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Learning polynomials with queries: The highly noisy case
, 1995
"... Given a function f mapping nvariate inputs from a finite Kearns et. al. [21] (see also [27, 28, 22]). In the setting of agfieldFintoF, we consider the task of reconstructing a list nostic learning, the learner is to make no assumptions regarding of allnvariate degreedpolynomials which agree withf ..."
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Cited by 97 (17 self)
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the examples. Therefore the black box and runs in time polynomial in1;nand exponential in best explanation may account for only part of the phenomena. d, provided is(pd=jFj). For the special case whend=1, In some situations, when the phenomena appears very irregular, we solve this problem for jFj>0
Sampling Signals with Finite Rate of Innovation: The Noisy Case
, 2002
"... In [1] a sampling theorem for a certain class of signals with finite rate of innovation (which includes for example stream of Diracs) has been developed. In essence, such non bandlimited signals can be sampled at or above the rate of innovation. In the present paper, we consider the case of such sig ..."
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Cited by 2 (1 self)
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In [1] a sampling theorem for a certain class of signals with finite rate of innovation (which includes for example stream of Diracs) has been developed. In essence, such non bandlimited signals can be sampled at or above the rate of innovation. In the present paper, we consider the case
Calibrating noise to sensitivity in private data analysis
 In Proceedings of the 3rd Theory of Cryptography Conference
, 2006
"... Abstract. We continue a line of research initiated in [10, 11] on privacypreserving statistical databases. Consider a trusted server that holds a database of sensitive information. Given a query function f mapping databases to reals, the socalled true answer is the result of applying f to the datab ..."
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Cited by 649 (60 self)
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to the database. To protect privacy, the true answer is perturbed by the addition of random noise generated according to a carefully chosen distribution, and this response, the true answer plus noise, is returned to the user. Previous work focused on the case of noisy sums, in which f =P i g(xi), where xi denotes
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 674 (15 self)
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and ap proximately 4000 findin nodes, with a number of ob served findings that varies per case. Due to the form of the noisyor CPTs the complexity of inference is ex ponential in the number of positive findings Results Initial experiments The experimental protocol for the PYRAMID network was as follows
Finding Genes by CaseBased Reasoning in the Presence of Noisy Case Boundaries
 Proceedings of the 1991 DARPA Workshop on CaseBased Reasoning
, 1991
"... Effectively using previous cases requires that a reasoner first match, in some fashion, the current problem against a large library of stored cases. One largely unaddressed task in casebased reasoning is the process of parsing continuous input into discrete cases. If this parsing is not done accura ..."
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Cited by 9 (0 self)
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accurately, the relevant previous cases may not be found and the advantages of casebased problem solving will be lost. Parsing the data into cases is further complicated when the input data is noisy. This paper presents an approach to applying the casebased paradigm in the presence of noisy case boundaries
CaseBased Reasoning with Noisy Case Boundaries: An Application in Molecular Biology
, 1990
"... This paper presents a method for performing casebased reasoning in the presence of noisy case boundaries. The task domain is molecular biology, and we have successfully used our technique to find genes in noisy DNA sequences. The following sections provide a brief introduction to molecular biology ..."
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Cited by 2 (1 self)
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This paper presents a method for performing casebased reasoning in the presence of noisy case boundaries. The task domain is molecular biology, and we have successfully used our technique to find genes in noisy DNA sequences. The following sections provide a brief introduction to molecular biology
Estimating Attributes: Analysis and Extensions of RELIEF
, 1994
"... . In the context of machine learning from examples this paper deals with the problem of estimating the quality of attributes with and without dependencies among them. Kira and Rendell (1992a,b) developed an algorithm called RELIEF, which was shown to be very efficient in estimating attributes. Origi ..."
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Cited by 474 (25 self)
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. Original RELIEF can deal with discrete and continuous attributes and is limited to only twoclass problems. In this paper RELIEF is analysed and extended to deal with noisy, incomplete, and multiclass data sets. The extensions are verified on various artificial and one well known realworld problem. 1
Godec: Randomized lowrank & sparse matrix decomposition in noisy case
 in International Conference on Machine Learning
, 2011
"... Lowrank and sparse structures have been profoundly studied in matrix completion and compressed sensing. In this paper, we develop “Go Decomposition ” (GoDec) to efficiently and robustly estimate the lowrank part L and the sparse part S of a matrix X = L + S + G with noise G. GoDec alternatively as ..."
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Cited by 33 (6 self)
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Lowrank and sparse structures have been profoundly studied in matrix completion and compressed sensing. In this paper, we develop “Go Decomposition ” (GoDec) to efficiently and robustly estimate the lowrank part L and the sparse part S of a matrix X = L + S + G with noise G. GoDec alternatively assigns the lowrank approximation of X − S to L and the sparse approximation of X − L to S. The algorithm can be significantly accelerated by bilateral random projections (BRP). We also propose GoDec for matrix completion as an important variant. We prove that the objective value ∥X − L − S ∥ 2 F converges to a local minimum, while L and S linearly converge to local optimums. Theoretically, we analyze the influence of L, S and G to the asymptotic/convergence speeds in order to discover the robustness of GoDec. Empirical studies suggest the efficiency, robustness and effectiveness of GoDec comparing with representative matrix decomposition and completion tools, e.g., Robust PCA and OptSpace. 1.
Protecting Circuits from Leakage: the ComputationallyBounded and Noisy Cases
, 2010
"... Abstract. Physical computational devices leak sidechannel information that may, and often does, reveal secret internal states. We present a general transformation that compiles any circuit into a new, functionally equivalent circuit which is resilient against welldefined classes of leakage. Our co ..."
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Cited by 13 (1 self)
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that it also uses MODp gates) which outputs a limited number of bits. – Noisy leakage, where the measurement apparatus reveals all the bits of the state of the circuit, perturbed by independent binomial noise. Namely, each bit of the computation is perturbed with probability p, and remains unchanged
Ingeniería y Ciencia Efficient Software Implementation of the Nearly Optimal Sparse Fast Fourier Transform for the Noisy Case 73 Efficient Software Implementation of the Nearly Optimal Sparse Fast Fourier Transform for the Noisy Case
"... Abstract In this paper we present an optimized software implementation (sFFT4.0) of the recently developed Nearly Optimal Sparse Fast Fourier Transform (sFFT) algorithm for the noisy case. First, we developed a modified version of the Nearly Optimal sFFT algorithm for the noisy case, this modified ..."
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Abstract In this paper we present an optimized software implementation (sFFT4.0) of the recently developed Nearly Optimal Sparse Fast Fourier Transform (sFFT) algorithm for the noisy case. First, we developed a modified version of the Nearly Optimal sFFT algorithm for the noisy case
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