Related papers: The Maximum Likelihood Data Singular Locus
We describe a four-level hierarchy mapping both all discrete estimation problems and all estimators on these problems, such that the hierarchy describes each estimator's consistency guarantees on each problem class. We show that no…
The MDL two-part coding $ \textit{index of resolvability} $ provides a finite-sample upper bound on the statistical risk of penalized likelihood estimators over countable models. However, the bound does not apply to unpenalized maximum…
The purpose of this note is to show that the regular locus of a complex variety is locally parabolic at the singular set. This yields that the regular locus of a compact complex variety, e.g., of a projective variety, is parabolic. We give…
Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of…
We give a numerical algorithm computing Euler obstruction functions using maximum likelihood degrees. The maximum likelihood degree is a well-studied property of a variety in algebraic statistics and computational algebraic geometry. In…
Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual…
Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…
Although the foundations of ranking are well established, the ranking literature has primarily been focused on simple, unimodal models, e.g. the Mallows and Plackett-Luce models, that define distributions centered around a single total…
We propose a classification of all one-dimensional discrete statistical models with maximum likelihood degree one based on their rational parametrization. We show how all such models can be constructed from members of a smaller class of…
This paper presents some results on the maximum likelihood (ML) estimation from incomplete data. Finite sample properties of conditional observed information matrices are established. They possess positive definiteness and the same Loewner…
Training the parameters of statistical models to describe a given data set is a central task in the field of data mining and machine learning. A very popular and powerful way of parameter estimation is the method of maximum likelihood…
Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i \in [0, 1]$ drawn from some unknown distribution $P^\star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i \sim…
Maximum likelihood estimates (MLEs) are asymptotically normally distributed, and this property is used in meta-analyses to test the heterogeneity of estimates, either for a single cluster or for several sub-groups. More recently, MLEs for…
The stationary distribution of allele frequencies under a variety of Wright--Fisher $k$-allele models with selection and parent independent mutation is well studied. However, the statistical properties of maximum likelihood estimates of…
This paper proposes and axiomatizes a new updating rule: Relative Maximum Likelihood (RML) for ambiguous beliefs represented by a set of priors (C). This rule takes the form of applying Bayes' rule to a subset of C. This subset is a linear…
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…
We explore the maximum likelihood degree of a homogeneous polynomial $F$ on a projective variety $X$, $\mathrm{MLD}_F(X)$, which generalizes the concept of Gaussian maximum likelihood degree. We show that $\mathrm{MLD}_F(X)$ is equal to the…
High dimensional data often contain multiple facets, and several clustering patterns can co-exist under different variable subspaces, also known as the views. While multi-view clustering algorithms were proposed, the uncertainty…
Ordinal regression (OR, also called ordinal classification) is classification of ordinal data, in which the underlying target variable is categorical and considered to have a natural ordinal relation for the underlying explanatory variable.…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…