Related papers: Equations defining probability tree models
The p_1 model is a directed random graph model used to describe dyadic interactions in a social network in terms of effects due to differential attraction (popularity) and expansiveness, as well as an additional effect due to reciprocation.…
Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods,…
Influence Diagrams (ID) are a flexible tool to represent discrete stochastic optimization problems, including Markov Decision Process (MDP) and Partially Observable MDP as standard examples. More precisely, given random variables considered…
Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical…
Consider jointly Gaussian random variables whose conditional independence structure is specified by a graphical model. If we observe realizations of the variables, we can compute the covariance matrix, and it is well known that the support…
We study a problem of model selection for data produced by two different context tree sources. Motivated by linguistic questions, we consider the case where the probabilistic context trees corresponding to the two sources are finite and…
We introduce Probabilistic Dependency Graphs (PDGs), a new class of directed graphical models. PDGs can capture inconsistent beliefs in a natural way and are more modular than Bayesian Networks (BNs), in that they make it easier to…
Staged trees are a relatively recent class of probabilistic graphical models that extend Bayesian networks to formally and graphically account for non-symmetric patterns of dependence. Machine learning algorithms to learn them from data…
In this paper, we learn dynamics models for parametrized families of dynamical systems with varying properties. The dynamics models are formulated as stochastic processes conditioned on a latent context variable which is inferred from…
We elaborate on an alternative representation of conditional probability to the usual tree diagram. We term the representation `turtleback diagram' for its resemblance to the pattern on turtle shells. Adopting the set theoretic view of…
Bayesian networks are basic graphical models, used widely both in statistics and artificial intelligence. These statistical models of conditional independence structure are described by acyclic directed graphs whose nodes correspond to…
We study the connection between probability distributions satisfying certain conditional independence (CI) constraints, and point and line arrangements in incidence geometry. To a family of CI statements, we associate a polynomial ideal…
A decision tree looks like a simple directed acyclic computational graph, where only the leaf nodes specify the output values and the non-terminals specify their tests or split conditions. From the numerical perspective, we express decision…
The increasing complexity of data requires methods and models that can effectively handle intricate structures, as simplifying them would result in loss of information. While several analytical tools have been developed to work with complex…
For a given $\delta \in (0,1)$, the randomly perturbed graph model is defined as the union of any $n$-vertex graph $G_0$ with minimum degree $\delta n$ and the binomial random graph $\mathbf{G}(n,p)$ on the same vertex set. Moreover, we say…
Inference of species networks from genomic data under the Network Multispecies Coalescent Model is currently severely limited by heavy computational demands. It also remains unclear how complicated networks can be for consistent inference…
As animals interact with their environments, they must infer properties of their surroundings. Some animals, including humans, can represent uncertainty about those properties. But when, if ever, do they use probability distributions to…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
Probability trees are one of the simplest models of causal generative processes. They possess clean semantics and -- unlike causal Bayesian networks -- they can represent context-specific causal dependencies, which are necessary for e.g.…
The conditional autoregressive model is a routinely used statistical model for areal data that arise from, for instances, epidemiological, socio-economic or ecological studies. Various multivariate conditional autoregressive models have…