Graphical Models for Probabilistic and Causal Reasoning

Pearl, Judea

doi:10.1007/978-94-017-1735-9_12

Cited by 98 publications

(60 citation statements)

References 44 publications

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“…They combine an acyclic directed graph with a probability distribution functions [29]: the graphical model represents the set of probabilistic relationships among the collection of variables modelling the specific problem, whereas the probability function illustrates on each node the strength of these relationships or edges in the graph [30]. The research on BNs has mainly focused on systems with discrete variables, linear Gaussian models or combinations of both since, except for linear models, continuous variables pose a problem for Bayesian networks [31] due to the inherent difficulty of representing a continuous quantity by an estimated magnitude and a range of uncertainty [30]. We have tackled this issue by clustering the values of the load (the variable to be predicted) for each hour (using Agglomerative Hierarchical clustering [32]) and then, by calculating the average load for each of the clusters.…”

Section: A Modelsmentioning

confidence: 99%

Short-term load forecasting in air-conditioned non-residential Buildings

Penya

Borges

Agote

et al. 2011

2011 IEEE International Symposium on Industrial Electronics

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Abstract-Short-term load forecasting (STLF) has become an essential tool in the electricity sector. It has been classically object of vast research since energy load prediction is known to be nonlinear. In a previous work, we focused on non-residential building STLF, an special case of STLF where weather has negligible influence on the load. Now we tackle more modern buildings in which the temperature does alter its energy consumption. This is, we address here fully-HVAC (Heating, Ventilating, and Air Conditioning) ones. Still, in this problem domain, the forecasting method selected must be simple, without tedious trial-and-error configuring or parametrising procedures, work with scarce (or any) training data and be able to predict an evolving demand curve. Following our preceding research, we have avoided the inherent non-linearity by using the work day schedule as day-type classifier. We have evaluated the most popular STLF systems in the literature, namely ARIMA (autoregressive integrated moving average) time series and Neural networks (NN), together with an Autoregressive Model (AR) time series and a Bayesian network (BN), concluding that the autoregressive time series outperforms its counterparts and suffices to fulfil the addressed requirements, even in a 6 day-ahead horizon.

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Section: A Modelsmentioning

confidence: 99%

Short-term load forecasting in air-conditioned non-residential Buildings

Penya

Borges

Agote

et al. 2011

2011 IEEE International Symposium on Industrial Electronics

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“…Graphical models have shed light on the identification of causal effects in many settings (Dahlhaus and Eichler, 2003;Didelez, Kreiner and Keiding, 2010;Freedman, 2004;Greenland, Pearl and Robins, 1999;Pearl, 1995Pearl, , 1997Pearl, , 2000Robins, 2003;Tian and Pearl, 2002a;Vansteelandt, 2007) but have not yet been applied to settings with interference. In this paper, we describe how to draw causal diagrams representing the complex interdependencies among individuals in the presence of interference, and how to use those diagrams to determine what variables must be measured in order to identify different causal effects of interest.…”

mentioning

confidence: 99%

Causal Diagrams for Interference

Ogburn¹,

VanderWeele²

2014

Statist. Sci.

118

114

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Abstract. The term "interference" has been used to describe any setting in which one subject's exposure may affect another subject's outcome. We use causal diagrams to distinguish among three causal mechanisms that give rise to interference. The first causal mechanism by which interference can operate is a direct causal effect of one individual's treatment on another individual's outcome; we call this direct interference. Interference by contagion is present when one individual's outcome may affect the outcomes of other individuals with whom he comes into contact. Then giving treatment to the first individual could have an indirect effect on others through the treated individual's outcome. The third pathway by which interference may operate is allocational interference. Treatment in this case allocates individuals to groups; through interactions within a group, individuals may affect one another's outcomes in any number of ways. In many settings, more than one type of interference will be present simultaneously. The causal effects of interest differ according to which types of interference are present, as do the conditions under which causal effects are identifiable. Using causal diagrams for interference, we describe these differences, give criteria for the identification of important causal effects, and discuss applications to infectious diseases.

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“…, X p ) be a p-dimensional random vector. Graphical models allow to represent the set of conditional independencies among these random variables by a graph G = {V, E}, where V is the set of nodes associated to X and E ⊆ V × V is the set of ordered pairs, called edges, representing the conditional dependencies among the p random variables (Lauritzen (1996), Pearl (1997), Whittaker (2009)). The Gaussian graphical model is a member of this class of models based on the assumption that X follows a multivariate Gaussian distribution with expected value µ = (µ 1 , .…”

Section: The Censored Gaussian Graphical Modelmentioning

confidence: 99%

$\ell_1$ -Penalized censored Gaussian graphical model

2018

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Graphical lasso is one of the most used estimators for inferring genetic networks. Despite its diffusion, there are several fields in applied research where the limits of detection of modern measurement technologies make the use of this estimator theoretically unfounded, even when the assumption of a multivariate Gaussian distribution is satisfied. Typical examples are data generated by polymerase chain reactions and flow cytometer. The combination of censoring and high-dimensionality make inference of the underlying genetic networks from these data very challenging. In this article, we propose an $\ell_1$-penalized Gaussian graphical model for censored data and derive two EM-like algorithms for inference. We evaluate the computational efficiency of the proposed algorithms by an extensive simulation study and show that, when censored data are available, our proposal is superior to existing competitors both in terms of network recovery and parameter estimation. We apply the proposed method to gene expression data generated by microfluidic Reverse Transcription quantitative Polymerase Chain Reaction technology in order to make inference on the regulatory mechanisms of blood development. A software implementation of our method is available on github (https://github.com/LuigiAugugliaro/cglasso).

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Graphical Models for Probabilistic and Causal Reasoning

Cited by 98 publications

References 44 publications

Short-term load forecasting in air-conditioned non-residential Buildings

Short-term load forecasting in air-conditioned non-residential Buildings

Causal Diagrams for Interference

$\ell_1$ -Penalized censored Gaussian graphical model

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