Above are papers related to the following paper: [Paper_ID] Paper #4637. 	[Title] Learning to model sequences generated by switching distributions [Abstract] We study efficient algorithms for solving the following problem, which we call the switching distributions learning problem. A sequence S = 1 2 : : : n , over a finite alphabet S is generated in the following way. The sequence is a concatenation of K runs, each of which is a consecutive subsequence. Each run is generated by independent random draws from a distribution ~p i over S, where ~p i is an element in a set of distributions f~p 1 ; : : : ; ~p N g. The learning algorithm is given this sequence and its goal is to find approximations of the distributions ~p 1 ; : : : ; ~p N , and give an approximate segmentation of the sequence into its constituting runs. We give an efficient algorithm for solving this problem and show conditions under which the algorithm is guaranteed to work with high probability. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #10177. 	[Title] Learning in the Presence of Malicious Errors [Abstract] In this paper we study an extension of the distribution-free model of learning introduced by Valiant [23] (also known as the probably approximately correct or PAC model) that allows the presence of malicious errors in the examples given to a learning algorithm. Such errors are generated by an adversary with unbounded computational power and access to the entire history of the learning algorithm's computation. Thus, we study a worst-case model of errors. Our results include general methods for bounding the rate of error tolerable by any learning algorithm, efficient algorithms tolerating nontrivial rates of malicious errors, and equivalences between problems of learning with errors and standard combinatorial optimization problems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4804. 	[Title] Toward Efficient Agnostic Learning [Abstract] In this paper we initiate an investigation of generalizations of the Probably Approximately Correct (PAC) learning model that attempt to significantly weaken the target function assumptions. The ultimate goal in this direction is informally termed agnostic learning, in which we make virtually no assumptions on the target function. The name derives from the fact that as designers of learning algorithms, we give up the belief that Nature (as represented by the target function) has a simple or succinct explanation. We give a number of positive and negative results that provide an initial outline of the possibilities for agnostic learning. Our results include hardness results for the most obvious generalization of the PAC model to an agnostic setting, an efficient and general agnostic learning method based on dynamic programming, relationships between loss functions for agnostic learning, and an algorithm for a learning problem that involves hidden variables. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #164. 	[Title] Learning polynomials with queries: The highly noisy case  task for the case when F [Abstract] Given a function f mapping n-variate inputs from a finite field F into F , we consider the task of reconstructing a list of all n-variate degree d polynomials which agree with f on a tiny but non-negligible fraction, ffi, of the input space. We give a randomized algorithm for solving this task which accesses f as a black box and runs in time polynomial in 1 d=jF j). For the special case when d = 1, we solve this problem for all * def jF j &gt; 0. In this case the running time of our algorithm is bounded by a polynomial in 1 * ; n and exponential in d. Our algorithm generalizes a previously known algorithm, due to Goldreich and Levin, that solves this Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12198. 	[Title] Exact Identification of Read-once Formulas Using Fixed Points of Amplification Functions [Abstract] In this paper we describe a new technique for exactly identifying certain classes of read-once Boolean formulas. The method is based on sampling the input-output behavior of the target formula on a probability distribution that is determined by the fixed point of the formula's amplification function (defined as the probability that a 1 is output by the formula when each input bit is 1 independently with probability p). By performing various statistical tests on easily sampled variants of the fixed-point distribution, we are able to efficiently infer all structural information about any logarithmic-depth formula (with high probability). We apply our results to prove the existence of short universal identification sequences for large classes of formulas. We also describe extensions of our algorithms to handle high rates of noise, and to learn formulas of unbounded depth in Valiant's model with respect to specific distributions. Most of this research was carried out while all three authors were at MIT Laboratory for Computer Science with support provided by ARO Grant DAAL03-86-K-0171, DARPA Contract N00014-89-J-1988, NSF Grant CCR-88914428, and a grant from the Siemens Corporation. R. Schapire received additional support from AFOSR Grant 89-0506 while at Harvard University. S. Goldman is currently supported in part by a G.E. Foundation Junior Faculty Grant and NSF Grant CCR-9110108. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12169. 	[Title] Learning With Unreliable Boundary Queries [Abstract] We introduce a model for learning from examples and membership queries in situations where the boundary between positive and negative examples is somewhat ill-defined. In our model, queries near the boundary of a target concept may receive incorrect or "don't care" responses, and the distribution of examples has zero probability mass on the boundary region. The motivation behind our model is that in many cases the boundary between positive and negative examples is complicated or "fuzzy." However, one may still hope to learn successfully, because the typical examples that one sees do not come from that region. We present several positive results in this new model. We show how to learn the intersection of two arbitrary halfspaces when membership queries near the boundary may be answered incorrectly. Our algorithm is an extension of an algorithm of Baum [7, 6] that learns the intersection of two halfspaces whose bounding planes pass through the origin in the PAC-with-membership-queries model. We also describe algorithms for learning several subclasses of monotone DNF formulas. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1119471. 	[Title] Learning from Incomplete Boundary Queries Using Split Graphs and Hypergraphs (Extended Abstract) [Abstract] We consider learnability with membership queries in the presence of incomplete information. In the incomplete boundary query model introduced by Blum et al. [7], it is assumed that membership queries on instances near the boundary of the target concept may receive a "don't know" answer. We show that zero-one threshold functions are efficiently learnable in this model. The learning algorithm uses split graphs when the boundary region has radius 1, and their generalization to split hypergraphs (for which we give a split-finding algorithm) when the boundary region has constant radius greater than 1. We use a notion of indistinguishability of concepts that is appropriate for this model. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #989397. 	[Title] PAC Learning Intersections of Halfspaces with Membership Queries (Extended Abstract) [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #67415. 	[Title] On the Learnability of Discrete Distributions (extended abstract) [Abstract]  Please summarise all the given information.

Paper #4637 has the title `Learning to model sequences generated by switching distributions  
` and the abstract `We study efficient algorithms for solving the following problem, which we call the switching distributions learning problem. A sequence S = 1 2 : : : n , over a finite alphabet S is generated in the following way. The sequence is a concatenation of K runs, each of which is a consecutive subsequence. Each run is generated by independent random draws from a distribution ~p i over S, where ~p i is an element in a set of distributions f~p 1 ; : : : ; ~p N g. The learning algorithm is given this sequence and its goal is to find approximations of the distributions ~p 1 ; : : : ; ~p N , and give an approximate segmentation of the sequence into its constituting runs. We give an efficient algorithm for solving this problem and show conditions under which the algorithm is guaranteed to work with high probability.
`.
Question: Which category should Paper #4637 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #4637 has the title `Learning to model sequences generated by switching distributions  
` and the abstract `We study efficient algorithms for solving the following problem, which we call the switching distributions learning problem. A sequence S = 1 2 : : : n , over a finite alphabet S is generated in the following way. The sequence is a concatenation of K runs, each of which is a consecutive subsequence. Each run is generated by independent random draws from a distribution ~p i over S, where ~p i is an element in a set of distributions f~p 1 ; : : : ; ~p N g. The learning algorithm is given this sequence and its goal is to find approximations of the distributions ~p 1 ; : : : ; ~p N , and give an approximate segmentation of the sequence into its constituting runs. We give an efficient algorithm for solving this problem and show conditions under which the algorithm is guaranteed to work with high probability.
`.
Question: Which category should Paper #4637 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