Related papers: Maximum Likelihood Estimates for Gaussian Mixtures…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
Mixture of experts (MoE) models are widely applied for conditional probability density estimation problems. We demonstrate the richness of the class of MoE models by proving denseness results in Lebesgue spaces, when inputs and outputs…
Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically…
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…
This paper develops several interesting, significant, and interconnected approaches to nonparametric or semi-parametric statistical inferences. The overwhelmingly favoured maximum likelihood estimator (MLE) under parametric model is…
For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as…
This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of…
Linear birth-and-death processes (LBDPs) are foundational stochastic models in population dynamics, evolutionary biology, and hematopoiesis. Estimating parameters from discretely observed data is computationally demanding due to irregular…
When constructing a Bayesian Machine Learning model, we might be faced with multiple different prior distributions and thus are required to properly consider them in a sensible manner in our model. While this situation is reasonably well…
The Gaussian mixture model is a classic technique for clustering and data modeling that is used in numerous applications. With the rise of big data, there is a need for parameter estimation techniques that can handle streaming data and…
We explore the possibility of evaluating flow harmonics by employing the maximum likelihood estimator (MLE). For a given finite multiplicity, the MLE simultaneously furnishes estimations for all the parameters of the underlying distribution…
A recent line of work provides new statistical tools based on game-theory and achieves safe anytime-valid inference without assuming regularity conditions. In particular, the framework of universal inference proposed by Wasserman, Ramdas…
The complexity of a maximum likelihood estimation is measured by its maximum likelihood degree ($ML$ degree). In this paper we study the maximum likelihood problem associated to chemical networks composed by one single chemical reaction…
In this work, we revisit the estimation of the model parameters of a Weibull distribution based on iid observations, using the maximum likelihood estimation (MLE) method which does not yield closed expressions of the estimators. Among other…
We introduce a mixture of generalized hyperbolic distributions as an alternative to the ubiquitous mixture of Gaussian distributions as well as their near relatives of which the mixture of multivariate t and skew-t distributions are…
We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…
We study the nonparametric maximum likelihood estimator (NPMLE) for Gaussian and Poisson mixture models, assuming the support of the true mixing distribution lies in a fixed bounded set. In this setting, we establish exact parametric rates…
This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…
Ranking problems based on pairwise comparisons, such as those arising in online gaming, often involve a large pool of items to order. In these situations, the gap in performance between any two items can be significant, and the smallest and…
Generative models have been successfully used for generating realistic signals. Because the likelihood function is typically intractable in most of these models, the common practice is to use "implicit" models that avoid likelihood…