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Dependency networks have advantages and disadvantages with respect to
Bayesian networks. In particular, they are easier to parameterize from data, as there are efficient algorithms for learning both the structure and probabilities of a dependency network from data. Such algorithms are not available
1585:
has many variables. So, the law of total probability along with the independencies encoded in a dependency network can be used to decompose the inference task into a set of inference tasks on single variables. This approach comes with the advantage that some terms may be obtained by direct lookup,
223:
of a node is the set of parents and children of that node, together with the children's parents. The values of the parents and children of a node evidently give information about that node. However, its children's parents also have to be included in the Markov blanket, because they can be used to
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Two important tasks in a dependency network are to learn its structure and probabilities from data. Essentially, the learning algorithm consists of independently performing a probabilistic regression or classification for each variable in the domain. It comes from observation that the local
825:
1037:, we independently estimate its local distribution from data using a classification algorithm, even though it is a distinct method for each variable. Here, we will briefly show how probabilistic decision trees are used to estimate the local distributions. For each variable
253:
Consistent dependency networks and Markov networks have the same representational power. Nonetheless, it is possible to construct non-consistent dependency networks, i.e., dependency networks for which there is no compatible valid
622:
861:. Dependency networks learned using large data sets with large sample sizes will almost always be consistent. A non-consistent network is a network for which there is no joint probability distribution compatible with the pair
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for
Bayesian networks, for which the problem of determining the optimal structure is NP-hard. Nonetheless, a dependency network may be more difficult to construct using a knowledge-based approach driven by expert-knowledge.
990:, which can be estimated by any number of classification or regression techniques, such as methods using a probabilistic decision tree, a neural network or a probabilistic support-vector machine. Hence, for each variable
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2364:(CF), which is the task of predicting preferences. Dependency networks are a natural model class on which to base CF predictions, once an algorithm for this task only needs estimation of
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207:, DNs may contain cycles. Each node is associated to a conditional probability table, which determines the realization of the random variable given its parents.
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1175:, the search algorithm begins with a singleton root node without children. Then, each leaf node in the tree is replaced with a binary split on some variable
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Another class of useful applications for dependency networks is related to data visualization, that is, visualization of predictive relationships.
2450:
Predicting what product a person will buy based on products he or she has already purchased and/or dropped into his or her shopping basket.
820:{\displaystyle p(x_{i}\mid \mathbf {pa_{i}} )=p(x_{i}\mid x_{1},\ldots ,x_{i-1},x_{i+1},\ldots ,x_{n})=p(x_{i}\mid \mathbf {x} -{x_{i}}).}
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893:. In that case, there is no joint probability distribution that satisfies the independence relationships subsumed by that pair.
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203:, wherein each vertex (node) corresponds to a random variable and each edge captures dependencies among variables. Unlike
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The dependency network is consistent in the sense that each local distribution can be obtained from the joint distribution
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to produce recommendations. In particular, these estimates may be obtained by a direct lookup in a dependency network.
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is small, then many iterations are required for an accurate probability estimate. Another approach for estimating
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In addition to the applications to probabilistic inference, the following applications are in the category of
1374:. A naive approach for this uses an ordered Gibbs sampler, an important difficulty of which is that if either
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HECKERMAN, David; MAXWELL C., David; MEEK, Christopher; ROUNTHWAITE, Robert; KADIE, Carl (October 2000).
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A probabilistic inference is the task in which we wish to answer probabilistic queries of the form
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Predicting what news stories a person is interested in based on other stories he or she read;
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617:{\displaystyle \mathbf {Pa_{i}} \subseteq (X_{1},\ldots ,X_{i-1},X_{i+1},\ldots ,X_{n})}
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for a node is simply its adjacent (or neighboring) nodes. In a dependency network, the
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Predicting what web pages a person will access based on his or her history on the site;
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Predicting what movies a person will like based on his or her ratings of movies seen;
2485:"Dependency Networks for Inference, Collaborative Filtering, and Data Visualization"
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is a cyclic directed graph, where each of its nodes corresponds to a variable in
1370:. One of the alternatives for performing probabilistic inference is using
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is a set of conditional probability distributions. The parents of node
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2114:{\displaystyle p(x_{i}|\mathbf {p} ):=p(x_{i}|\mathbf {pa_{i}} )}
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are the input variables. To learn a decision tree structure for
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A consistent dependency network for a set of random variables
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56:
15:
1237:, until no more replacements increase the score of the tree.
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You can see below an algorithm that can be used for obtain
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is small is to use modified ordered Gibbs sampler, where
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in a dependency network is the conditional distribution
2507:"Large-Sample Learning of Bayesian Networks is NP-Hard"
258:. Markov networks, in contrast, are always consistent.
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that satisfy the following independence relationships
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may be too technical for most readers to understand
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2128:Use a modified ordered Gibbs sampler to determine
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2430:{\displaystyle p(x_{i}=1|\mathbf {x} -{x_{i}}=0)}
1607:
1086:, a probabilistic decision tree is learned where
1348:(the 'input' variables) are disjoint subsets of
319:{\textstyle \mathbf {X} =(X_{1},\ldots ,X_{n})}
1800:(* the processed and conditioning variables *)
983:{\displaystyle p(x_{i}|\mathbf {x} -{x_{i}})}
236:for a node is simply the set of its parents.
8:
1681:{\displaystyle \mathbf {z} \in \mathbf {Z} }
1651:{\displaystyle \mathbf {y} \in \mathbf {Y} }
1876:{\displaystyle \mathbf {U} \neq \emptyset }
240:Dependency network versus Bayesian networks
50:Learn how and when to remove these messages
249:Dependency networks versus Markov networks
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180:Learn how and when to remove this message
162:Learn how and when to remove this message
146:, without removing the technical details.
107:Learn how and when to remove this message
2306:Returns the product of the conditionals
224:explain away the node in question. In a
70:This article includes a list of general
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2536:
2525:
1586:thereby avoiding some Gibbs sampling.
2345:{\displaystyle p(x_{i}|\mathbf {p} )}
2295:{\displaystyle \mathbf {p:=p} +x_{i}}
2253:{\displaystyle \mathbf {P:=P} +X_{i}}
2211:{\displaystyle \mathbf {U:=U} -X_{i}}
2167:{\displaystyle p(x_{i}|\mathbf {p} )}
1914:{\displaystyle X_{i}\in \mathbf {U} }
1472:{\displaystyle p(\mathbf {y\mid z} )}
1404:{\displaystyle p(\mathbf {y\mid z} )}
1275:{\displaystyle p(\mathbf {y\mid z} )}
144:make it understandable to non-experts
7:
2492:Journal of Machine Learning Research
1870:
1230:{\displaystyle \mathbf {X} -X_{i}}
1141:{\displaystyle \mathbf {X} -X_{i}}
76:it lacks sufficient corresponding
14:
1621:{\displaystyle p(\mathbf {y|z} )}
897:Structure and parameters learning
503:{\displaystyle \mathbf {Pa_{i}} }
31:This article has multiple issues.
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1823:{\displaystyle \mathbf {p:=z} }
1793:{\displaystyle \mathbf {P:=Z} }
1770:(* the unprocessed variables *)
1763:{\displaystyle \mathbf {U:=Y} }
1503:{\displaystyle p(\mathbf {z} )}
1435:{\displaystyle p(\mathbf {z} )}
854:{\displaystyle p(\mathbf {x} )}
350:{\displaystyle p(\mathbf {x} )}
39:or discuss these issues on the
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1531:{\displaystyle \mathbf {Z=z} }
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1282:, given a graphical model for
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256:joint probability distribution
1:
2464:Relational dependency network
1628:for a particular instance of
2025:{\displaystyle \mathbf {P} }
1845:{\displaystyle \mathbf {P} }
1725:{\displaystyle \mathbf {Z} }
1703:{\displaystyle \mathbf {Y} }
1578:{\displaystyle \mathbf {Y} }
1556:{\displaystyle \mathbf {y} }
1363:{\displaystyle \mathbf {X} }
1341:{\displaystyle \mathbf {Z} }
1319:{\displaystyle \mathbf {Y} }
1297:{\displaystyle \mathbf {X} }
1079:{\displaystyle \mathbf {X} }
424:{\displaystyle \mathbf {X} }
1113:is the target variable and
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902:distribution for variable
2505:HECKERMAN, David (2012).
1326:(the 'target' variables)
193:Dependency networks (DNs)
1541:It may also happen that
326:with joint distribution
2362:Collaborative Filtering
1948:has no more parents in
1241:Probabilistic Inference
91:more precise citations.
2535:Cite journal requires
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2003:{\displaystyle X}
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1961:{\displaystyle U}
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444:{\displaystyle P}
402:{\displaystyle G}
205:Bayesian networks
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197:graphical models
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2528:cite journal
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2356:Applications
1737:Algorithm 1:
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152:January 2020
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97:January 2020
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33:Please help
30:
89:introducing
2566:Algorithms
2555:Categories
2470:References
1921:such that
1017:in domain
478:, denoted
357:is a pair
262:Definition
72:references
36:improve it
2519:1212.2468
2404:−
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533:⊆
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42:talk page
2458:See also
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1886:Choose
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138:Please
85:improve
1855:While
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74:, but
2514:arXiv
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