Related papers: Superfast maximum likelihood reconstruction for qu…
Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We…
Recent works have proposed various explanations for the ability of modern large language models (LLMs) to perform in-context prediction. We propose an alternative conceptual viewpoint from an information-geometric and statistical…
Many important geometric estimation problems take the form of synchronization over the special Euclidean group: estimate the values of a set of poses given a set of relative measurements between them. This problem is typically formulated as…
We introduce a simple modification to the standard maximum likelihood estimation (MLE) framework. Rather than maximizing a single unconditional likelihood of the data under the model, we maximize a family of \textit{noise conditional}…
Dynamical properties of image restoration and hyper-parameter estimation are investigated by means of statistical mechanics. We introduce an exactly solvable model for image restoration and derive differential equations with respect to…
The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios,…
In this paper, acceleration of gradient methods for convex optimization problems with weak levels of convexity and smoothness is considered. Starting from the universal fast gradient method which was designed to be an optimal method for…
The Laplace approximation (LA) has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators (MLEs) based on the LA are often…
The maximum-likelihood method for quantum estimation is reviewed and applied to the reconstruction of density matrix of spin and radiation as well as to the determination of several parameters of interest in quantum optics.
We build a general quantum state tomography framework that makes use of machine learning techniques to reconstruct quantum states from a given set of coincidence measurements. For a wide range of pure and mixed input states we demonstrate…
Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of…
Quantum State Tomography is the task of determining an unknown quantum state by making measurements on identical copies of the state. Current algorithms are costly both on the experimental front -- requiring vast numbers of measurements --…
We introduce an approach for performing quantum state reconstruction on systems of $n$ qubits using a machine-learning-based reconstruction system trained exclusively on $m$ qubits, where $m\geq n$. This approach removes the necessity of…
Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known…
Maximum-likelihood estimation (MLE) is arguably the most important tool for statisticians, and many methods have been developed to find the MLE. We present a new inequality involving posterior distributions of a latent variable that holds…
Many geometric estimation problems take the form of synchronization over the special Euclidean group: estimate the values of a set of poses given noisy measurements of a subset of their pairwise relative transforms. This problem is…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
Bayesian inference for hierarchical models can be very challenging. MCMC methods have difficulty scaling to large models with many observations and latent variables. While variational inference (VI) and reweighted wake-sleep (RWS) can be…
Projected least squares (PLS) is an intuitive and numerically cheap technique for quantum state tomography. The method first computes the least-squares estimator (or a linear inversion estimator) and then projects the initial estimate onto…
Partial tomography, which focuses on reconstructing reduced density matrices (RDMs), has emerged as a promising approach for characterizing complex quantum systems, particularly when full state tomography is impractical. Recently,…