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David Heckerman

Publications and source records attributed to David Heckerman.

At least 55 records · Page 3Linked to original sources
arXiv2015

Causal Independence for Knowledge Acquisition and Inference

I introduce a temporal belief-network representation of causal independence that a knowledge engineer can use to elicit probabilistic models. Like the current, atemporal belief-network representation of causal independence, the new representation makes knowledge acquisition tractable. Unlike the atemproal representation, however, the temporal representation can simplify inference, and does not require the use of unobservable variables. The representation is less general than is the atemporal representation, but appears to be useful for many practical applications.

cs.AI↗
arXiv2015

Inference Algorithms for Similarity Networks

We examine two types of similarity networks each based on a distinct notion of relevance. For both types of similarity networks we present an efficient inference algorithm that works under the assumption that every event has a nonzero probability of occurrence. Another inference algorithm is developed for type 1 similarity networks that works under no restriction, albeit less efficiently.

cs.AI↗
arXiv2015

Advances in Probabilistic Reasoning

This paper discuses multiple Bayesian networks representation paradigms for encoding asymmetric independence assertions. We offer three contributions: (1) an inference mechanism that makes explicit use of asymmetric independence to speed up computations, (2) a simplified definition of similarity networks and extensions of their theory, and (3) a generalized representation scheme that encodes more types of asymmetric independence assertions than do similarity networks.

cs.AI↗
arXiv2015

An Approximate Nonmyopic Computation for Value of Information

Value-of-information analyses provide a straightforward means for selecting the best next observation to make, and for determining whether it is better to gather additional information or to act immediately. Determining the next best test to perform, given a state of uncertainty about the world, requires a consideration of the value of making all possible sequences of observations. In practice, decision analysts and expert-system designers have avoided the intractability of exact computation of the value of information by relying on a myopic approximation. Myopic analyses are based on the assumption that only one additional test will be performed, even when there is an opportunity to make a large number of observations. We present a nonmyopic approximation for value of information that bypasses the traditional myopic analyses by exploiting the statistical properties of large samples.

cs.AI↗
arXiv2015

Problem Formulation as the Reduction of a Decision Model

In this paper, we extend the QMRDT probabilistic model for the domain of internal medicine to include decisions about treatments. In addition, we describe how we can use the comprehensive decision model to construct a simpler decision model for a specific patient. In so doing, we transform the task of problem formulation to that of narrowing of a larger problem.

cs.AI↗
arXiv2015

Separable and transitive graphoids

We examine three probabilistic formulations of the sentence a and b are totally unrelated with respect to a given set of variables U. First, two variables a and b are totally independent if they are independent given any value of any subset of the variables in U. Second, two variables are totally uncoupled if U can be partitioned into two marginally independent sets containing a and b respectively. Third, two variables are totally disconnected if the corresponding nodes are disconnected in every belief network representation. We explore the relationship between these three formulations of unrelatedness and explain their relevance to the process of acquiring probabilistic knowledge from human experts.

cs.AI↗
arXiv2014

Modular Belief Updates and Confusion about Measures of Certainty in Artificial Intelligence Research

Over the last decade, there has been growing interest in the use or measures or change in belief for reasoning with uncertainty in artificial intelligence research. An important characteristic of several methodologies that reason with changes in belief or belief updates, is a property that we term modularity. We call updates that satisfy this property modular updates. Whereas probabilistic measures of belief update - which satisfy the modularity property were first discovered in the nineteenth century, knowledge and discussion of these quantities remains obscure in artificial intelligence research. We define modular updates and discuss their inappropriate use in two influential expert systems.

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arXiv2013

A powerful and efficient set test for genetic markers that handles confounders

Approaches for testing sets of variants, such as a set of rare or common variants within a gene or pathway, for association with complex traits are important. In particular, set tests allow for aggregation of weak signal within a set, can capture interplay among variants, and reduce the burden of multiple hypothesis testing. Until now, these approaches did not address confounding by family relatedness and population structure, a problem that is becoming more important as larger data sets are used to increase power. Results: We introduce a new approach for set tests that handles confounders. Our model is based on the linear mixed model and uses two random effects-one to capture the set association signal and one to capture confounders. We also introduce a computational speedup for two-random-effects models that makes this approach feasible even for extremely large cohorts. Using this model with both the likelihood ratio test and score test, we find that the former yields more power while controlling type I error. Application of our approach to richly structured GAW14 data demonstrates that our method successfully corrects for population structure and family relatedness, while application of our method to a 15,000 individual Crohn's disease case-control cohort demonstrates that it additionally recovers genes not recoverable by univariate analysis. Availability: A Python-based library implementing our approach is available at http://mscompbio.codeplex.com

q-bio.GN↗
arXiv2013

A Combination of Cutset Conditioning with Clique-Tree Propagation in the Pathfinder System

Cutset conditioning and clique-tree propagation are two popular methods for performing exact probabilistic inference in Bayesian belief networks. Cutset conditioning is based on decomposition of a subset of network nodes, whereas clique-tree propagation depends on aggregation of nodes. We describe a means to combine cutset conditioning and clique- tree propagation in an approach called aggregation after decomposition (AD). We discuss the application of the AD method in the Pathfinder system, a medical expert system that offers assistance with diagnosis in hematopathology.

cs.AI↗
arXiv2013

The Compilation of Decision Models

We introduce and analyze the problem of the compilation of decision models from a decision-theoretic perspective. The techniques described allow us to evaluate various configurations of compiled knowledge given the nature of evidential relationships in a domain, the utilities associated with alternative actions, the costs of run-time delays, and the costs of memory. We describe procedures for selecting a subset of the total observations available to be incorporated into a compiled situation-action mapping, in the context of a binary decision with conditional independence of evidence. The methods allow us to incrementally select the best pieces of evidence to add to the set of compiled knowledge in an engineering setting. After presenting several approaches to compilation, we exercise one of the methods to provide insight into the relationship between the distribution over weights of evidence and the preferred degree of compilation.

cs.AI↗
arXiv2013

A Perspective on Confidence and Its Use in Focusing Attention During Knowledge Acquisition

We present a representation of partial confidence in belief and preference that is consistent with the tenets of decision-theory. The fundamental insight underlying the representation is that if a person is not completely confident in a probability or utility assessment, additional modeling of the assessment may improve decisions to which it is relevant. We show how a traditional decision-analytic approach can be used to balance the benefits of additional modeling with associated costs. The approach can be used during knowledge acquisition to focus the attention of a knowledge engineer or expert on parts of a decision model that deserve additional refinement.

cs.AI↗
arXiv2013

The Role of Calculi in Uncertain Inference Systems

Much of the controversy about methods for automated decision making has focused on specific calculi for combining beliefs or propagating uncertainty. We broaden the debate by (1) exploring the constellation of secondary tasks surrounding any primary decision problem, and (2) identifying knowledge engineering concerns that present additional representational tradeoffs. We argue on pragmatic grounds that the attempt to support all of these tasks within a single calculus is misguided. In the process, we note several uncertain reasoning objectives that conflict with the Bayesian ideal of complete specification of probabilities and utilities. In response, we advocate treating the uncertainty calculus as an object language for reasoning mechanisms that support the secondary tasks. Arguments against Bayesian decision theory are weakened when the calculus is relegated to this role. Architectures for uncertainty handling that take statements in the calculus as objects to be reasoned about offer the prospect of retaining normative status with respect to decision making while supporting the other tasks in uncertain reasoning.

cs.AI↗
arXiv2013

The Myth of Modularity in Rule-Based Systems

In this paper, we examine the concept of modularity, an often cited advantage of the ruled-based representation methodology. We argue that the notion of modularity consists of two distinct concepts which we call syntactic modularity and semantic modularity. We argue that when reasoning under certainty, it is reasonable to regard the rule-based approach as both syntactically and semantically modular. However, we argue that in the case of plausible reasoning, rules are syntactically modular but are rarely semantically modular. To illustrate this point, we examine a particular approach for managing uncertainty in rule-based systems called the MYCIN certainty factor model. We formally define the concept of semantic modularity with respect to the certainty factor model and discuss logical consequences of the definition. We show that the assumption of semantic modularity imposes strong restrictions on rules in a knowledge base. We argue that such restrictions are rarely valid in practical applications. Finally, we suggest how the concept of semantic modularity can be relaxed in a manner that makes it appropriate for plausible reasoning.

cs.AI↗
arXiv2013

An Axiomatic Framework for Belief Updates

In the 1940's, a physicist named Cox provided the first formal justification for the axioms of probability based on the subjective or Bayesian interpretation. He showed that if a measure of belief satisfies several fundamental properties, then the measure must be some monotonic transformation of a probability. In this paper, measures of change in belief or belief updates are examined. In the spirit of Cox, properties for a measure of change in belief are enumerated. It is shown that if a measure satisfies these properties, it must satisfy other restrictive conditions. For example, it is shown that belief updates in a probabilistic context must be equal to some monotonic transformation of a likelihood ratio. It is hoped that this formal explication of the belief update paradigm will facilitate critical discussion and useful extensions of the approach.

cs.AI↗
arXiv2013

A Backwards View for Assessment

Much artificial intelligence research focuses on the problem of deducing the validity of unobservable propositions or hypotheses from observable evidence.! Many of the knowledge representation techniques designed for this problem encode the relationship between evidence and hypothesis in a directed manner. Moreover, the direction in which evidence is stored is typically from evidence to hypothesis.

cs.AI↗
arXiv2013

Probabilistic Interpretations for MYCIN's Certainty Factors

This paper examines the quantities used by MYCIN to reason with uncertainty, called certainty factors. It is shown that the original definition of certainty factors is inconsistent with the functions used in MYCIN to combine the quantities. This inconsistency is used to argue for a redefinition of certainty factors in terms of the intuitively appealing desiderata associated with the combining functions. It is shown that this redefinition accommodates an unlimited number of probabilistic interpretations. These interpretations are shown to be monotonic transformations of the likelihood ratio p(EIH)/p(El H). The construction of these interpretations provides insight into the assumptions implicit in the certainty factor model. In particular, it is shown that if uncertainty is to be propagated through an inference network in accordance with the desiderata, evidence must be conditionally independent given the hypothesis and its negation and the inference network must have a tree structure. It is emphasized that assumptions implicit in the model are rarely true in practical applications. Methods for relaxing the assumptions are suggested.

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