Related papers: Optimal E-Values for Exponential Families: the Sim…

We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application,…

Expansion was introduced at the end of the 1970s for calculating principal typings for $\lambda$-terms in intersection type systems. Expansion variables (E-variables) were introduced at the end of the 1990s to simplify and help mechanise…

We study the optimal stopping time problem $v(S)={\rm ess}\sup_{\theta \geq S} E[\phi(\theta)|\mathcal {F}_S]$, for any stopping time $S$, where the reward is given by a family $(\phi(\theta),\theta\in\mathcal{T}_0)$ \emph{of non negative…

Exponential family distributions are highly useful in machine learning since their calculation can be performed efficiently through natural parameters. The exponential family has recently been extended to the t-exponential family, which…

We propose a method to infer causal structures containing both discrete and continuous variables. The idea is to select causal hypotheses for which the conditional density of every variable, given its causes, becomes smooth. We define a…

In many families of distributions, maximum likelihood estimation is intractable because the normalization constant for the density which enters into the likelihood function is not easily available. The score matching estimator of…

We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We…

Expansion was invented at the end of the 1970s for calculating principal typings for $\lambda$-terms in type systems with intersection types. Expansion variables (E-variables) were invented at the end of the 1990s to simplify and help…

Generation of deviates from random graph models with non-trivial edge dependence is an increasingly important problem. Here, we introduce a method which allows perfect sampling from random graph models in exponential family form…

We propose a sequential, anytime-valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood…

We consider the matrix completion problem of recovering a structured matrix from noisy and partial measurements. Recent works have proposed tractable estimators with strong statistical guarantees for the case where the underlying matrix is…

Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary…

In many practical situations we would like to estimate the covariance matrix of a set of variables from an insufficient amount of data. More specifically, if we have a set of $N$ independent, identically distributed measurements of an $M$…

Here, in this paper it has been considered a sub family of exponential family. Maximum likelihood estimations (MLE) for the parameter of this family, probability density function, and cumulative density function based on a sample and based…

It is well-known that in some situations it is not easy to compute the likelihood function as the datasets might be large or the model is too complex. In that contexts composite likelihood, derived by multiplying the likelihoods of subjects…

The versatility of exponential families, along with their attendant convexity properties, make them a popular and effective statistical model. A central issue is learning these models in high-dimensions, such as when there is some sparsity…

We study a general factor analysis framework where the $n$-by-$p$ data matrix is assumed to follow a general exponential family distribution entry-wise. While this model framework has been proposed before, we here further relax its…

Many statistical experiments involve comparing multiple population groups. For example, a public opinion poll may ask which of several political candidates commands the most support; a social scientific survey may report the most common of…

We consider the structural change in a class of discrete valued time series that the conditional distribution follows a one-parameter exponential family. We propose a change-point test based on the maximum likelihood estimator of the…

Let $G$ be a connected exponential Lie group and $R$ be the solvable radical of $G$. We describe a condition on $G/R$ under which one can then conclude that $R$ is an exponential Lie group. The condition holds in particular when $G$ is a…