Related papers: Marginalization using the metric of the likelihood
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
Beta regression models are a suitable choice for continuous response variables on the unity interval. Random effects add further flexibility to the models and accommodate data structures such as hierarchical, repeated measures and…
Learning an appropriate (dis)similarity function from the available data is a central problem in machine learning, since the success of many machine learning algorithms critically depends on the choice of a similarity function to compare…
The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…
We provide a simple abstract formalism of integration by parts under which we obtain some regularization lemmas. These lemmas apply to any sequence of random variables $(F_n)$ which are smooth and non-degenerated in some sense and enable…
We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by…
Mathematical inequalities, combined with atomic-physics sum rules, enable one to derive lower and upper bounds for the Rosseland and/or Planck mean opacities. The resulting constraints must be satisfied, either for pure elements or…
The polarization tomography problem consists of recovering a matrix function f from the fundamental matrix of the equation $D\eta/dt=\pi_{\dot\gamma}f\eta$ known for every geodesic $\gamma$ of a given Riemannian metric. Here…
Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. The problem is to maximize the likelihood function with respect to given data on a statistical model. An algebraic approach to this problem is to…
A strongly non-integrable system is expected to satisfy the eigenstate thermalization hypothesis, which states that the expectation value of an observable in an energy eigenstate is the same as the thermal value. This must be revised if the…
Machine learning models have exhibited exceptional results in various domains. The most prevalent approach for learning is the empirical risk minimizer (ERM), which adapts the model's weights to reduce the loss on a training set and…
A formal linear vector field representation for scientific equations is developed to rationalize the intuitive methods that are constantly employed. It is shown that unlike mechanical units that appear in the basis of the space, the reduced…
We construct a rigourous model of quantum measurement. A two-state model of a negative temperature amplifier, such as a laser, is taken to a classical thermodynamic limit. In the limit, it becomes a classical measurement apparatus obeying…
We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…
Experimental studies are a cornerstone of Machine Learning (ML) research. A common and often implicit assumption is that the study's results will generalize beyond the study itself, e.g., to new data. That is, repeating the same study under…
Random matrix theory has played an important role in various areas of pure mathematics, mathematical physics, and machine learning. From a practical perspective of data science, input data are usually normalized prior to processing. Thus,…
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a…
A new parameter choice rule for inverse problems is introduced. This parameter choice rule was developed for total variation regularization in electron tomography and might in general be useful for $L^1$ regularization of inverse problems…
Triangular distributions are a well-known class of distributions that are often used as elementary example of a probability model. In the past, enumeration and order statistic-based methods have been suggested for the maximum likelihood…
The paper offers a novel unified approach to studying the accuracy of parameter estimation by the quasi likelihood method. Important features of the approach are: (1) The underlying model {is not assumed to be parametric}. (2) No conditions…