Related papers: A continuation technique for maximum likelihood es…

Dynamical systems are frequently used to model biological systems. When these models are fit to data it is necessary to ascertain the uncertainty in the model fit. Here we present prediction deviation, a new metric of uncertainty that…

A new likelihood based AR approximation is given for ARMA models. The usual algorithms for the computation of the likelihood of an ARMA model require $O(n)$ flops per function evaluation. Using our new approximation, an algorithm is…

This paper uses the invariance principle to solve the incidental parameter problem of [Econometrica 16 (1948) 1--32]. We seek group actions that preserve the structural parameter and yield a maximal invariant in the parameter space with…

A famous characterization theorem due to C.F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean for all samples of all sample sizes if and only if the family is Gaussian. There…

Maximum likelihood estimators (MLE) and control variate estimators (CVE) have been used in conjunction with known information across sketching algorithms and applications in machine learning. We prove that under certain conditions in an…

Data science projects often involve various machine learning (ML) methods that depend on data, code, and models. One of the key activities in these projects is the selection of a model or algorithm that is appropriate for the data analysis…

A fundamental question in the field of molecular computation is what computational tasks a biochemical system can carry out. In this work, we focus on the problem of finding the maximum likelihood estimate (MLE) for log-affine models. We…

Protesting mildly against the notion of an exactly correct parametric model the view is adopted that the logistic regression equation is merely an approximation to the underlying, true function. The behaviour of likelihood based estimators…

Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…

Single Particle Tracking (SPT) can aid in understanding complex spatio-temporal processes. However, quantifying diffusivity and forces from individual live cell trajectories is complicated by inter- & intra-trajectory kinetic heterogeneity,…

Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach…

Humans and animals can learn complex predictive models that allow them to accurately and reliably reason about real-world phenomena, and they can adapt such models extremely quickly in the face of unexpected changes. Deep neural network…

Boltzmann machines (BMs) are a class of binary neural networks for which there have been numerous proposed methods of estimation. Recently, it has been shown that in the fully visible case of the BM, the method of maximum pseudolikelihood…

For biological experiments aiming at calibrating models with unknown parameters, a good experimental design is crucial, especially for those subject to various constraints, such as financial limitations, time consumption and physical…

The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have…

We consider nonlinear mixed effects models including high-dimensional covariates to model individual parameters variability. The objective is to identify relevant covariates among a large set under sparsity assumption and to estimate model…

When fitting the learning data of an individual to algorithm-like learning models, the observations are so dependent and non-stationary that one may wonder what the classical Maximum Likelihood Estimator (MLE) could do, even if it is the…

In this paper we study the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our first approach discretizes this infinite dimensional convex optimization problem by fixing the support…

Recently there has been a great deal of interest surrounding the calibration of quantum sensors using machine learning techniques. In this work, we explore the use of regression to infer a machine-learned point estimate of an unknown…

We study the parameter estimation method for linear regression models with possibly skewed stable distributed errors. Our estimation procedure consists of two stages: first, for the regression coefficients, the Cauchy quasi-maximum…