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…
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We consider the geometric formulation of the Hamiltonian formalism for field theory in terms of {\em Hamiltonian connections} and {\em multisymplectic forms}. In this framework the covariant Hamilton equations for Mechanics and field theory are defined in terms of multisymplectic --forms, where is the dimens…
Cryo-electron microscopy (cryo-EM) is a powerful technique for determining the structure of proteins and other macromolecular complexes at near-atomic resolution. In single particle cryo-EM, the central problem is to reconstruct the three-dimensional structure of a macromolecule from noisy and randomly orien…
Tensor-EM method learns MoLDS from complex, noisy data.
problem Modeling diverse temporal dynamics in neural data.
method Tensor-based moment method followed by EM updates.
result Tensor-EM achieves more reliable recovery and robustness.
Inference and learning for probabilistic generative networks is often very challenging and typically prevents scalability to as large networks as used for deep discriminative approaches. To obtain efficiently trainable, large-scale and well performing generative networks for semi-supervised learning, we here combine tw…
Model-based clustering approaches concern the paradigm of exploratory data analysis relying on the finite mixture model to automatically find a latent structure governing observed data. They are one of the most popular and successful approaches in cluster analysis. The mixture density estimation is generally performed …
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.
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…
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.
Efficiently clusters incomplete data without imputation or full EM, faster and more accurate.
problem Clustering partially recorded data efficiently.
method Model-based approach using multivariate t-distributions, considering only observed values.
result Approach is more accurate and computationally efficient than alternatives.
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.
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.
Combines PCA and CEM for fast clustering and embedding.
problem Dimensionality and slow EM algorithm convergence for clustering.
method Combines PCA and CEM for simultaneous clustering and data embedding.
result Demonstrates improved clustering and embedding performance.
We consider the problem of inference in a linear regression model in which the relative ordering of the input features and output labels is not known. Such datasets naturally arise from experiments in which the samples are shuffled or permuted during the protocol. In this work, we propose a framework that treats the un…
Regression mixture models are widely studied in statistics, machine learning and data analysis. Fitting regression mixtures is challenging and is usually performed by maximum likelihood by using the expectation-maximization (EM) algorithm. However, it is well-known that the initialization is crucial for EM. If the init…
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 …
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.
Two-Timescale EM Methods improve EM for nonconvex models.
problem Nonconvex latent variable models are challenging for EM.
method Two-stage stochastic updates to handle nonconvex optimization.
result Global convergence for nonconvex objective functions.
We review a resent {\em time-dependent} performance measure for economical time series -- the (optimal) investment horizon approach. For stock indices, the approach shows a pronounced gain-loss asymmetry that is {\em not} observed for the individual stocks that comprise the index. This difference may hint towards an sy…
Sequence-guided protein structure determination using graph convolutional and recurrent networksq-bio.BM
Automated protein structure prediction from cryo-EM data.
problem Challenging to build atomic models from cryo-EM densities without prior structure.
method Uses GCN and LSTM to automate model building from amino acid identities and candidate locations.
result Automated approach reduces time and eliminates human intervention for protein structure determination.
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.
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.
Expectation-Maximization (EM) is a prominent approach for parameter estimation of hidden (aka latent) variable models. Given the full batch of data, EM forms an upper-bound of the negative log-likelihood of the model at each iteration and updates to the minimizer of this upper-bound. We first provide a "model level" in…
This paper compares unstructured and structured EM-based semi-supervised learning methods.
problem Semi-supervised learning with EM algorithm for structured prediction.
method Comparative study between unstructured and structured EM-based semi-supervised learning methods.
result Structured EM is more robust to class confusion in flood mapping datasets.
The performance of EM in learning mixtures of product distributions often depends on the initialization. This can be problematic in crowdsourcing and other applications, e.g. when a small number of 'experts' are diluted by a large number of noisy, unreliable participants. We develop a new EM algorithm that is driven by…
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 …
Proposes EM-HRNN model for better hierarchical language representation.
problem Learning hierarchical representations in natural language processing.
method Introduces latent indicator layer and EM algorithm for training.
result EM-HRNN model outperforms other RNN-based models in document classification.
We study inference and learning based on a sparse coding model with `spike-and-slab' prior. As in standard sparse coding, the model used assumes independent latent sources that linearly combine to generate data points. However, instead of using a standard sparse prior such as a Laplace distribution, we study the applic…
In this paper, we demonstrate a computationally efficient new approach based on deep learning (DL) techniques for analysis, design, and optimization of electromagnetic (EM) nanostructures. We use the strong correlation among features of a generic EM problem to considerably reduce the dimensionality of the problem and t…
EM Distillation simplifies diffusion models to one-step generators.
problem Efficient sampling from complex diffusion models with minimal loss of quality.
method EM Distillation, a maximum likelihood approach based on Expectation-Maximization.
result EM Distillation outperforms existing one-step generative methods in FID scores.
Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transportcs.LG
Differentiable EM for Gaussian Mixture Models improves model integration.
problem Non-differentiability of EM algorithm limits its use in modern learning pipelines.
method Presented and compared several differentiation strategies for EM.
result Differentiable EM enables the use of Mixture Wasserstein distance in machine learning tasks.
A non linear regression approach which consists of a specific regression model incorporating a latent process, allowing various polynomial regression models to be activated preferentially and smoothly, is introduced in this paper. The model parameters are estimated by maximum likelihood performed via a dedicated expeca…
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.
We derive a novel variational expectation maximization approach based on truncated posterior distributions. Truncated distributions are proportional to exact posteriors within subsets of a discrete state space and equal zero otherwise. The treatment of the distributions' subsets as variational parameters distinguishes …
In this paper we continue our systematic analysis of the operatorial approach previously proposed in an economical context and we discuss a {\em mixed} toy model of a simplified stock market, i.e. a model in which the price of the shares is given as an input. We deduce the time evolution of the portfolio of the various…
In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant gauge--natural bundle this density is the divergence of a skew--symmetric (tenso…
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 compares hard and soft EM for BN learning from incomplete data.
problem Learning BNs from incomplete data using EM algorithms.
method Investigates the impact of imputation vs. belief propagation in hard and soft EM.
result A decision tree can guide practitioners in choosing the best EM algorithm.
In this paper we continue our descriptions of stock markets in terms of some non abelian operators which are used to describe the portfolio of the various traders and other {\em observable} quantities. After a first prototype model with only two traders, we discuss a more realistic model of market with an arbitrary num…
Proposes EM for sparse horseshoe estimation.
problem Sparse estimation of sparse parameter vectors using the horseshoe prior.
method Expectation-Maximisation (EM) procedure for MAP estimates.
result Our approach performs comparable or superior to state-of-the-art methods.
In the modal approach to clustering, clusters are defined as the local maxima of the underlying probability density function, where the latter can be estimated either non-parametrically or using finite mixture models. Thus, clusters are closely related to certain regions around the density modes, and every cluster corr…
Mixed linear regression involves the recovery of two (or more) unknown vectors from unlabeled linear measurements; that is, where each sample comes from exactly one of the vectors, but we do not know which one. It is a classic problem, and the natural and empirically most popular approach to its solution has been the E…
Cryo-EM reconstruction is reformulated as a stochastic inverse problem to handle structural heterogeneity.
problem Handling structural heterogeneity in cryo-EM 3D reconstruction.
method Formulated as a stochastic inverse problem over probability measures, using variational discrepancy and Wasserstein gradient flow.
result Validated approach using synthetic examples, demonstrating recovery of continuous structural distributions.
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape, researchers in practice areas such as marketing and social sciences also frequen…
Paper proposes a method to estimate consumer valuations from bundle sales data.
problem Estimating consumer valuations from bundle sales data using classical methods is challenging.
method Proposes an approach using EM algorithm and Monte Carlo simulation to estimate consumer valuations from bundle sales data.
result The approach can recover the distribution of consumers' valuations and is robust to unobserved no-purchases and clustered market segments.
New approach improves AI's handling of incomplete data.
problem Improving AI's ability to work with incomplete data.
method Proposes a new likelihood-free EM algorithm for faster, more efficient inference.
result More statistically efficient than masking approach and faster than conventional EM.
New method clusters incomplete data by fusing subspaces.
problem Learning low-dimensional structures from highly incomplete data.
method Assign each datum to its own subspace, then fuse subspaces of the same cluster.
result Our method performs comparably to state-of-the-art with complete data and better with missing data.
A new approach for signal parametrization, which consists of a specific regression model incorporating a discrete hidden logistic process, is proposed. The model parameters are estimated by the maximum likelihood method performed by a dedicated Expectation Maximization (EM) algorithm. The parameters of the hidden logis…