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Single particle cryo-electron microscopy has become a critical tool in structural biology over the last decade, able to achieve atomic scale resolution in three dimensional models from hundreds of thousands of (noisy) two-dimensional…
We unify Ramsey, twist-untwist, and random quantum sensors using operator algebra and account for the Fisher scaling of various sensor designs. We illustrate how the operator orbits associated with state preparation inform the scaling of…
Recent breakthroughs in high-resolution imaging of biomolecules in solution with cryo-electron microscopy (cryo-EM) have unlocked new doors for the reconstruction of molecular volumes, thereby promising further advances in biology,…
Empirical Risk Minimization (ERM) algorithms are widely used in a variety of estimation and prediction tasks in signal-processing and machine learning applications. Despite their popularity, a theory that explains their statistical…
Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable…
Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these…
The Fisher Information Metric (FIM) and the associated Cram\'er-Rao Bound (CRB) are fundamental tools in statistical signal processing, which inform the efficient design of experiments and algorithms for estimating the underlying…
In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric…
We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or…
The notion of low-noise channels was recently proposed and analyzed in detail in order to describe noise-processes driven by environment [M. Hotta, T. Karasawa and M. Ozawa, Phys. Rev. A72, 052334 (2005)]. An estimation theory of low-noise…
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM…
Single particle electron cryomicroscopy (cryo-EM) allows for structures of proteins and protein complexes to be determined from images of non-crystalline specimens. Cryo-EM data analysis requires electron microscope images of randomly…
The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…
As we enter the era of quantum technologies, quantum estimation theory provides an operationally motivating framework for determining high precision devices in modern technological applications. The aim of any estimation process is to…
Cryo-electron microscopy (EM) single particle reconstruction is an entirely general technique for 3D structure determination of macromolecular complexes. However, because the images are taken at low electron dose, it is extremely hard to…
Quantum metrology promises precision beyond classical limits, yet environmental noise typically degrades the quantum resources required for such enhancement. In this work, we investigate frequency estimation in noisy continuous-variable…
We derive an asymptotic expansion for the log likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for…
Probit models are useful for modeling correlated discrete responses in many disciplines, including consumer choice data in economics and marketing. However, the Gaussian latent variable feature of probit models coupled with identification…
The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…
Fast Incremental Expectation Maximization (FIEM) is a version of the EM framework for large datasets. In this paper, we first recast FIEM and other incremental EM type algorithms in the {\em Stochastic Approximation within EM} framework.…