Long, P. and Tan, L. (1996). PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. In Proceedings of the 9th Annual Conference on Computational Learning Theory, pages 228--234.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....data, which is the only benchmark test data for multi instance learning until now, show that the iterated discrim APR algorithm achieves the best result, while the performance of popular supervised learning algorithms such as C4.5 decision tree and BP neural network is very poor. Long and Tan [8] described a polynomial time theoretical algorithm and showed that if the instances in the bags are independent drawn from product distribution, then the APR is PAC leamable. Auer et al. 3] showed that if the instances in the bags are not independent then APR learning under the multi instance ....

P.M. Long and L. Tan. "PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples," Machine Learning, vol.30, no. 1, pp.7-21, 1998.

....mapped to 1 by the target concept. Their model is primarily motivated by the problem of predicting whether a molecule would bind at a particular site. They argued empirically that axis parallel rectangles are good hypotheses for this and other similar learning problems. Subsequently, Long and Tan [65] described an efficient PAC algorithm for learning a single axis parallel box in Q d (where Q denotes the set of rationals) from multiple instance examples if each instance is drawn independently from a product distribution and d need not be constant. Auer et al. 11] gave an efficient PAC ....

P. M. Long and L. Tan. PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. In Proceedings of the Ninth Annual Conference on Computational Learning Theory, pages 228--234. ACM Press, New York, NY, 1996.

....be chosen and one function to be preferred to another. The description of object is often referred to as an instance of object . Recent research has shown that this traditional framework could be too limited for complex learning problems (Zucker and Ganascia 1994; Dietterich, Lathrop et al. 1996; Long and Tan 1996; Zucker and Ganascia 1996; Auer 1997) This is particularly the case when several descriptions of the same object are associated with the same result, baptized a multiple instance problem (MIP) by Dietterich et al. Dietterich, Lathrop et al. 1996) Thus the term multiple instance characterizes ....

....It should be added that the number # i can vary depending on object and that the suffix j of 1 to # i given to instances instance i,j is purely arbitrary. Note that in the limited theoretical research that has been done on the PAClearnability of this problem, the number vi is equal to a constant r (Long and Tan 1996; Auer 1997; Auer, Long et al. 1997; Blum and Kalai 1997) In the multiple instance framework, Dietterich et al. 1997) suggest that if the result of f is positive for an object it is because at least one of its instances ij has produced this result. If the result is negative it means that none ....

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Long, P. and L. Tan. 1996. PAC Learning Axis-aligned Rectangles with respect to Product Distributions from Multiple-instance Examples. Proceedings of the 9th Annual Conference on Computational Learning Theory, COLT' 96, Desenzano del Garda, Italy, ACM, Inc.

....description by generalizing training data. Dietterich et al. 1997) assumed that the classifier could be represented as an axis parallel rectangle, and developed several algorithms to learn such a rectangle in the musk drug activity prediction application. Following Dietterich s original work, Long Tan (1996) showed from theoretical aspect that it is possible to PAC learn an axis parallel concept from multiple instance examples. Auer (1997) also focused on theoretical research and presented the MULTINST algorithm to efficiently learn axis parallel concept. Maron Lozano Prez (1998) described a new ....

Long, P.M., & Tan, L. (1996). PAC-learning axis aligned rectangles with respect to product distributions from multiple-instance examples. Proceedings of the Ninth Annual Conference on Computational Learning Theory (pp. 228--234). New York: ACM Press.

....is a musk molecule, yet as they indicated themselves, this setting is atypical in that for most drug discovery applications a real valued a#nity value would be used as the label. Recently, there has a been a significant amount of work in studying the multiple instance model (Wang and Zucker, 2000; Long and Tan, 1998; Auer et al. 1998; Auer, 1997; Goldman et al. 2000a; Maron and Lozano Perez, 1998; Maron, 1998; Maron and Ratan, 1998; Blum and Kalai, 1998) yet al..l of this work has only considered boolean classification. One of the contributions of our work is initiating the study of a real valued ....

....only a#ects the application of the virtual weights technique, which becomes significantly more complicated when the maximum function is used. 4. Related Learning Models Recently, there has a been a significant amount of work in studying the multiple instance model (Wang and Zucker, 2000; Long and Tan, 1998; Auer et al. 1998; Auer, 1997; Maron and Lozano Perez, 1998; Maron, 1998; Maron and Ratan, 1998; Blum and Kalai, 1998) in the boolean domain. Most of this work addresses the problem of learning a multiple instance concept defined by a single axis aligned box. There also has been some work on ....

Long, P. M. and L. Tan: 1998, `PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples'. Machine Learning 30, 7--21.

....is primarily motivated by the problem of predicting whether a molecule would bind at a particular site. They argued empirically that axis parallel rectangles are good hypotheses for this and other similar learning problems. Subsequently, multi instance learning has been extensively studied (e.g. Long Tan, 1998; Auer et al. 1997; Auer, 1997; Blum Kalai, 1998; Maron LozanoP erez, 1998; Maron, 1998; Maron Ratan, 1998; Blum Kalai, 1998) In several of these papers, the target concept is a single axis parallel box and a bag is classified as positive if at least one of the points in the bag is ....

Long, P. M., & Tan, L. (1998). PAC learning axis-aligned rectangles with respect to product distributions from multipleinstance examples. Machine Learning, 30, 7--21.

....examples [10] In the multiple instance learning model, the target concept is a boolean function, each example is a collection of instances, and the example (collection) is classified as positive iff at least one of its elements is mapped to positive by the target concept. Long and Tan [27] described an efficient PAC algorithm for learning a single axisparallel box in Q d from multiple instance examples under a product distribution where Q denotes the set of rationals and d need not be constant. Auer et al. 4] gave an efficient PAC algorithm for learning a single axis parallel ....

....mapped to 1 by the target concept. Their model is primarily motivated by the problem of predicting whether a molecule would bind at a particular site. They argued empirically that axis parallel rectangles are good hypotheses for this and other similar learning problems. Subsequently, Long and Tan [27] described an efficient PAC algorithm for learning a single axis parallel box in Q d (where Q denotes the set of rationals) from multiple instance examples if each instance is drawn independently from a product distribution and d need not be constant. Auer et al. 4] gave an efficient PAC ....

Philip M. Long and Lei Tan. PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. In Proc. 9th Annu. Conf. on Comput. Learning Theory, pages 228--234. ACM Press, New York, NY, 1996.

....n m = f0; Delta Delta Delta Delta; mg n , n arbitrary, and F is any class of negative robustly learnable feature class. Alternatively, one can view this result as a generalization of the work of Chen and Maass [CM94] on learning boxes. The earlier results on learning boxes and union of boxes [Aue93, BGGM94, CM94, FGMP94, Maa94, Ame95, BGM95, MW95, LT96, FK96] either assumes the dimension is constant or the number of boxes in the target is bounded by some constant. Our class of monotone disjunctions of (B n m ; F) indicator feature pairs can be viewed as a stack of arbitrary number of arbitrary dimensional boxes of decreasing base volume . The ....

Philip M. Long and Lei Tan. Pac learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. In Proceedings of the Ninth Annual ACM Conference on Computational Learning Theory, pages 228--234. ACM Press, New York, NY, 1996.

....examples [4] In the multiple instance learning model, the target concept is a boolean function and each example is a collection of instances and the example (collection) is classified as positive iff at least one of its elements is mapped to positive by the target concept. Long and Tan [17] described an efficient PAC algorithm for learning a single axis parallel box in Q d from multiple instance examples under a product distribution where Q denotes the set of rationals and d need not be constant. In their paper, each example is classified as positive if at least one of its points ....

....mapped to 1 by the target concept. Their model is primarily motivated by the problem of predicting whether a molecule would bind at a particular site. They argued empirically that axis parallel rectangles are good hypotheses for this and other similar learning problems. Subsequently, Long and Tan [17] described an efficient PAC algorithm for learning a single axis parallel box in Q d from multiple instance examples under a product distribution where Q denotes the set of rationals and d need not be constant. In their paper, each example is classified as positive if at least one of its points ....

P. Long and L. Tan. PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. In Proceedings of the Ninth Annual ACM Conference on Computational Learning Theory, pages 228--234. ACM Press, New York, NY, 1996.

....Formally, given a concept c over instance space X, let us define c multi over X as: c multi (x 1 ; x 2 ; x r ) c(x 1 ) c(x 2 ) c(x r ) Similarly, given a concept class C, let C multi = fc multi : c 2 Cg. We will call x = x 1 ; x r ) an r example or r instance. Long and Tan (1996) give a natural PAC style formalization of the multiple instance example learning problem, which we may phrase as follows: 2 A. BLUM AND A. KALAI Definition 1. An algorithm A PAC learns concept class C from multiple instance examples if for any r 0, and any distribution D over single ....

....same distribution D. Previous work on learning from multiple instance examples has focused on the problem of learning d dimensional axis parallel rectangles. Dietterich et al. 1997) present several algorithms and describe experimental results of their performance on a molecule binding domain. Long and Tan (1996) describe an algorithm that learns axis parallel rectangles in the above PAC setting, under the condition that D is a product distribution (i.e. the coordinates of each single instance are chosen independently) with sample complexity O(d 2 r 6 =ffl 10 ) Auer et al. 1997) give an ....

Long, P. and Tan, L. (1996). PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. In Proceedings of the 9th Annual Conference on Computational Learning Theory, pages 228--234.

....is supposed to output a hypothesis H R n which is close to the target rectangle B, in the sense that it is likely to correctly classify another r instance example as to whether any of its instances are in B. This problem has previously been studied in Valiant s PAC framework [36] In [26], it was proved that if all instances are drawn independently from a product distribution on R n , the target rectangle can be learned from r instance examples in O i n 5 r 12 ffl 20 j time, where ffl and ffi are accuracy and confidence parameters. In this paper we present a new ....

....similar results in the statistical query model; applying the results of Kearns [21] this implies that it can be made robust against classification noise. Blum and Kalai [8] recently improved on these results. Our algorithm is substantially different from those previously proposed for this problem [12, 26]. We believe that a variant of our algorithm will prove useful in practice. Initial empirical results [7] support this belief: a straightforward implementation of a variant of our algorithm performs competitively on datasets used in [12] Our analysis still requires that all instances are drawn ....

P.M. Long and L. Tan. PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. Machine Learning, 30:1--22, 1998.

....is supposed to output a hypothesis H R n which is close to the target rectangle B, in the sense that it is likely to correctly classify another r instance example as to whether any of its instances are in B. This problem has previously been studied in Valiant s PAC framework [34] In [25], it was proved that if all instances are drawn independently from a product distribution on R n , the target rectangle can be learned from r instance examples in O i n 5 r 12 ffl 20 log 2 nr fflffi j time, where ffl and ffi are accuracy and confidence parameters. In this paper we ....

....This algorithm can be modified slightly to achieve similar results in the statistical query model; applying the results of Kearns [20] this implies that it can be made robust against classification noise. Our algorithm is substantially different from those previously proposed for this problem [11, 25]. We believe that a variant of our algorithm will prove useful in practice. Initial empirical results [7] support this belief: a straightforward implementation of a variant of our algorithm performs competitively on datasets used in [11] Our analysis still requires that all instances are drawn ....

P.M. Long and L. Tan. PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. The 1996 Conference on Computational Learning Theory, pages 228--234, 1996.

No context found.

Long, P. and Tan, L. (1996). PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. In Proceedings of the 9th Annual Conference on Computational Learning Theory, pages 228--234.

No context found.

P.M. Long and L. Tan. PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. Machine Learning, vol.30, no.1, pp.7-- 21, 1998.

No context found.

Long, P.M., Tan, L.: PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. Machine Learning 30 (1998) 7--21

No context found.

P.M. Long and L. Tan. PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. Machine Learning, vol.30, no.1, pp.7-- 21, 1998.

No context found.

Long, P.M., Tan, L.: PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. Machine Learning 30 (1998) 7--21

No context found.

P. M. Long and L. Tan. PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. In Proceedings of the Ninth Annual Conference on Computational Learning Theory, pages 228--234. ACM Press, New York, NY, 1996.

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