Above are papers related to the following paper: [Paper_ID] Paper #1133390. 	[Title] Decision Trees: Equivalence and Propositional Operations [Abstract] For the well-known concept of decision trees as it is used for inductive inference we study the natural concept of equivalence: two decision trees are equivalent if and only if they represent the same hypothesis. We present a simple efficient algorithm to establish whether two decision trees are equivalent or not. The complexity of this algorithm is bounded by the product of the sizes of both decision trees. The hypothesis represented by a decision tree is essentially a boolean function, just like a proposition. Although every boolean function can be represented in this way, we show that disjunctions and conjunctions of decision trees can not efficiently be represented as decision trees, and simply shaped propositions may require exponential size for representation as de cision trees. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #8961. 	[Title] Machine Learning Research: Four Current Directions [Abstract] Machine Learning research has been making great progress is many directions. This article summarizes four of these directions and discusses some current open problems. The four directions are (a) improving classification accuracy by learning ensembles of classifiers, (b) methods for scaling up supervised learning algorithms, (c) reinforcement learning, and (d) learning complex stochastic models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1103610. 	[Title] A hierarchical ensemble of decision trees applied to classifying data from a psychological experiment [Abstract] Classifying by hand complex data coming from psychology experiments can be a long and difficult task, because of the quantity of data to classify and the amount of training it may require. One way to alleviate this problem is to use machine learning techniques. We built a classifier based on decision trees that reproduces the classifying process used by two humans on a sample of data and that learns how to classify unseen data. The automatic classifier proved to be more accurate, more constant and much faster than classification by hand. Please summarise all the given information.

Paper #1133390 has the title `Decision Trees: Equivalence and Propositional Operations  
` and the abstract `For the well-known concept of decision trees as it is used for inductive inference we study the natural concept of equivalence: two decision trees are equivalent if and only if they represent the same hypothesis. We present a simple efficient algorithm to establish whether two decision trees are equivalent or not. The complexity of this algorithm is bounded by the product of the sizes of both decision trees. The hypothesis represented by a decision tree is essentially a boolean function, just like a proposition. Although every boolean function can be represented in this way, we show that disjunctions and conjunctions of decision trees can not efficiently be represented as decision trees, and simply shaped propositions may require exponential size for representation as de cision trees.
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Question: Which category should Paper #1133390 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1133390 has the title `Decision Trees: Equivalence and Propositional Operations  
` and the abstract `For the well-known concept of decision trees as it is used for inductive inference we study the natural concept of equivalence: two decision trees are equivalent if and only if they represent the same hypothesis. We present a simple efficient algorithm to establish whether two decision trees are equivalent or not. The complexity of this algorithm is bounded by the product of the sizes of both decision trees. The hypothesis represented by a decision tree is essentially a boolean function, just like a proposition. Although every boolean function can be represented in this way, we show that disjunctions and conjunctions of decision trees can not efficiently be represented as decision trees, and simply shaped propositions may require exponential size for representation as de cision trees.
`.
Question: Which category should Paper #1133390 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Theory