Related papers: Algebra in probabilistic reasoning
We consider testing whether a set of Gaussian variables, selected from the data, is independent of the remaining variables. We assume that this set is selected via a very simple approach that is commonly used across scientific disciplines:…
In this paper, we show that coherent sets of gambles and coherent lower and upper previsions can be embedded into the algebraic structure of information algebra. This leads firstly, to a new perspective of the algebraic and logical…
We introduce a term algebra as a new formal specification language for the coordinating architectures of distributed systems consisting of a finite yet unbounded number of components. The language allows to describe infinite sets of systems…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
This paper studies the form and complexity of inference in graphical models using the abstraction offered by algebraic structures. In particular, we broadly formalize inference problems in graphical models by viewing them as a sequence of…
Studies of issues related to computability and computational complexity involve the use of a model of computation. Pivotal to such a model are the computational processes considered. Processes of this kind can be described using an…
Bayesian belief networks have grown to prominence because they provide compact representations for many problems for which probabilistic inference is appropriate, and there are algorithms to exploit this compactness. The next step is to…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
We discuss the application of computer algebra to problems commonly arising in numerical relativity, such as the derivation of 3+1-splits, manipulation of evolution equations and automatic code generation. Particular emphasis is put on…
Expert systems applications that involve uncertain inference can be represented by a multidimensional contingency table. These tables offer a general approach to inferring with uncertain evidence, because they can embody any form of…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
Typical arguments for results like Kleene's Second Recursion Theorem and the existence of self-writing computer programs bear the fingerprints of equational reasoning and combinatory logic. In fact, the connection of combinatory logic and…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
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…
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field,…
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…
We consider the problem of rational uncertainty about unproven mathematical statements, remarked on by G\"odel and others. Using Bayesian-inspired arguments we build a normative model of fair bets under deductive uncertainty which draws…
In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…
We introduce and discuss, through a computational algebraic geometry approach, the automatic reasoning handling of propositions that are simultaneously true and false over some relevant collections of instances. A rigorous, algorithmic…
Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior…