| N. Littlestone. Learning quickly when irrelevant attributes abound: A new linearthreshold algorithm. Machine Learning, 2:285--318, 1988. |
....thus is of size (nm) ut We note that all of the lower bounds above apply to unate or Horn CNF DNF as well. This follows from the fact that monotone CNF DNF is a special case of unate or Horn CNF DNF and that the function f is outside the class (has size more than m in all cases) It is known [20] that the VC dimension of m term monotone DNF is (mn) so a result in [21] implies a (mn) lower bound on the number of queries to learn this class. Our result gives an alternative proof of this fact. For the Horn case we have a gap between the (mn) and O(m ) bounds on certi cate size, ....
N. Littlestone. Learning quickly when irrelevant attributes abound: A new linearthreshold algorithm. Machine Learning, 2:285-318, 1988.
....decrease its performance when irrelevant or redundant attributes arise. To overcome this problem, different approaches have been proposed to select the more relevant attributes that define a concept (or class) 4] Some works on attribute selection were the WINNOW algorithm proposed by Littlestone [16], the FOCUS algorithm proposed by Almuallim and Dietterich [3] and the Relief algorithm proposed by Kira and Rendell [11] All these algorithms have a common feature, they do not include the performance of the classifier as a measure to guide the selection of the attributes. John et al. 10] ....
N. Littlestone. Learning quickly when irrelevant attributes abound: A new linearthreshold algorithm. Machine Learning, 2:285--318, 1988.
....Number of Irrelevant Features Real world datasets may contain unequally relevant features. For example, medical domains usually contain more information than is actually required for distinguishing one disease from others. Most probably some of these features are not as relevant as the others [39]. The voting mechanism used in the FIL algorithms allows correct classifications in the presence of irrelevant features to a certain extent. To investigate the behaviors of the FIL algorithms in the presence of irrelevant features, we conducted a series of experiments. We generated six datasets ....
N. Littlestone, Learning Quickly When Irrelevant Attributes Abound: A New Linear-Threshold Algorithm, Machine Learning, 1:47-80, 1986.
....the convergence conditions in (16) that can be shown to hold for the t . There are many modi cations and enhancements that can be applied to gradient descent procedures, see [1] The Winnow approach that uses exponentiated gradient descent and multiplicative weight updating is described in [12]. Techniques of linear programming can also be used for solving the problem, see e.g. 26 [6] One advantage of gradient descent procedures lies in the fact, that learning works incrementally. This is especially usefully in the so called life long learning framework, when the distributions of the ....
N. Littlestone. Learning quickly when irrelevant attributes abound: A new linear-threshold algorithm. Machine Learning, 2(4):285-318, 1988.
....algorithms make a number of mistakes or queries which has only a sublinear dependence on the number of irrelevant attributes in the target function. Littlestone developed a polynomial time, log n attribute efficient algorithm for learning threshold functions in the mistake bound model [15]. Subsequently, Blum, Hellerstein, and Littlestone [4] considered the following general question: If a class of functions can be learned in polynomial time in a query or mistake bound model, can it be learned by a polynomial time I(n) attribute efficient algorithm in that model (In particular, ....
....are polynomial size boolean formulas of depth 3. We also show that polynomial size Boolean formulas of depth 2 are not sufficient for attributeefficient learning of this class. Littlestone s WINNOW algorithm learns this class log n attributeefficiently with hypotheses that are threshold functions [15]. Our techniques extend the results of Bshouty, Cleve, Kannan, and Tamon [7] on equivalence query learning with simple hypotheses. 2 Definitions We use log to denote the logarithm base 2, and ln to denote the natural logarithm. Let V n = fx 1 ; x 2 ; x n g. Let a 2 f0; 1g be an ....
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N. Littlestone. Learning quickly when irrelevant attributes abound: a new linear-threshold algorithm. Machine Learning, 2:285--318, 1988.
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N. Littlestone. Learning quickly when irrelevant attributes abound: A new linearthreshold algorithm. Machine Learning, 2:285--318, 1988.
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