Related papers: The generalized method of moments for multi-refere…
In this note, we consider the performance of the classic method of moments for parameter estimation of symmetric variance-gamma (generalized Laplace) distributions. We do this through both theoretical analysis (multivariate delta method)…
Gaussian mixture models (GMMs) are fundamental tools in statistical and data sciences. We study the moments of multivariate Gaussians and GMMs. The $d$-th moment of an $n$-dimensional random variable is a symmetric $d$-way tensor of size…
The multi-reference alignment (MRA) problem entails estimating an image from multiple noisy and rotated copies of itself. If the noise level is low, one can reconstruct the image by estimating the missing rotations, aligning the images, and…
This paper proposes a simple and efficient estimation procedure for the model with non-ignorable missing data studied by Morikawa and Kim (2016). Their semiparametrically efficient estimator requires explicit nonparametric estimation and so…
We study the dihedral multi-reference alignment problem of estimating the orbit of a signal from multiple noisy observations of the signal, acted on by random elements of the dihedral group. We show that if the group elements are drawn from…
We consider the problem of estimating a signal from noisy circularly-translated versions of itself, called multireference alignment (MRA). One natural approach to MRA could be to estimate the shifts of the observations first, and infer the…
Gaussian mixture models are universal approximators in the sense that any smooth density can be approximated arbitrarily well with a Gaussian mixture model with enough components. Due to their broad expressive power, Gaussian mixture models…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
Longitudinal studies frequently incorporate covariates that evolve over time, creating complex dependence structures between outcomes and predictors. When covariates are time dependent, standard power analysis tools--largely developed for…
From molecular imaging to wireless communications, the ability to align and reconstruct signals from multiple misaligned observations is crucial for system performance. We study the problem of multi-reference alignment (MRA), which arises…
We study estimation and inference using data collected by reinforcement learning (RL) algorithms. These algorithms adaptively experiment by interacting with individual units over multiple stages, updating their strategies based on past…
Generalized empirical likelihood and generalized method of moments are well spread methods of resolution of inverse problems in econometrics. Each method defines a specific semiparametric model for which it is possible to calculate…
Classifying the training data correctly without over-fitting is one of the goals in machine learning. In this paper, we propose a generalization-memorization mechanism, including a generalization-memorization decision and a memory modeling…
Video Moment Retrieval (VMR) aims to localize temporal segments in videos that correspond to a natural language query, but typically assumes only a single matching moment for each query. This assumption does not always hold in real-world…
In the classic measurement error framework, covariates are contaminated by independent additive noise. This paper considers parameter estimation in such a linear errors-in-variables model where the unknown measurement error distribution is…
The growing role of data-driven approaches to scientific discovery has unveiled a large class of models that involve latent transformations with a rigid algebraic constraint. Three-dimensional molecule reconstruction in Cryo-Electron…
We propose a semi-partitioned Generalized Method of Moments (GMM) framework for analyzing longitudinal data with time-dependent covariates, within a marginal modeling paradigm. This approach addresses limitations of both aggregated and…
Inference in models where the parameter is defined by moment inequalities is of interest in many areas of economics. This paper develops a new method for improving the performance of generalized moment selection (GMS) testing procedures in…
Instrumental variable analysis is a powerful tool for estimating causal effects when randomization or full control of confounders is not possible. The application of standard methods such as 2SLS, GMM, and more recent variants are…
Discrete-state stochastic models have become a well-established approach to describe biochemical reaction networks that are influenced by the inherent randomness of cellular events. In the last years severalmethods for accurately…