Related papers: On the physics of nested Markov models: a generali…
In many problems, the measured variables (e.g., image pixels) are just mathematical functions of the latent causal variables (e.g., the underlying concepts or objects). For the purpose of making predictions in changing environments or…
Current concepts of neural networks have emerged over two centuries of progress beginning with the neural doctrine to the idea of neural cell assemblies. Presently the model of neural networks involves distributed neural circuits of nodes,…
To distinguish Markov equivalent graphs in causal discovery, it is necessary to restrict the structural causal model. Crucially, we need to be able to distinguish cause $X$ from effect $Y$ in bivariate models, that is, distinguish the two…
The goal of this paper is to analyze distributional Markov Decision Processes as a class of control problems in which the objective is to learn policies that steer the distribution of a cumulative reward toward a prescribed target law,…
Causal models in statistics are often described using acyclic directed mixed graphs (ADMGs), which contain directed and bidirected edges and no directed cycles. This article surveys various interpretations of ADMGs, discusses their…
Causal relationships among variables are commonly represented via directed acyclic graphs. There are many methods in the literature to quantify the strength of arrows in a causal acyclic graph. These methods, however, have undesirable…
This paper reviews generalized Pareto copulas (GPC), which turn out to be a key to multivariate extreme value theory. Any GPC can be represented in an easy analytic way using a particular type of norm on $\mathbb{R}^d$, called $D$-norm. The…
We consider a Spatial Markov Chain model for the spread of viruses. The model is based on the principle to represent a graph connecting nodes, which represent humans. The vertices between the nodes represent relations between humans. In…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
We consider evaluation of proper posterior distributions obtained from improper prior distributions. Our context is estimating a bounded function $\phi$ of a parameter when the loss is quadratic. If the posterior mean of $\phi$ is…
Recent years have seen a rapid expansion of the model space explored in statistical phylogenetics, emphasizing the need for new approaches to statistical model representation and software development. Clear communication and representation…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
Datasets involving sequences of different types of events without meaningful time stamps are prevalent in many applications, for instance when extracted from textual corpora. We propose a family of models for such event sequences -- summary…
In machine learning, exploring data correlations to predict outcomes is a fundamental task. Recognizing causal relationships embedded within data is pivotal for a comprehensive understanding of system dynamics, the significance of which is…
In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…
Many of the stochastic models used in inference of phylogenetic trees from biological sequence data have polynomial parameterization maps. The image of such a map --- the collection of joint distributions for a model --- forms the model…
A new and rather broad class of stationary (i.e. stochastically translation invariant) random tessellations of the $d$-dimensional Euclidean space is introduced, which are called shape-driven nested Markov tessellations. Locally, these…
Graphical causal models are an important tool for knowledge discovery because they can represent both the causal relations between variables and the multivariate probability distributions over the data. Once learned, causal graphs can be…
Causal reasoning has gained great attention over the last half century as it allows (or at least intends) to answer questions which go above those within the capabilities of classical inferential statistics using just observational data. So…
The assumption that data samples are independent and identically distributed (iid) is standard in many areas of statistics and machine learning. Nevertheless, in some settings, such as social networks, infectious disease modeling, and…