arXiv research

Differentiable EM for Gaussian Mixture Models improves model integration.

Develops a high-dimensional differentially-private EM algorithm with near-optimal statistical guarantees.

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…

Paper proposes a faster SPIDER-EM variant for large-scale nonconvex optimization.

A new EM algorithm improves inference from large datasets.

The paper defines and analyzes $abla$-Sobolev spaces and operators on manifolds.

New DP EM algorithm with statistical guarantees for mixture models.

Study EM and GD for clustering with penalties for misspecification and high dimensions.

We solve the local equivalence problem for second order (smooth or analytic) ordinary differential equations. We do so by presenting a {\em complete convergent normal form} for this class of ODEs. The normal form is optimal in the sense that it is defined up to the automorphism group of the model (flat) ODE $y"=0$. For…

We show that, in many situations, a homeomorphism $f$ of a manifold $M$ may be recovered from the (marked) isomorphism class of a finitely generated group of homeomorphisms containing $f$. As an application, we relate the notions of {\em critical regularity} and of {\em differentiable rigidity}, give examples of groups…

EM-GAN uses GANs for fast stress analysis of multi-segment interconnects.

The paper develops a method to learn SDE drift functions from sparse, noisy data.

We introduce a class of hermitian metrics with {\em Lee potential}, that generalize the notion of l.c.K. metrics with potential introduced in \cite{ov} and show that in the classical examples of Calabi and Eckmann of complex structures on $S^{2p+1}\x S^{2q+1}$, the corresponding hermitian metrics are of this type. Thes…

This work proves a strong convergence result for a geometric EM scheme on Riemannian manifolds.

In this paper we continue the study of bi-conformal vector fields started in {\em Class. Quantum Grav.} {\bf 21} 2153-2177. These are vector fields defined on a pseudo-Riemannian manifold by the differential conditions $\lie P_{ab}=φP_{ab}$, $\lieΠ_{ab}=χΠ_{ab}$ where $P_{ab}$, $Π_{ab}$ are orthogonal and complementary…

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a Petrov-Galerkin version of PINNs based on the nonlinear approximation of deep neur…

A neural network method for topic modeling from few documents.

We prove a semi-Riemannian version of the celebrated Morse Index Theorem for geodesics in semi-Riemannian manifolds; we consider the general case of both endpoints variable on two submanifolds. The key role of the theory is played by the notion of the {\em Maslov index} of a semi-Riemannian geodesic, which is a homolog…

New integration method improves BSDE-based PDE solvers.

Convex optimization is a vibrant and successful area due to the existence of a variety of efficient algorithms that leverage the rich structure provided by convexity. Convexity of a smooth set or a function in a Euclidean space is defined by how it interacts with the standard differential structure in this space -- the…

Meta-learning method for accurate classifier from noisy annotators' data.

A systematic study of (smooth, strong) cone structures $\C$ and Lorentz-Finsler metrics $L$ is carried out. As a link between both notions, cone triples $(Ω,T, F)$, where $Ω$ (resp. $T$) is a 1-form (resp. vector field) with $Ω(T)\equiv 1$ and $F$, a Finsler metric on $\ker (Ω)$, are introduced. Explicit descriptions o…

Generalized meshes for non-regular geometries, including fractures.

We derive both {\em local} and {\em global} generalized {\em Bianchi identities} for classical Lagrangian field theories on gauge-natural bundles. We show that globally defined generalized Bianchi identities can be found without the {\em a priori} introduction of a connection. The proof is based on a {\em global} decom…

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 $(n+2)$--forms, where $n$ is the dimens…

In this paper a thorough study of the normal form and the first integrability conditions arising from {\em bi-conformal vector fields} is presented. These new symmetry transformations were introduced in {\em Class. Quantum Grav.}\textbf{21}, 2153-2177 and some of their basic properties were addressed there. Bi-conforma…

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…

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…

Gradient EM converges globally for over-parameterized Gaussian mixtures.

EM algorithm converges in KL divergence for exponential families via mirror descent.

Improves EM algorithm for better local optima in mixture models.

The study characterizes Hermitian manifolds with parallel Bismut-Strominger torsion.

sEM uses optimal transport to improve EM algorithm for better convergence and avoiding local optima.

Paper analyzes EM algorithm's trajectory in 2MLR, revealing cycloid behavior.

A new EM gradient algorithm for mixture models with skewed components.

Paper introduces deterministic EM approximations for non-convex likelihood functions.

New policy minimizes error in finding best arm with privacy constraints.

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…

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 …

This work addresses the {\em singularity formation} of complete non-compact solutions to the conformally flat Yamabe flow whose conformal factors have {\em cylindrical behavior at infinity}. Their singularity profiles happen to be {\em Yamabe solitons}, which are {\em self-similar solutions} to the fast diffusion equat…

Paper addresses online identification and clustering for mixed linear regression models.

EM algorithm achieves optimal sample complexity for learning two-component mixed linear regression.

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 $10^{4-7}$ noisy and randomly orien…

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.

The expectation-maximization (EM) algorithm has been widely used in minimizing the negative log likelihood (also known as cross entropy) of mixture models. However, little is understood about the goodness of the fixed points it converges to. In this paper, we study the regions where one component is missing in two-comp…

This paper compares unstructured and structured EM-based semi-supervised learning methods.

Two-Timescale EM Methods improve EM for nonconvex models.