Related papers: Exploiting Contextual Independence In Probabilisti…
Network data are increasingly collected along with other variables of interest. Our motivation is drawn from neurophysiology studies measuring brain connectivity networks for a sample of individuals along with their membership to a low or…
Standard methods of using categorical variables as predictors either endow them with an ordinal structure or assume they have no structure at all. However, categorical variables often possess structure that is more complicated than a linear…
Causal discovery algorithms estimate causal graphs from observational data. This can provide a valuable complement to analyses focussing on the causal relation between individual treatment-outcome pairs. Constraint-based causal discovery…
Algorithms for learning the conditional probabilities of Bayesian networks with hidden variables typically operate within a high-dimensional search space and yield only locally optimal solutions. One way of limiting the search space and…
In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…
To effectively study complex causal systems, it is often useful to construct abstractions of parts of the system by discarding irrelevant details while preserving key features. The Information Bottleneck (IB) method is a widely used…
Inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
Noisy probabilistic relational rules are a promising world model representation for several reasons. They are compact and generalize over world instantiations. They are usually interpretable and they can be learned effectively from the…
Despite the empirical success of foundation models, we do not have a systematic characterization of the representations that these models learn. In this paper, we establish the contexture theory. It shows that a large class of…
We study two-layer belief networks of binary random variables in which the conditional probabilities Pr[childlparents] depend monotonically on weighted sums of the parents. In large networks where exact probabilistic inference is…
Inference is a versatile tool that underlies scientific discovery, machine learning, and everyday decision-making: it describes how an agent updates a probability distribution as partial information is acquired from multiple measurements,…
We focus on credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. We replace the notion of strong independence commonly used in credal nets with the weaker notion of epistemic irrelevance, which is…
We propose a method to infer causal structures containing both discrete and continuous variables. The idea is to select causal hypotheses for which the conditional density of every variable, given its causes, becomes smooth. We define a…
This paper presents an approximate method for performing Bayesian inference in models with conditional independence over a decentralized network of learning agents. The method first employs variational inference on each individual learning…
Analysing non-Gaussian spatial-temporal data requires introducing spatial as well as temporal dependence in generalised linear models through the link function of an exponential family distribution. Unlike in Gaussian likelihoods, inference…
We consider the problem of inferring the directed, causal graph from observational data, assuming no hidden confounders. We take an information theoretic approach, and make three main contributions. First, we show how through algorithmic…
AThe paper gives a few arguments in favour of the use of chain graphs for description of probabilistic conditional independence structures. Every Bayesian network model can be equivalently introduced by means of a factorization formula with…
The assumption of independence between observations (units) in a dataset is prevalent across various methodologies for learning causal graphical models. However, this assumption often finds itself in conflict with real-world data, posing…
We introduce a graceful approach to probabilistic inference called bounded conditioning. Bounded conditioning monotonically refines the bounds on posterior probabilities in a belief network with computation, and converges on final…