Related papers: Estimation of the control parameter from symbolic …
Directed acyclic graphs (DAGs) are commonly used to model causal relationships among random variables. In general, learning the DAG structure is both computationally and statistically challenging. Moreover, without additional information,…
Classical graphical modeling of multivariate random vectors uses graphs to encode conditional independence. In graphical modeling of multivariate stochastic processes, graphs may encode so-called local independence analogously. If some…
We employ uncertain parametric CTMCs with parametric transition rates and a prior on the parameter values. The prior encodes uncertainty about the actual transition rates, while the parameters allow dependencies between transition rates.…
Graph drawings are commonly used to visualize relational data. User understanding and performance are linked to the quality of such drawings, which is measured by quality metrics. The tacit knowledge in the graph drawing community about…
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
A probabilistic circuit (PC) succinctly expresses a function that represents a multivariate probability distribution and, given sufficient structural properties of the circuit, supports efficient probabilistic inference. Typically a PC…
This paper details how to parameterize the posterior distribution of state-space systems to generate improved optimization problems for system identification using variational inference. Three different parameterizations of the assumed…
Mathematical programming formulations of influence diagrams can bridge the gap between representing and solving decision problems. However, they suffer from both modeling and computational limitations. Aiming to address modeling…
We study raw coding of trajectories of a chaotic dynamical system by sequences of elements from a finite alphabet and show that there is a fundamental constraint on differences between codes corresponding to different trajectories of the…
In this contribution we deal with the problem of learning an undirected graph which encodes the conditional dependence relationship between variables of a complex system, given a set of observations of this system. This is a very central…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
Probabilistic graphical models are widely used to model complex systems under uncertainty. Traditionally, Gaussian directed graphical models are applied for analysis of large networks with continuous variables as they can provide…
We define a characteristic function for probability measures on the signatures of geometric rough paths. We determine sufficient conditions under which a random variable is uniquely determined by its expected signature, thus partially…
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…
In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external…
Even if path planning can be solved using standard techniques from dynamic programming and control, the problem can also be approached using probabilistic inference. The algorithms that emerge using the latter framework bear some appealing…
A causal query will commonly not be identifiable from observed data, in which case no estimator of the query can be contrived without further assumptions or measured variables, regardless of the amount or precision of the measurements of…
We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different parametric form. In particular, we assume that each node's…
Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical…