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Maximum likelihood estimation is an important statistical technique for estimating missing data, for example in climate and environmental applications, which are usually large and feature data points that are irregularly spaced. In…

Numerical Analysis · Computer Science 2019-07-25 Sameh Abdulah , Hatem Ltaief , Ying Sun , Marc G. Genton , David E. Keyes

In this paper, we provide a multiscale perspective on the problem of maximum marginal likelihood estimation. We consider and analyse a diffusion-based maximum marginal likelihood estimation scheme using ideas from multiscale dynamics. Our…

Computation · Statistics 2024-06-11 O. Deniz Akyildiz , Michela Ottobre , Iain Souttar

We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The…

Machine Learning · Computer Science 2024-05-09 Dwight Nwaigwe , Marek Rychlik

Maximum likelihood estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution that best explain the observed data. In the context of text generation, MLE is often used to train generative language…

Computation and Language · Computer Science 2023-10-27 Chenze Shao , Zhengrui Ma , Min Zhang , Yang Feng

We introduce a new smooth estimator of the ROC curve based on log-concave density estimates of the constituent distributions. We show that our estimate is asymptotically equivalent to the empirical ROC curve if the underlying densities are…

Methodology · Statistics 2023-04-17 Kaspar Rufibach

Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we…

Quantum Physics · Physics 2017-06-28 Jiangwei Shang , Zhengyun Zhang , Hui Khoon Ng

The log-density method is a powerful algorithmic framework which in recent years has given rise to the best-known approximations for a variety of problems, including Densest-$k$-Subgraph and Bipartite Small Set Vertex Expansion. These…

Data Structures and Algorithms · Computer Science 2018-04-24 Eden Chlamtáč , Pasin Manurangsi

We provide full theoretical guarantees for the convergence behaviour of diffusion-based generative models under the assumption of strongly log-concave data distributions while our approximating class of functions used for score estimation…

Machine Learning · Computer Science 2025-02-18 Stefano Bruno , Ying Zhang , Dong-Young Lim , Ömer Deniz Akyildiz , Sotirios Sabanis

Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. While efficient algorithms are known for log-concave densities, the worst-case…

Machine Learning · Statistics 2026-04-24 David Holzmüller , Francis Bach

We propose an algorithm to sample from composite log-concave distributions over $\mathbb{R}^d$, i.e., densities of the form $\pi\propto e^{-f-g}$, assuming access to gradient evaluations of $f$ and a restricted Gaussian oracle (RGO) for…

Statistics Theory · Mathematics 2026-05-13 Linghai Liu , Sinho Chewi

This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We…

Statistics Theory · Mathematics 2012-05-31 Jushan Bai , Kunpeng Li

Many statistical models in cosmology can be simulated forwards but have intractable likelihood functions. Likelihood-free inference methods allow us to perform Bayesian inference from these models using only forward simulations, free from…

Cosmology and Nongalactic Astrophysics · Physics 2018-04-11 Justin Alsing , Benjamin Wandelt , Stephen Feeney

We consider a finite mixture of regressions (FMR) model for high-dimensional inhomogeneous data where the number of covariates may be much larger than sample size. We propose an l1-penalized maximum likelihood estimator in an appropriate…

Methodology · Statistics 2012-02-28 Nicolas Städler , Peter Bühlmann , Sara van de Geer

Pseudo log-likelihood is a type of maximum likelihood estimation (MLE) method used in various fields including contextual bandits, influence maximization of social networks, and causal bandits. However, in previous literature…

Machine Learning · Computer Science 2024-03-28 Shi Feng , Nuoya Xiong , Zhijie Zhang , Wei Chen

Algorithms for jointly obtaining projection estimates of the density and distribution function of a random variable using Legendre polynomials are proposed. For these algorithms, a problem of the conditional optimization is solved. Such…

Computation · Statistics 2025-07-29 Tatyana A. Averina , Konstantin A. Rybakov

If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…

Statistics Theory · Mathematics 2012-07-06 Charles J. Geyer

We study the maximum likelihood estimator of density of $n$ independent observations, under the assumption that it is well approximated by a mixture with a large number of components. The main focus is on statistical properties with respect…

Statistics Theory · Mathematics 2017-01-19 Arnak S. Dalalyan , Mehdi Sebbar

In exploratory factor analysis, model parameters are usually estimated by maximum likelihood method. The maximum likelihood estimate is obtained by solving a complicated multivariate algebraic equation. Since the solution to the equation is…

Statistics Theory · Mathematics 2026-01-14 Ryoya Fukasaku , Kei Hirose , Yutaro Kabata , Keisuke Teramoto

We introduce an optimization model for maximum likelihood-type estimation (M-estimation) that generalizes a large class of existing statistical models, including Huber's concomitant M-estimator, Owen's Huber/Berhu concomitant estimator, the…

Statistics Theory · Mathematics 2018-10-09 Patrick L. Combettes , Christian L. Müller

We investigate the optimization landscape of maximum likelihood estimation (MLE) for the Cavender-Farris-Neyman (CFN) model, a two-state latent tree model fundamental to statistical phylogenetics and the ferromagnetic Ising model. Although…

Statistics Theory · Mathematics 2026-05-22 David Clancy , Hanbaek Lyu , Sebastien Roch