalability and effectiveness in learning multi-valued functions and high-dimensional inputs.
MLE and CVE are equivalent under exponential families, leading to faster and more stable EM algorithms.
problem Finding maximum likelihood estimators (MLE) efficiently and stably.
method Proved equivalence between MLE and CVE under exponential families, leading to an EM algorithm.
result EM algorithm achieves the same asymptotic variance as MLE and is faster and more stable.
Appropriately designing the proposal kernel of particle filters is an issue of significant importance, since a bad choice may lead to deterioration of the particle sample and, consequently, waste of computational power. In this paper we introduce a novel algorithm adaptively approximating the so-called optimal proposal…
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.
The speed of convergence of the Expectation Maximization (EM) algorithm for Gaussian mixture model fitting is known to be dependent on the amount of overlap among the mixture components. In this paper, we study the impact of mixing coefficients on the convergence of EM. We show that when the mixture components exhibit …
Paper refutes EM convergence theory and introduces a new EM algorithm.
problem The convergence theory of the EM algorithm is incorrect and affects its performance.
method Proposes a new EM algorithm called the Channel Matching (CM) EM algorithm and provides an initialization map.
result The locally maximal Q can affect the convergent speed but not the global convergence.
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.
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.
EM algorithm converges in KL divergence for exponential families via mirror descent.
problem Lack of understanding of EM's non-asymptotic convergence properties.
method Viewing EM as a mirror descent algorithm, showing convergence rates in KL divergence.
result KL divergence rates for EM in exponential families, invariant to parametrization.
The EM algorithm is a novel numerical method to obtain maximum likelihood estimates and is often used for practical calculations. However, many of maximum likelihood estimation problems are nonconvex, and it is known that the EM algorithm fails to give the optimal estimate by being trapped by local optima. In order to …
This paper develops a federated EM algorithm for unsupervised learning of mixture models.
problem Theoretical foundations of unsupervised federated learning are lacking.
method Introduces a federated gradient EM algorithm (FedGrEM) for unsupervised learning of mixture models.
result Theoretical analysis shows FedGrEM outperforms local single-task learning.
Algorithme EM régulariséstat.ML
Regularized EM algorithm improves clustering performance with small sample sizes.
problem Performance reduction in EM algorithm due to small sample size and poorly conditioned covariance matrices.
method Regularized EM algorithm that uses prior knowledge to ensure positive definiteness of covariance matrices.
result The regularized EM algorithm outperforms standard EM in clustering tasks with small sample sizes.
New algorithm for estimating MLR parameters with non-Gaussian noise.
problem Estimating MLR parameters with non-Gaussian noise.
method Combining ADMM with EM algorithm idea.
result Our method outperforms EM algorithm in non-Gaussian noise case.
Matching datasets of multiple modalities has become an important task in data analysis. Existing methods often rely on the embedding and transformation of each single modality without utilizing any correspondence information, which often results in sub-optimal matching performance. In this paper, we propose a nonlinear…
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.
Regularized EM algorithmstat.ML
Regularized EM algorithm improves GMM clustering in low sample settings.
problem Numerical instability and convergence issues in EM-GMM for low sample support.
method Regularized EM algorithm that maximizes penalized GMM likelihood, ensuring positive definiteness and structured covariance matrices.
result The regularized EM algorithm leads to better performing EM for structured covariance matrix models or low sample settings.
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…
We develop a general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM. Our analysis is divided into two parts: a treatment of these algorithms at the population level (in the limit of infinite data), followed by results that apply to updates based on a …
Paper proposes a new framework for robust multi-modal data fusion under uncertainty.
problem Unexpected modality failures in nonlinear non-Gaussian dynamic processes.
method Dynamic model averaging (DMA) based particle filter (PF) algorithm.
result The proposed solution outperforms state-of-the-art methods in experiments.
On the Minimax Optimality of the EM Algorithm for Learning Two-Component Mixed Linear Regressionstat.ML
EM algorithm achieves optimal sample complexity for learning two-component mixed linear regression.
problem Learning two-component mixed linear regression under varying signal-to-noise ratios.
method Analysis of EM algorithm convergence rates under different SNR regimes.
result EM algorithm achieves minimax optimal sample complexity in all SNR regimes.
EM algorithm converges to global max in latent Gaussian tree models.
problem Optimizing log-likelihood in latent Gaussian tree models.
method Analyzed the optimization landscape and convergence of EM algorithm.
result EM algorithm converges to global maximum in latent Gaussian tree models.
Paper analyzes EM algorithm's trajectory in 2MLR, revealing cycloid behavior.
problem Understanding the convergence and trajectory of EM algorithm in 2MLR.
method Explicit closed-form expressions for EM updates, recurrence relation derivation at population level.
result EM iterations lie on a cycloid trajectory, leading to theoretical estimate of convergence exponent.
We present the particle stochastic approximation EM (PSAEM) algorithm for learning of dynamical systems. The method builds on the EM algorithm, an iterative procedure for maximum likelihood inference in latent variable models. By combining stochastic approximation EM and particle Gibbs with ancestor sampling (PGAS), PS…
MEx: Multi-modal Exercises Dataset is a multi-sensor, multi-modal dataset, implemented to benchmark Human Activity Recognition(HAR) and Multi-modal Fusion algorithms. Collection of this dataset was inspired by the need for recognising and evaluating quality of exercise performance to support patients with Musculoskelet…
COBRA reduces modality gap in cross-modal tasks.
problem Joint embedding spaces fail to sufficiently reduce modality gap in multi-modal tasks.
method COBRA trains image and text modalities in a joint fashion using Contrastive Predictive Coding and Noise Contrastive Estimation.
result COBRA significantly reduces the modality gap and generates robust joint-embedding space.
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…
Proposes an EM algorithm for high-dimensional Markov-switching VAR models.
problem Estimating regime shifts in high-dimensional time series data.
method Approximate EM algorithm for Markov-switching VAR models.
result Established consistency of the proposed EM algorithm in high dimensions.
Strongly polynomial algorithm for approximate Forster transforms and halfspace learning.
problem Computing approximate Forster transforms and halfspace learning.
method Strongly polynomial time algorithm for approximate Forster transforms and halfspace learning.
result First strongly polynomial time algorithm for distribution-free PAC learning of halfspaces.
Framework for reconstructing nonlinear systems from multi-modal time series data.
problem Reconstructing nonlinear dynamical systems from multi-modal time series data.
method Dynamic interpretable recurrent neural networks coupled with generalized linear models for multi-modal data integration.
result Framework efficiently compensates for noisy or missing information in one data channel using other channels.