Related papers: Relational Marginal Problems: Theory and Estimatio…
The concept of Relative Divergence of one Grading Function from another is extended from totally ordered chains to power sets of finite event spaces. Shannon Entropy concept is extended to normalized grading functions on such power sets.…
The problem of the estimation of relevance to a set of histograms generated by samples of a discrete time process is discussed on the base of the variational principles proposed in the previous paper [1]. Some conditions for dimension…
Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this…
We study a generalization of the multi-marginal optimal transport problem, which has no fixed number of marginals $N$ and is inspired of statistical mechanics. It consists in optimizing a linear combination of the costs for all the possible…
Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first…
We review some not well known results about marginal log-linear models, derive some new ones and show how they might be relevant in mediation analysis within logistic regression. In particular, we elaborate on the relation between…
Maximum-entropy distributions are shown to appear in the probability calculus as approximations of a model by exchangeability or a model by sufficiency, the former model being preferable. The implications of this fact are discussed,…
Marginal-likelihood based model-selection, even though promising, is rarely used in deep learning due to estimation difficulties. Instead, most approaches rely on validation data, which may not be readily available. In this work, we present…
For statistical decision problems with finite parameter space, it is well-known that the upper value (minimax value) agrees with the lower value (maximin value). Only under a generalized notion of prior does such an equivalence carry over…
We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium…
Suppose data are fitted to some parametric model but that the true model happens to be one with an additional parameter. When a parameter is to be estimated one can use likelihood estimation in the wider model or in the narrow model.…
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…
Ranking problems, also known as preference learning problems, define a widely spread class of statistical learning problems with many applications, including fraud detection, document ranking, medicine, credit risk screening, image ranking…
Problem definition: Traditional monopoly pricing assumes sellers have full information about consumer valuations. We consider monopoly pricing under limited information, where a seller only knows the mean, variance and support of the…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
In this paper, we obtain fundamental $\mathcal{L}_{p}$ bounds in sequential prediction and recursive algorithms via an entropic analysis. Both classes of problems are examined by investigating the underlying entropic relationships of the…
The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…
We show continuity of the martingale optimal transport optimisation problem as a functional of its marginals. This is achieved via an estimate on the projection in the nested/causal Wasserstein distance of an arbitrary coupling on to the…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
We study the influence of additional intermediate marginal distributions on the value of the martingale optimal transport problem. From a financial point of view, this corresponds to taking into account call option prices not only, as…