Above are papers related to the following paper: [Paper_ID] Paper #128203. 	[Title] Learning Hierarchical Rule Sets [Abstract] We present an algorithm for learning sets of rules that are organized into up to k levels. Each level can contain an arbitrary number of rules "if c then l" where l is the class associated to the level and c is a concept from a given class of basic concepts. The rules of higher levels have precedence over the rules of lower levels and can be used to represent exceptions. As basic concepts we can use Boolean attributes in the infinite attribute space model, or certain concepts defined in terms of substrings. Given a sample of m examples, the algorithm runs in polynomial time and produces a consistent concept representation of size O((log m) k n k ), where n is the size of the smallest consistent representation with k levels of rules. This implies that the algorithm learns in the PAC model. The algorithm repeatedly applies the greedy heuristics for weighted set cover. The weights are obtained from approximate solutions to previous set cover problems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #128202. 	[Title] Learning rules with local exceptions [Abstract] We present a learning algorithm for rule-based concept representations called ripple-down rule sets. Ripple-down rule sets allow us to deal with the exceptions for each rule separately by introducing exception rules, exception rules for each exception rule etc. up to a constant depth. These local exception rules are in contrast to decision lists, in which the exception rules must be placed into a global ordering of the rules. The localization of exceptions makes it possible to represent concepts that have no decision list representation. On the other hand, decision lists with a constant number of alternations between rules for different classes can be represented by constant depth ripple-down rule sets with only a polynomial increase in size. Our algorithm is an Occam algorithm for constant depth ripple-down rule sets and, hence, a PAC learning algorithm. It is based on repeatedly applying the greedy approximation method for the weighted set cover problem to find good exception rule sets. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #10186. 	[Title] Learning Default Concepts [Abstract] Classical concepts, based on necessary and sufficient defining conditions, cannot classify logically insufficient object descriptions. Many reasoning systems avoid this limitation by using "default concepts" to classify incompletely described objects. We address the task of learning such default concepts from observational data. We model the underlying performance task | classifying incomplete examples | by a probabilistic process where random test examples are passed through a "blocker" that can hide object attributes from the classifier. We then address the task of learning accurate default concepts from random training examples. We survey the learning techniques that have been proposed for this task in the machine learning and knowledge representation literatures, investigate the relative merits of each, and show that a superior learning technique can be developed from well known statistical principles. Finally, we extend Valiant's pac-learning framework to this context and obtain a number of useful learnability results. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #2354. 	[Title] A Statistical Approach to Solving the EBL Utility Problem [Abstract] Many "learning from experience" systems use information extracted from problem solving experiences to modify a performance element PE, forming a new element PE 0 that can solve these and similar problems more efficiently. However, as transformations that improve performance on one set of problems can degrade performance on other sets, the new PE 0 is not always better than the original PE; this depends on the distribution of problems. We therefore seek the performance element whose expected performance, over this distribution, is optimal. Unfortunately, the actual distribution, which is needed to determine which element is optimal, is usually not known. Moreover, the task of finding the optimal element, even knowing the distribution, is intractable for most interesting spaces of elements. This paper presents a method, palo, that side-steps these problems by using a set of samples to estimate the unknown distribution, and by using a set of transformations to hill-climb to a local optimum. This process is based on a mathematically rigorous form of utility analysis: in particular, it uses statistical techniques to determine whether the result of a proposed transformation will be better than the original system. We also present an efficient way of implementing this learning system in the context of a general class of performance elements, and include empirical evidence that this approach can work effectively. fl Much of this work was performed at the University of Toronto, where it was supported by the Institute for Robotics and Intelligent Systems and by an operating grant from the National Science and Engineering Research Council of Canada. We also gratefully acknowledge receiving many helpful comments from William Cohen, Dave Mitchell, Dale Schuurmans and the anonymous referees. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1113852. 	[Title] Learning an Optimally Accurate Representational System [Abstract] The multiple extension problem arises because a default theory can use different subsets of its defaults to propose different, mutually incompatible, answers to some queries. This paper presents an algorithm that uses a set of observations to learn a credulous version of this default theory that is (essentially) "optimally accurate". In more detail, we can associate a given default theory with a set of related credulous theories R = fR i g, where each R i uses its own total ordering of the defaults to determine which single answer to return for each query. Our goal is to select the credulous theory that has the highest "expected accuracy", where each R i 's expected accuracy is the probability that the answer it produces to a query will correspond correctly to the world. Unfortunately, a theory's expected accuracy depends on the distribution of queries, which is usually not known. Moreover, the task of identifying the optimal R opt 2 R, even given that distribution information, is intractable. This paper presents a method, OptAcc, that sidesteps these problems by using a set of samples to estimate the unknown distribution, and by hill-climbing to a local optimum. In particular, given any parameters *; ffi &gt; 0, OptAcc produces an R oa 2 R whose expected accuracy is, with probability at least 1 ffi, within * of a local optimum. Appeared in ECAI Workshop on Theoretical Foundations of Knowledge Representation and Reasoning, Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #74749. 	[Title] Probably Approximately Optimal Derivation Strategies [Abstract] An inference graph can have many "derivation strategies", each a particular ordering of the steps involved in reducing a given query to a sequence of database retrievals. An "optimal strategy" for a given distribution of queries is a complete strategy whose "expected cost" is minimal, where the expected cost depends on the conditional probabilities that each requested retrieval succeeds, given that a member of this class of queries is posed. This paper describes the PAO algorithm that first uses a set of training examples to approximate these probability values, and then uses these estimates to produce a "probably approximately optimal" strategy | i.e., given any *; ffi &gt; 0, PAO produces a strategy whose cost is within * of the cost of the optimal strategy, with probability greater than 1 ffi. This paper also shows how to obtain these strategies in time polynomial in 1=*, 1=ffi and the size of the inference graph, for many important classes of graphs, including all and-or trees. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #137790. 	[Title] ON THE SAMPLE COMPLEXITY OF FINDING GOOD SEARCH STRATEGIES 2n trials of each undetermined experiment [Abstract] A satisficing search problem consists of a set of probabilistic experiments to be performed in some order, without repetitions, until a satisfying configuration of successes and failures has been reached. The cost of performing the experiments depends on the order chosen. Earlier work has concentrated on finding optimal search strategies in special cases of this model, such as search trees and and-or graphs, when the cost function and the success probabilities for the experiments are given. In contrast, we study the complexity of "learning" an approximately optimal search strategy when some of the success probabilities are not known at the outset. Working in the fully general model, we show that if n is the number of unknown probabilities, and C is the maximum cost of performing all the experiments, then Please summarise all the given information.

Paper #128203 has the title `Learning Hierarchical Rule Sets  
` and the abstract `We present an algorithm for learning sets of rules that are organized into up to k levels. Each level can contain an arbitrary number of rules "if c then l" where l is the class associated to the level and c is a concept from a given class of basic concepts. The rules of higher levels have precedence over the rules of lower levels and can be used to represent exceptions. As basic concepts we can use Boolean attributes in the infinite attribute space model, or certain concepts defined in terms of substrings. Given a sample of m examples, the algorithm runs in polynomial time and produces a consistent concept representation of size O((log m) k n k ), where n is the size of the smallest consistent representation with k levels of rules. This implies that the algorithm learns in the PAC model. The algorithm repeatedly applies the greedy heuristics for weighted set cover. The weights are obtained from approximate solutions to previous set cover problems.
`.
Question: Which category should Paper #128203 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #128203 has the title `Learning Hierarchical Rule Sets  
` and the abstract `We present an algorithm for learning sets of rules that are organized into up to k levels. Each level can contain an arbitrary number of rules "if c then l" where l is the class associated to the level and c is a concept from a given class of basic concepts. The rules of higher levels have precedence over the rules of lower levels and can be used to represent exceptions. As basic concepts we can use Boolean attributes in the infinite attribute space model, or certain concepts defined in terms of substrings. Given a sample of m examples, the algorithm runs in polynomial time and produces a consistent concept representation of size O((log m) k n k ), where n is the size of the smallest consistent representation with k levels of rules. This implies that the algorithm learns in the PAC model. The algorithm repeatedly applies the greedy heuristics for weighted set cover. The weights are obtained from approximate solutions to previous set cover problems.
`.
Question: Which category should Paper #128203 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