arXiv subjects

Roy Lederman

Publications and source records attributed to Roy Lederman.

3 recordsLinked to original sources

arXiv2026

On the discretization of the object space in inverse problems with application to cryo-electron microscopy

In many inverse problems, the aim is to recover a probability distribution on a latent (or object state) space from indirect, noisy observations. When the observations can be modelled as noisy samples from the mixing latent distribution, the recovery problem is a deconvolution problem on the space of probability measures. A common strategy is to fix a finite set of candidate points and estimate a weight for each, turning the problem into a finite-dimensional concave maximum likelihood problem on the simplex. We study the combined effect of this discretization and of the noise in the context of cryo-electron microscopy (cryo-EM), where the candidate points are biomolecular conformations and the weights describe the relative frequency of each conformation. Our results pertain to both statistical and algorithmic aspects of the estimator. We analyze the weight-recovery problem in which the candidate states and their likelihoods are known. A nearby pair of candidates forces a near-null direction. More generally, the grid and the noise level impose a uniform lower bound on the achievable Kullback--Leibler divergence between observation densities, even with infinite data. The finite-grid estimator is asymptotically normal when its population target is in the interior of the simplex; at a boundary target, its limit is a cone-projected Gaussian. Finally, the exact proximal form of Expectation--Maximization leads to a global high-noise comparison between an early iterate and a KL-penalized likelihood, without a basin assumption or a linearization of the recursion. Tests on synthetic images of the Hsp90 molecule illustrate the theoretical findings and translate them into practical guidelines for interpreting reweighted ensembles.

stat.ME↗

arXiv2022

Integrating molecular models into CryoEM heterogeneity analysis using scalable high-resolution deep Gaussian mixture models

Resolving the structural variability of proteins is often key to understanding the structure-function relationship of those macromolecular machines. Single particle analysis using Cryogenic electron microscopy (CryoEM), combined with machine learning algorithms, provides a way to reveal the dynamics within the protein system from noisy micrographs. Here, we introduce an improved computational method that uses Gaussian mixture models for protein structure representation and deep neural networks for conformation space embedding. By integrating information from molecular models into the heterogeneity analysis, we can resolve complex protein conformational changes at near atomic resolution and present the results in a more interpretable form.

q-bio.QM↗

arXiv2015

Common Variable Learning and Invariant Representation Learning using Siamese Neural Networks

We consider the statistical problem of learning common source of variability in data which are synchronously captured by multiple sensors, and demonstrate that Siamese neural networks can be naturally applied to this problem. This approach is useful in particular in exploratory, data-driven applications, where neither a model nor label information is available. In recent years, many researchers have successfully applied Siamese neural networks to obtain an embedding of data which corresponds to a "semantic similarity". We present an interpretation of this "semantic similarity" as learning of equivalence classes. We discuss properties of the embedding obtained by Siamese networks and provide empirical results that demonstrate the ability of Siamese networks to learn common variability.

stat.ML↗