On the impact of causal independence

2006

One practical problem with building large scale Bayesian network models is an exponential growth of the number of numerical parameters in conditional probability tables. Obtaining large number of probabilities from domain experts is too expensive and too time demanding in practice. A widely accepted solution to this problem is the assumption of independence of causal influences (ICI) which allows for parametric models that define conditional probability distributions using only a number of parameters that is linear in the number of causes. ICI models, such as the noisy-OR and the noisy-AND gates, have been widely used by practitioners. In this paper we propose PICI, probabilistic ICI, an extension of the ICI assumption that leads to more expressive parametric models. We provide examples of three PICI models and demonstrate how they can cope with a combination of positive and negative influences, something that is hard for noisy-OR and noisy-AND gates.

Computational Intelligence, 2017

Testing independencies is a fundamental task in reasoning with Bayesian networks (BNs). In practice, d-separation is often used for this task, since it has linear-time complexity. However, many have had difficulties understanding d-separation in BNs. An equivalent method that is easier to understand, called m-separation, transforms the problem from directed separation in BNs into classical separation in undirected graphs. Two main steps of this transformation are pruning the BN and adding undirected edges. In this paper, we propose u-separation as an even simpler method for testing independencies in a BN. Our approach also converts the problem into classical separation in an undirected graph. However, our method is based upon the novel concepts of inaugural variables and rationalization. Thereby, the primary advantage of u-separation over m-separation is that m-separation can prune unnecessarily and add superfluous edges. Our experiment results show that u-separation performs 73% fewer modifications on average than m-separation.

International Journal of Approximate Reasoning, 1998

Among the several representations of uncertainty, possibility theory allows also for the management of imprecision coming from data. Domain models with inherent uncertainty and imprecision can be represented by means of possibilistic causal networks that, the possibilistic counterpart of Bayesian belief networks. Only recently the definition of possibilistic network has been clearly stated and the corresponding inference algorithms developed. However, and in contrast to the corresponding developments in Bayesian networks, learning methods for possibilistic networks are still few. We present here a new approach that hybridizes two of the most used approaches in uncertain network learning: those methods based on conditional dependency information and those based on information quality measures. The resulting algorithm, POSSCAUSE, admits easily a parallel formulation. In the present paper POSSCAUSE is presented and its main features discussed together with the underlying new concepts used.

arXiv (Cornell University), 2017

2013

We propose a new principles and technique to speed up constraint-based algorithms for learning dependency structures from data. Novelty of proposed framework comes from implementing the rules of inductive inference acceleration, which can radically reduce a searching space for model’s skeleton inference. The inductive inference acceleration rules facilitate fast identification of skeleton by performing such functions: recognition of edge presence (absence); recognition of some variables as non-members (obligate members) of supposed separator. It has been demonstrated that an algorithm, equipped with the proposed rules, can learn Bayesian networks (of moderate density) multiple times faster than well-known PC algorithm. Such improvement can be extended to the case of non-recursive graphical models, i.e. causal networks with hidden variables.

2006

Causal independence modelling is a well-known method both for reducing the size of probability tables and for explaining the underlying mechanisms in Bayesian networks. Many Bayesian network models incorporate causal independence assumptions; however, only the noisy OR and noisy AND, two examples of causal independence models, are used in practice. Their underlying assumption that either at least one cause, or all causes together, give rise to an effect, however, seems unnecessarily restrictive. In the present paper a new, more flexible, causal independence model is proposed, based on the Boolean threshold function. A connection is established between conditional probability distributions based on the noisy threshold model and Poisson binomial distributions, and the basic properties of this probability distribution are studied in some depth. We present and analyse recursive methods as well as approximation and bounding techniques to assess the conditional probabilities in the noisy threshold models.

Cornell University - arXiv, 2022

Causal identification is at the core of the causal inference literature, where complete algorithms have been proposed to identify causal queries of interest. The validity of these algorithms hinges on the restrictive assumption of having access to a correctly specified causal structure. In this work, we study the setting where a probabilistic model of the causal structure is available. Specifically, the edges in a causal graph are assigned probabilities which may, for example, represent degree of belief from domain experts. Alternatively, the uncertainly about an edge may reflect the confidence of a particular statistical test. The question that naturally arises in this setting is: Given such a probabilistic graph and a specific causal effect of interest, what is the subgraph which has the highest plausibility and for which the causal effect is identifiable? We show that answering this question reduces to solving an NP-hard combinatorial optimization problem which we call the edge ID problem. We propose efficient algorithms to approximate this problem, and evaluate our proposed algorithms against real-world networks and randomly generated graphs. Preprint. Under review.

ArXiv, 2020

Spirtes, Glymour and Scheines formulated a Conjecture that a direct dependence test and a head-to-head meeting test would suffice to construe directed acyclic graph decompositions of a joint probability distribution (Bayesian network) for which Pearl's d-separation applies. This Conjecture was later shown to be a direct consequence of a result of Pearl and Verma. This paper is intended to prove this Conjecture in a new way, by exploiting the concept of p-d-separation (partial dependency separation). While Pearl's d-separation works with Bayesian networks, p-d-separation is intended to apply to causal networks: that is partially oriented networks in which orientations are given to only to those edges, that express statistically confirmed causal influence, whereas undirected edges express existence of direct influence without possibility of determination of direction of causation. As a consequence of the particular way of proving the validity of this Conjecture, an algorithm f...

1991

In constructing probabilistic networks from human judgments, we use causal relationships to convey useful patterns of dependencies. The converse task, that of inferring causal relationships from patterns of dependencies, is far less understood. Th' 1s paper establishes conditions under which the directionality of some interactions can be determined from non-temporal probabilistic information-an essential prerequisite for attributing a causal interpretation to these interactions. An efficient algorithm is developed that, given data generated by an undisclosed causal polytree, recovers the structure of the underlying polytree, as well as the directionality of all its identifiable links.

Ai Communications, 1997

Causal concepts play a crucial role in many reasoning tasks. Organised as a model revealing the causal structure of a domain, they can guide inference through relevant knowledge. This is an especially difficult kind of knowledge to acquire, so some methods for automating the induction of causal models from data have been put forth. Here we review those that have a graph representation. Most work has been done on the problem of recovering belief nets from data but some extensions are appearing that claim to exhibit a true causal semantics. We will review the analogies between belief networks and "true" causal networks and to what extent methods for learning belief networks can be used in learning causal representations. Some new results in recovering possibilistic causal networks will also be presented.

robabilistic graphical models are useful tools for modeling systems governed by probabilistic structure. Bayesian networks are one class of prob- abilistic graphical model that have proven useful for characterizing both formal systems and for reasoning with those systems. Probabilistic dependencies in Bayesian networks are graphically expressed in terms of directed links from parents to their children. Casual Bayesian networks are a generalization of Bayesian networks that allow one to "intervene" and perform "graph surgery" — cutting nodes off from their parents. Causal theories are a formal framework for generating causal Bayesian networks. This report provides a brief introduction to the formal tools needed to compre- hend Bayesian networks, including probability theory and graph theory. Then, it describes Bayesian networks and causal Bayesian networks. It introduces some of the most basic functionality of the extensive NetworkX python package for working with complex graphs and networks [HSS08]. I introduce some utilities I have build on top of NetworkX including conditional graph enumeration and sampling from discrete valued Bayesian networks encoded in NetworkX graphs [Pac15]. I call this Causal Bayesian NetworkX, or CBNX. I conclude by introducing a formal framework for generating causal Bayesian networks called theory based causal induction [GT09], out of which these utilities emerged. I discuss the background motivations for frameworks of this sort, their use in computational cognitive science, and the use of computational cognitive science for the machine learning community at large

International Journal of Intelligent Systems, 1997

Belief networks are graphic structures capable of representing dependence and independence relationships among variables in a given domain of knowledge. We focus on the problem of automatic learning of these structures from data, and restrict our study to a specific type of belief network: simple graphs, i.e., directed acyclic graphs where every pair of nodes with a common direct child has no common ancestor nor is one an ancestor of the other. Our study is based on an analysis of the independence relationships that may be represented by means of simple graphs. This theoretical study, which includes new characterizations of simple graphs in terms of independence relationships, is the basis of an efficient algorithm that recovers simple graphs using only zero and first-order conditional independence tests, thereby overcoming some of the practical difficulties of existing algorithms.

European Conference on Artificial Intelligence, 2010

A b stract. Algorithms for probabilistic inference in Bayesian net works are known to have running times that are worst-case expo nential in the size of the network. For networks with a moralised graph of bounded treewidth, however, these algorithms take a time which is linear in the netw ork's size. In this paper, we show that under the assumption of the Exponential Time Hypothesis (ETH), small treewidth of the moralised graph actually is a necessary condi tion for a Bayesian network to render inference efficient by an algo rithm accepting arbitrary instances. We thus show that no algorithm can exist that performs inference on arbitrary Bayesian networks of unbounded treewidth in polynom ial time, unless the ETH fails.

International Journal of Approximate Reasoning, 1998

A definition for similarity between possibility distributions is introduced and discussed as a basis for detecting dependence between variables by measuring the similarity degree of their respective distributions. This definition is used to detect conditional independence relations in possibility distributions derived from data. This is the basis for a new hybrid algorithm for recovering possibilistic causal networks. The algorithm POSS-CAUSE is presented and its applications discussed and compared with analogous developments in possibilistic and probabilistic causal networks learning.

National Conference on Artificial Intelligence, 2006

This paper addresses the problem of identifying causal effects from nonexperimental data in a causal Bayesian network, i.e., a directed acyclic graph that represents causal relationships. The identifiability question asks whether it is possible to com- pute the probability of some set of (effect) variables given intervention on another set of (intervention) variables, in the presence of non-observable (i.e., hidden