Comparing two samples of data, we observe a change in the distribution of an outcome variable. In the presence of multiple explanatory variables, how much of the change can be explained by each possible cause? We develop a new estimation strategy that, given a causal model, combines regression and re-weighting methods to quantify the contribution of each causal mechanism. Our proposed methodology is multiply robust, meaning that it still recovers the target parameter under partial misspecification. We prove that our estimator is consistent and asymptotically normal. Moreover, it can be incorporated into existing frameworks for causal attribution, such as Shapley values, which will inherit the consistency and large-sample distribution properties. Our method demonstrates excellent performance in Monte Carlo simulations, and we show its usefulness in an empirical application. Our method is implemented as part of the Python library “DoWhy“ (Sharma & Kiciman, 2020; Blöbaum et al., 2022).

We study the problem of observational causal inference with continuous treatment. We focus on the challenge of estimating the causal response curve for infrequently-observed treatment values. We design a new algorithm based on the framework of entropy balancing which learns weights that directly maximize causal inference accuracy using end-to-end optimization. Our weights can be customized for different datasets and causal inference algorithms. We propose a new theory for consistency of entropy balancing for continuous treatments. Using synthetic and real-world data, we show that our proposed algorithm outperforms the entropy balancing in terms of causal inference accuracy.

There are two aspects of data that make them big: sample size and dimensionality. The advantages of large sample size have long been touted. In contrast, high dimensionality has typically been seen as an obstacle to successful analysis. In this talk, using the area of genomics as an example, I will illustrate some of the advantages of high dimensionality.

Hidden common causes make it difficult to infer causal relationships from observational data. Here, we begin an investigation into a new method to account for a hidden common cause that infers its presence from the data. As with other approaches that can account for common causes, this approach is successful only in some cases. We describe such a case taken from the field of genomics, wherein one tries to identify which genomic markers causally influence a trait of interest.

In order to solve large-scale lasso problems, screening algorithms have been developed that discard features with zero coefficients based on a computationally efficient screening rule. Most existing screening rules were developed from a spherical constraint and half-space constraints on a dual optimal solution. However, existing rules admit at most two half-space constraints due to the computational cost incurred by the half-spaces, even though additional constraints may be useful to discard more features. In this paper, we present AdaScreen, an adaptive lasso screening rule ensemble, which allows to combine any one sphere with multiple half-space constraints on a dual optimal solution. Thanks to geometrical considerations that lead to a simple closed form solution for AdaScreen, we can incorporate multiple half-space constraints at small computational cost. In our experiments, we show that AdaScreen with multiple half-space constraints simultaneously improves screening performance and speeds up lasso solvers.

As a result of improvements in genome assembly algorithms and the ever decreasing costs of high-throughput sequencing technologies, new high quality draft genome sequences are published at a striking pace. With well-established methodologies, larger and more complex genomes are being tackled, including polyploid plant genomes. Given the similarity between multiple copies of a basic genome in polyploid individuals, assembly of such data usually results in collapsed contigs that represent a variable number of homoeologous genomic regions. Unfortunately, such collapse is often not ideal, as keeping contigs separate can lead both to improved assembly and also insights about how haplotypes influence phenotype. Here, we describe a first step in avoiding inappropriate collapse during assembly. In particular, we describe ConPADE (Contig Ploidy and Allele Dosage Estimation), a probabilistic method that estimates the ploidy of any given contig/scaffold based on its allele proportions. In the process, we report findings regarding errors in sequencing. The method can be used for whole genome shotgun (WGS) sequencing data. We also show applicability of the method for variant calling and allele dosage estimation. Results for simulated and real datasets are discussed and provide evidence that ConPADE performs well as long as enough sequencing coverage is available, or the true contig ploidy is low. We show that ConPADE may also be used for related applications, such as the identification of duplicated genes in fragmented assemblies, although refinements are needed.

MOTIVATION: Set-based variance component tests have been identified as a way to increase power in association studies by aggregating weak individual effects. However, the choice of test statistic has been largely ignored even though it may play an important role in obtaining optimal power. We compared a standard statistical test-a score test-with a recently developed likelihood ratio (LR) test. Further, when correction for hidden structure is needed, or gene-gene interactions are sought, state-of-the art algorithms for both the score and LR tests can be computationally impractical. Thus we develop new computationally efficient methods. RESULTS: After reviewing theoretical differences in performance between the score and LR tests, we find empirically on real data that the LR test generally has more power. In particular, on 15 of 17 real datasets, the LR test yielded at least as many associations as the score test-up to 23 more associations-whereas the score test yielded at most one more association than the LR test in the two remaining datasets. On synthetic data, we find that the LR test yielded up to 12% more associations, consistent with our results on real data, but also observe a regime of extremely small signal where the score test yielded up to 25% more associations than the LR test, consistent with theory. Finally, our computational speedups now enable (i) efficient LR testing when the background kernel is full rank, and (ii) efficient score testing when the background kernel changes with each test, as for gene-gene interaction tests. The latter yielded a factor of 2000 speedup on a cohort of size 13 500. AVAILABILITY: Software available at http://research.microsoft.com/en-us/um/redmond/projects/MSCompBio/Fastlmm/. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Advances in sequencing technology have led to an exponential growth of genomics data, yet it remains a formidable challenge to interpret such data for identifying disease genes and drug targets. There has been increasing interest in adopting a systems approach that incorporates prior knowledge such as gene networks and genotype-phenotype associations. The majority of such knowledge resides in text such as journal publications, which has been undergoing its own exponential growth. It has thus become a significant bottleneck to identify relevant knowledge for genomic interpretation as well as to keep up with new genomics findings. RESULTS: In the Literome project, we have developed an automatic curation system to extract genomic knowledge from PubMed articles and made this knowledge available in the cloud with a Web site to facilitate browsing, searching and reasoning. Currently, Literome focuses on two types of knowledge most pertinent to genomic medicine: directed genic interactions such as pathways and genotype-phenotype associations. Users can search for interacting genes and the nature of the interactions, as well as diseases and drugs associated with a single nucleotide polymorphism or gene. Users can also search for indirect connections between two entities, e.g. a gene and a disease might be linked because an interacting gene is associated with a related disease. AVAILABILITY AND IMPLEMENTATION: Literome is freely available at literome.azurewebsites.net. Download for non-commercial use is available via Web services.

MOTIVATION: 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 datasets 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 Genetic Analysis Workshop 14 data demonstrates that our method successfully corrects for population structure and family relatedness, whereas 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.

UNLABELLED: Evolutionary biologists are often interested in finding correlations among biological traits across a number of species, as such correlations may lead to testable hypotheses about the underlying function. Because some species are more closely related than others, computing and visualizing these correlations must be done in the context of the evolutionary tree that relates species. In this note, we introduce PhyloDet (short for PhyloDetective), an evolutionary tree visualization tool that enables biologists to visualize multiple traits mapped to the tree. AVAILABILITY: http://research.microsoft.com/cue/phylodet/

HIV avoids elimination by cytotoxic T-lymphocytes (CTLs) through the evolution of escape mutations. Although there is mounting evidence that these escape pathways are broadly consistent among individuals with similar human leukocyte antigen (HLA) class I alleles, previous population-based studies have been limited by the inability to simultaneously account for HIV codon covariation, linkage disequilibrium among HLA alleles, and the confounding effects of HIV phylogeny when attempting to identify HLA-associated viral evolution. We have developed a statistical model of evolution, called a phylogenetic dependency network, that accounts for these three sources of confounding and identifies the primary sources of selection pressure acting on each HIV codon. Using synthetic data, we demonstrate the utility of this approach for identifying sites of HLA-mediated selection pressure and codon evolution as well as the deleterious effects of failing to account for all three sources of confounding. We then apply our approach to a large, clinically-derived dataset of Gag p17 and p24 sequences from a multicenter cohort of 1144 HIV-infected individuals from British Columbia, Canada (predominantly HIV-1 clade B) and Durban, South Africa (predominantly HIV-1 clade C). The resulting phylogenetic dependency network is dense, containing 149 associations between HLA alleles and HIV codons and 1386 associations among HIV codons. These associations include the complete reconstruction of several recently defined escape and compensatory mutation pathways and agree with emerging data on patterns of epitope targeting. The phylogenetic dependency network adds to the growing body of literature suggesting that sites of escape, order of escape, and compensatory mutations are largely consistent even across different clades, although we also identify several differences between clades. As recent case studies have demonstrated, understanding both the complexity and the consistency of immune escape has important implications for CTL-based vaccine design. Phylogenetic dependency networks represent a major step toward systematically expanding our understanding of CTL escape to diverse populations and whole viral genes.

High-resolution HLA typing plays a central role in many areas of immunology, such as in identifying immunogenetic risk factors for disease, in studying how the genomes of pathogens evolve in response to immune selection pressures, and also in vaccine design, where identification of HLA-restricted epitopes may be used to guide the selection of vaccine immunogens. Perhaps one of the most immediate applications is in direct medical decisions concerning the matching of stem cell transplant donors to unrelated recipients. However, high-resolution HLA typing is frequently unavailable due to its high cost or the inability to re-type historical data. In this paper, we introduce and evaluate a method for statistical, in silico refinement of ambiguous and/or low-resolution HLA data. Our method, which requires an independent, high-resolution training data set drawn from the same population as the data to be refined, uses linkage disequilibrium in HLA haplotypes as well as four-digit allele frequency data to probabilistically refine HLA typings. Central to our approach is the use of haplotype inference. We introduce new methodology to this area, improving upon the Expectation-Maximization (EM)-based approaches currently used within the HLA community. Our improvements are achieved by using a parsimonious parameterization for haplotype distributions and by smoothing the maximum likelihood (ML) solution. These improvements make it possible to scale the refinement to a larger number of alleles and loci in a more computationally efficient and stable manner. We also show how to augment our method in order to incorporate ethnicity information (as HLA allele distributions vary widely according to race/ethnicity as well as geographic area), and demonstrate the potential utility of this experimentally. A tool based on our approach is freely available for research purposes at http://microsoft.com/science.

In our paper “Coping with Viral Diversity in HIV Vaccine Design” [1], we presented several approaches to incorporate viral variability within vaccine immunogens, including judicious choice of natural strains. Most of our approaches included at least one collinear gene length corresponding to the Center-of-Tree (COT) sequence, which has near-optimal peptide coverage for a single gene. Inclusion of a COT sequence and optimizing the rest of the immunogen for coverage, as suggested in [2], yielded a construct (COT+) with the greatest coverage of peptide diversity, minimally sacrificing peptide coverage in comparison with unconstrained diversity optimization. Fischer et al. [3] introduced mosaics—a different approach to increasing coverage while maintaining collinearity using an optimization algorithm based on simulated recombination. In their response to Nickle et al. [1], Fischer et al. [4] suggest that maintaining full collinearity of viral gene sequences with native viral proteins is the only tractable approach to producing immunogens inclusive of viral variability. This claim was based on the observation that mosaics had slightly higher coverage than COT+ at 3× and 4× strain lengths, despite the fact that all mosaic components are constrained to be collinear with the full gene. However, as we pointed out, a variety of optimization algorithms can be used to perform coverage optimization, with computationally intensive approaches typically yielding better results. Figure 1 compares the coverage of mosaics with COT+ constructs produced by two optimization algorithms—the simple greedy extension described in Nickle et al. [1], which can be implemented in hours and run in seconds on any modern personal computer, and the more complex combinatiorial optimization approach of [5] run for one day on a cluster of 300 PCs. We also include the coverage of a construct optimized without any collinearity constraints, derived using the Kirovski et al. [5] algorithm. The coverage of COT+ created by combinatorial optimization is greater than that of mosaics, especially at larger lengths where even the simple greedy algorithm surpasses the mosaic coverage. Furthermore, the optimized COT+ coverage is almost identical to the coverage of constructs optimized with no collinearity constraints, indicating that the price for imposing a constraint on the immunogen to include a single virus-like strain is small. Figure 1 Comparison of Peptide Coverage Scores Achievable with Different Immunogen Formats and Algorithms Fischer and colleagues also argued that COT+ creates unnatural peptide sequences by concatenation. However, similar concatenation of their mosaics would have produced about 18 unnatural 9-mer peptides. Furthermore, the COT+ approach can be tuned to both penalize the introduction of unnatural peptides on concatenation, and to define the number of segments to be separately expressed, and thus reduce the requirement for concatenation. Several additional inferences were made in the response by Fischer et al. that should be commented upon. First, COT+ may, of course, be optimized for arbitrary HIV clades or combinations of clades, but the publication of our paper in PLoS Computational Biology reflects our focus on approaches to immunogen design rather than on the production of an exhaustive series of constructs. Also, just as in the mosaic approach, COT+ can be optimized to exclude rare variants (referred to as smoothing in our paper). Fischer et al. also discussed disappointing unpublished findings on the immunogenicity induced against Nef by a construct obtained by fusing a full-length Gag gene and the central portion of the Nef gene. However, these results can only be fairly assessed in light of what would be expected for the full-length Nef protein, and in the case of cellular immune responses, in the context of the same MHC specificities. However, these controls were not provided. We certainly agree that there are substantial challenges to the establishment of a multivalent CD8 response, yet multiple strategies have been and are being devised to overcome this important problem. For example, different groups have shown that CD8+ T cell responses can be successfully elicited against CD8+ T cell epitope strings when they are separated by short linker sequences and not in the context of the native protein, implying that they can be processed and presented in vivo [6–11]. Finally, despite 25 years of AIDS research and intensive yet uniformly failed efforts to develop an AIDS vaccine, the scientific community is poorly positioned to determine which, if any, approach to vaccine immunogen design will prove successful. Thus, arguing over methodologies developed with the same goal of incorporating variability has little significance as long as we do not know whether maximizing variability or inclusion of the entire full-length viral proteins are valid strategies. It may very well be that removing certain epitopes could be a more judicious approach than an overall epitope maximization strategy [12]. Indeed, the flexibility afforded by the COT+ approach, which is not limited to full-length proteins, may well prove superior to immunization with full-length viral protein immunogens.

The identification of T cell epitopes and their HLA (human leukocyte antigen) restrictions is important for applications such as the design of cellular vaccines for HIV. Traditional methods for such identification are costly and time-consuming. Recently, a more expeditious laboratory technique using ELISpot assays has been developed that allows for rapid screening of specific responses. However, this assay does not directly provide information concerning the HLA restriction of a response, a critical piece of information for vaccine design. Thus, we introduce, apply, and validate a statistical model for identifying HLA-restricted epitopes from ELISpot data. By looking at patterns across a broad range of donors, in conjunction with our statistical model, we can determine (probabilistically) which of the HLA alleles are likely to be responsible for the observed reactivities. Additionally, we can provide a good estimate of the number of false positives generated by our analysis (i.e., the false discovery rate). This model allows us to learn about new HLA-restricted epitopes from ELISpot data in an efficient, cost-effective, and high-throughput manner. We applied our approach to data from donors infected with HIV and identified many potential new HLA restrictions. Among 134 such predictions, six were confirmed in the lab and the remainder could not be ruled as invalid. These results shed light on the extent of HLA class I promiscuity, which has significant implications for the understanding of HLA class I antigen presentation and vaccine development.

The ability of human immunodeficiency virus type 1 (HIV-1) to develop high levels of genetic diversity, and thereby acquire mutations to escape immune pressures, contributes to the difficulties in producing a vaccine. Possibly no single HIV-1 sequence can induce sufficiently broad immunity to protect against a wide variety of infectious strains, or block mutational escape pathways available to the virus after infection. The authors describe the generation of HIV-1 immunogens that minimizes the phylogenetic distance of viral strains throughout the known viral population (the center of tree [COT]) and then extend the COT immunogen by addition of a composite sequence that includes high-frequency variable sites preserved in their native contexts. The resulting COT(+) antigens compress the variation found in many independent HIV-1 isolates into lengths suitable for vaccine immunogens. It is possible to capture 62% of the variation found in the Nef protein and 82% of the variation in the Gag protein into immunogens of three gene lengths. The authors put forward immunogen designs that maximize representation of the diverse antigenic features present in a spectrum of HIV-1 strains. These immunogens should elicit immune responses against high-frequency viral strains as well as against most mutant forms of the virus.

We present a model for predicting HLA class I restricted CTL epitopes. In contrast to almost all other work in this area, we train a single model on epitopes from all HLA alleles and supertypes, yet retain the ability to make epitope predictions for specific HLA alleles. We are therefore able to leverage data across all HLA alleles and/or their supertypes, automatically learning what information should be shared and also how to combine allele-specific, supertype-specific, and global information in a principled way. We show that this leveraging can improve prediction of epitopes having HLA alleles with known supertypes, and dramatically increases our ability to predict epitopes having alleles which do not fall into any of the known supertypes. Our model, which is based on logistic regression, is simple to implement and understand, is solved by finding a single global maximum, and is more accurate (to our knowledge) than any other model. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Receiver Operating Characteristic (ROC) curves are a standard way to display the performance of a set of binary classifiers for all feasible ratios of the costs associated with false positives and false negatives. For linear classifiers, the set of classifiers is typically obtained by training once, holding constant the estimated slope and then varying the intercept to obtain a parameterized set of classifiers whose performances can be plotted in the ROC plane. We consider the alternative of varying the asymmetry of the cost function used for training. We show that the ROC curve obtained by varying both the intercept and the asymmetry, and hence the slope, always outperforms the ROC curve obtained by varying only the intercept. In addition, we present a path-following algorithm for the support vector machine (SVM) that can compute efficiently the entire ROC curve, and that has the same computational complexity as training a single classifier. Finally, we provide a theoretical analysis of the relationship between the asymmetric cost model assumed when training a classifier and the cost model assumed in applying the classifier. In particular, we show that the mismatch between the step function used for testing and its convex upper bounds, usually used for training, leads to a provable and quantifiable difference around extreme asymmetries.

Typical recommender systems adopt a static view of the recommendation process and treat it as a prediction problem. We argue that it is more appropriate to view the problem of generating recommendations as a sequential optimization problem and, consequently, that Markov decision processes (MDPs) provide a more appropriate model for recommender systems. MDPs introduce two benefits: they take into account the long-term effects of each recommendation and the expected value of each recommendation. To succeed in practice, an MDP-based recommender system must employ a strong initial model, must be solvable quickly, and should not consume too much memory. In this paper, we describe our particular MDP model, its initialization using a predictive model, the solution and update algorithm, and its actual performance on a commercial site. We also describe the particular predictive model we used which outperforms previous models. Our system is one of a small number of commercially deployed recommender systems. As far as we know, it is the first to report experimental analysis conducted on a real commercial site. These results validate the commercial value of recommender systems, and in particular, of our MDP-based approach.

I will discuss the use of graphical models for data mining. I will review key research areas including structure learning, variational methods, a relational modeling, and describe applications ranging from web traffic analysis to AIDS vaccine design.

1 Introduction The analysis and modeling of time-series data is an important area of research for many communities. In this paper, our goal is to identify models for continuousvalued time-series data that are useful for data mining in that they (1) can be learned eficiently from data, (2) support accurate predictions, and (3) are easy to interpret. To these ends, we describe an interpretable class of models that we call AutoRegressive Tree models, or ART models, that are a generalization of standard autoregressive (AR) models. We describe learning methods for ART models and compare these methods to those for alternative models. Our experiments, performed on 2,494 time-series data sets from the International Institute of Forecasters, demonstrate that ART models provide superior predictive accuracy. We concentrate on the problem of modeling the evolution of values of a continuous variable over time; that is, we model a univariate time series. The generalization to multivariate time-series analysis is straightforward and is discussed in Section 6.

By representing images and image prototypes by linear subspaces spanned by "tangent vectors" (derivatives of an image with respect to translation, rotation, etc.), impressive invariance to known types of uniform distortion can be built into feedforward discriminators. We describe a new probability model that can jointly cluster data and learn mixtures of nonuniform, smooth deformation fields. Our fields are based on low-frequency wavelets, so they use very few parameters to model a wide range of smooth deformations (unlike, e.g., factor analysis, which uses a large number of parameters to model deformations). In spirit, our ideas are most similar to the idea of separating content from style published by Tenenbaum and Freeman. However, our models do not need labeled data for training, and thus allow for unsupervised separation of appearance from deformation. We give results on handwritten digit recognition and face recognition.

We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we first partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for each cluster, we display these paths for users within that cluster. The clustering approach we employ is model based (as opposed to distance based) and partitions users according to the order in which they request Web pages. In particular, we cluster users by learning a mixture of first-order Markov models using the Expectation-Maximization algorithm. Our algorithm scales linearly with both number of users and number of clusters, and our implementation easily handles millions of users and thousands of clusters. In the paper, we describe the details of our technology and a tool based on it called WebCANVAS. We illustrate the use of our technology on user-traffic data from msnbc.com.

Companies that maintain web sites can make considerable revenue through advertising, and consequently attracting advertisers has become an important and competitive endeavor.A property that can attract advertisers is high clickthrough rates; and therefore companies can bene t from delivery systems that serve advertisements selectively to those visitors most likely to click.In order to satisfy contractual obligations, however, these systems must simultaneously perform inventory management.For example, if a company has agreed to serve a certain number of a particular advertisement, it must do so regardless of how likely it is to be clicked.In this paper, we describe how t o u s e a linear program to identify a schedule, based on known attributes of each visitor, that maximizes the expected number of clicks give n a l l o f t h e i n ventory-management constraints.We present experimental results using real data that demonstrate that a delivery schedule from our system realizes more clicks than a schedule that was hand constructed.

The intuition behind the construction of Bayesian networks and other graph-based representations of joint probability distributions from expert judgments is based on the assumed relationship between "connectedness" in the graphical model and "relatedness" among the variables involved. We show that several plausible definitions of relatedness do not adhere to such an equivalence. We then provide a definition of probabilistic relatedness that is closely related to connectedness in the graphical model and prove that the two concepts are equivalent whenever the model uses only propositional variables and assuming every combination of value assignment to these variables is feasible. We conjecture that the equivalence established holds also when these restrictions are lifted.

Graphical techniques for modeling the dependencies of random variables have been explored in a variety of different areas, including statistics, statistical physics, artificial intelligence, speech recognition, image processing, and genetics. Formalisms for manipulating these models have been developed relatively independently in these research communities. In this paper we explore hidden Markov models (HMMs) and related structures within the general framework of probabilistic independence networks (PINs). The paper presents a self-contained review of the basic principles of PINs. It is shown that the well-known forward-backward (F-B) and Viterbi algorithms for HMMs are special cases of more general inference algorithms for arbitrary PINs. Furthermore, the existence of inference and estimation algorithms for more general graphical models provides a set of analysis tools for HMM practitioners who wish to explore a richer class of HMM structures. Examples of relatively complex models to handle sensor fusion and coarticulation in speech recognition are introduced and treated within the graphical model framework to illustrate the advantages of the general approach.

We describe a decision-theoretic methodology for case-based reasoning in diagnosis and troubleshooting applications. The system utilizes a special-structure Bayesian network to represent diagnostic cases, with nodes representing issues, causes, and symptoms. Dirichlet distributions are assessed at knowledge acquisition time to indicate the strength of relationships between variables. During a diagnosis session, a relevant subnetwork is extracted from a Bayesian-network database that describes a very large number of diagnostic interactions and cases. The constructed network is used to make recommendations regarding possible repairs and additional observations, based on an estimate of expected repair costs. As cases are resolved, observations of issues, causes, symptoms, and the success of repairs are recorded. New variables are added to the database, and the probabilities associated with variables already in the database are updated. In this way, the inferential behavior of system adjusts to the characteristics of the target population of users. We show how these elements work together in a cycle of troubleshooting tasks, and describe some results from a pilot system implementation and deployment.

A Bayesian network is a probabilistic representation for uncertain relationships, which has proven to be useful for modeling real-world problems. When there are many potential causes of a given effect, however, both probability assessment and inference using a Bayesian network can be difficult. In this paper, we describe causal independence, a collection of conditional independence assertions and functional relationships that are often appropriate to apply to the representation of the uncertain interactions between causes and effect. We show how the use of causal independence in a Bayesian network can greatly simplify probability assessment as well as probabilistic inference.

We present a definition of cause and effect in terms of decision-theoretic primitives and thereby provide a principled foundation for causal reasoning. Our definition departs from the traditional view of causation in that causal assertions may vary with the set of decisions available. We argue that this approach provides added clarity to the notion of cause. Also in this paper, we examine the encoding of causal relationships in directed acyclic graphs. We describe a special class of influence diagrams, those in canonical form, and show its relationship to Pearl's representation of cause and effect. Finally, we show how canonical form facilitates counterfactual reasoning.

It is argued that decision analysts and expert-system designers have avoided the intractability of exact computation of the value of information by relying on a myopic assumption that only one additional test will be performed, even when there is an opportunity to make large number of observations. An alternative to the myopic analysis is presented. In particular, an approximate method for computing the value of information of a set of tests, which exploits the statistical properties of large samples, is given. The approximation is linear in the number of tests, in contrast with the exact computation, which is exponential in the number of tests. The approach is not as general as in a complete nonmyopic analysis, in which all possible sequences of observations are considered. In addition, the approximation is limited to specific classes of dependencies among evidence and to binary hypothesis and decision variables. Nonetheless, as demonstrated with a simple application, the approach can offer an improvement over the myopic analysis.>

Abstract We address the pragmatics of constructing normative expert systems and examine the influence diagram as a potential framework for representing knowledge in such systems. We introduce an extension of the influence‐diagram representation called asimilarity network.A similarity network is a tool for constructing large and complex influence diagrams. The representation allows a user to construct independent influence diagrams for subsets of a given domain. A valid influence diagram for the entire domain can then be constructed from the individual diagrams. Similarity networks represent forms of conditional independence that are not represented conveniently in an ordinary influence diagram. We discuss in detail one such conditional independence, calledsubset independence, and examine how similarity networks exploit this form of independence to facilitate the construction of an influence diagram. Also, we investigate the assessment of probability distributions for influence diagrams. We see that similarity networks exploit subset independence to simplify such probability assessments. We introduce a representation that is closely related to similarity networks, called apartition.This representation further exploits subset independence to simplify probability assessment. Finally, we examine a real‐world normative expert system for the diagnosis of lymph‐node pathology, called Pathfinder. The similarity‐network and partition representations played a crucial role in the construction of this expert system.