Related papers: Parameters not empirically identifiable or disting…
We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation…
We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are…
We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…
A common assumption in causal inference from observational data is that there is no hidden confounding. Yet it is, in general, impossible to verify this assumption from a single dataset. Under the assumption of independent causal mechanisms…
One obstacle to ``elevating" correlation to causation is the phenomenon of confounding, i.e., when a correlation between two variables exists because both variables are in fact caused by a third variable. The situation where the confounders…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
Learning the unknown causal parameters of a linear structural causal model is a fundamental task in causal analysis. The task, known as the problem of identification, asks to estimate the parameters of the model from a combination of…
This paper introduces a new framework to study the asymptotical behavior of the empirical distribution function (e.d.f.) of Gaussian vector components, whose correlation matrix $\Gamma^{(m)}$ is dimension-dependent. Hence, by contrast with…
When employing mechanistic models to study biological phenomena, practical parameter identifiability is important for making accurate predictions across wide range of unseen scenarios, as well as for understanding the underlying mechanisms.…
A new analytical framework consisting of two phenomena: single sample and multiple samples, is proposed to deal with the identification problem of Boolean control networks (BCNs) systematically and comprehensively. Under this framework, the…
In the context of cluster analysis and graph partitioning, many external evaluation measures have been proposed in the literature to compare two partitions of the same set. This makes the task of selecting the most appropriate measure for a…
A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…
Multi-category data arise in diverse fields including marketing, chemistry, public policy, genomics, political science, and ecology. We consider the problem of estimating ratios of category-specific means in a fully nonparametric setting,…
An important task in data analysis is the discovery of causal relationships between observed variables. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and the inference of…
Many methods are available for assessing the importance of omitted variables in linear regression. These methods typically make different, non-falsifiable assumptions. Hence the data alone cannot tell us which method is most appropriate.…
What does it mean to say that a quantity is identifiable from the data? Statisticians seem to agree on a definition in the context of parametric statistical models --- roughly, a parameter $\theta$ in a model $\mathcal{P} = \{P_\theta:…
Commonalities and differences in correlation analysis in terms of phase space, conditioning and uncorrelatedness are discussed. The Poisson process is not generally appropriate as reference distribution for normalisation and cumulants, so…
Information-theoretical quantities such as statistical distinguishability typically result from optimisations over all conceivable observables. Physical theories, however, are not generally considered valid for all mathematically allowed…
Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…
The problems of observability and identifiability have been of great interest as previous steps to estimating parameters and initial conditions of dynamical systems to which some known data (observations) are associated. While most works…