Optimizing Privacy in High-Dimensional Data Mining
Differential Privacy is a cutting-edge approach to safeguarding data privacy, especially in high-dimensional datasets. This proposal focuses on reducing computing complexity and improving signal-to-noise ratio by approximating the dataset distribution with low-dimensional marginals. Key research areas include constructing Bayesian networks, generating synthetic data, and exploring differential privacy mechanisms.
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Virginia Virginia http://star.aust.edu.cn/~xjfang Email: xjfang@aliyun.com
Virginia Charset[26]={ a , b , , z } =26 Coding[26]={0, 1, , 25}
Virginia Virginia M=m1m2 mn mi charset, n K=k1k2 kd ki charset, d C=c1c2 cn ci charset, n
Virginia cj+td=(mj+td+kj) mod 26 j=1 d, t=0 ceiling(n/d)-1 ceiling(x) x mj+td=(cj+td-kj) mod 26 j=1 d, t=0 ceiling(n/d)-1 ceiling(x) x
Virginia m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 M ( ) n o t h i n g (6) i s t o (13) (14) (19) (7) (8) (13) (8) (18) (19) (14) K ( ) C ( ) j o y j o y j o y j o (9) w (22) j=1 t=0 (14) c (2) j=2 t=0 (24) r (17) j=3 t=0 (9) q (16) j=1 t=1 (14) w (22) j=2 t=1 (24) l (11) j=3 t=1 (9) p (15) j=1 t=2 (14) w (22) j=2 t=2 (24) q (16) j=3 t=2 (9) c (2) j=1 t=3 (14) c (2) j=2 t=3 n=11 d=3 t=ceiling(11/3)-1=3
Differential Privacy is the state-of-the-art goal for the problem of privacy-preserving data release and privacy-preserving data mining. Existing techniques using differential privacy, however, cannot effectively handle the publication of high-dimensional data. In particular, when the input dataset contains a large number of attributes, existing methods incur higher computing complexity and lower information to noise ratio, which renders the published data next to useless. This proposal aims to reduce computing complexity and signal to noise ratio. The starting point is to approximate the full distribution of high-dimensional dataset with a set of low-dimensional marginal distributions via optimizing score function and reducing sensitivity, in which generation of noisy conditional distributions with differential privacy is computed in a set of low-dimensional subspaces, and then, the sample tuples from the noisy approximation distribution are used to generate and release the synthetic dataset. Some crucial science problems would be investigated below: (i) constructing a low k-degree Bayesian network over the high-dimensional dataset via exponential mechanism in differential privacy, where the score function is optimized to reduce the sensitivity using mutual information, equivalence classes in maximum joint distribution and dynamic programming; (ii)studying the algorithm to compute a set of noisy conditional distributions from joint distributions in the subspace of Bayesian network, via the Laplace mechanism of differential privacy. (iii)exploring how to generate synthetic data from the differentially private Bayesian network and conditional distributions, without explicitly materializing the noisy global distribution. The proposed solution may have theoretical and technical significance for synthetic data generation with differential privacy on business prospects.
( ) differentialprivacyisthestateoftheartgoalfortheproblemofprivacypreservingdatarelease andprivacypreservingdataminingexistingtechniquesusingdifferentialprivacyhoweverca nnoteffectivelyhandlethepublicationofhighdimensionaldatainparticularwhentheinputd atasetcontainsalargenumberofattributesexistingmethodsincurhighercomputingcomple xityandlowerinformationtonoiseratiowhichrendersthepublisheddatanexttouselessthisp roposalaimstoreducecomputingcomplexityandsignaltonoiseratiothestartingpointistoap proximatethefulldistributionofhighdimensionaldatasetwithasetoflowdimensionalmargi naldistributionsviaoptimizingscorefunctionandreducingsensitivityinwhichgenerationof noisyconditionaldistributionswithdifferentialprivacyiscomputedinasetoflowdimensiona lsubspacesandthenthesampletuplesfromthenoisyapproximationdistributionareusedto generateandreleasethesyntheticdatasetsomecrucialscienceproblemswouldbeinvestiga tedbelowiconstructingalowkdegreebayesiannetworkoverthehighdimensionaldatasetvi aexponentialmechanismindifferentialprivacywherethescorefunctionisoptimizedtoredu cethesensitivityusingmutualinformationequivalenceclassesinmaximumjointdistributio nanddynamicprogrammingiistudyingthealgorithmtocomputeasetofnoisyconditionaldis tributionsfromjointdistributionsinthesubspaceofbayesiannetworkviathelaplacemechan ismofdifferentialprivacyiiiexploringhowtogeneratesyntheticdatafromthedifferentiallypr ivatebayesiannetworkandconditionaldistributionswithoutexplicitlymaterializingthenois yglobaldistributiontheproposedsolutionmayhavetheoreticalandtechnicalsignificancefo rsyntheticdatagenerationwithdifferentialprivacyonbusinessprospects
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n i pi(1 i n) IC = IC xi i L n n IC p i = 1 i IC IC. IC IC ( ( 1) 1) x x L L n = i i ' IC = 1 i
IC 1. IC 0.038. 2. IC 0.065. 3. IC 3
Example 1: IC IC 0.0388
Example 2: text Differential Privacy is the state-of-the-art goal for the problem of privacy-preserving data release and privacy-preserving data mining. Existing techniques using differential privacy, however, cannot effectively handle the publication of high-dimensional data. In particular, when the input dataset contains a large number of attributes, existing methods incur higher computing complexity and lower information to noise ratio, which renders the published data next to useless. This proposal aims to reduce computing complexity and signal to noise ratio. The starting point is to approximate the full distribution of high-dimensional dataset with a set of low-dimensional marginal distributions via optimizing score function and reducing sensitivity, in which generation of noisy conditional distributions with differential privacy is computed in a set of low-dimensional subspaces, and then, the sample tuples from the noisy approximation distribution are used to generate and release the synthetic dataset. Some crucial science problems would be investigated below: (i) constructing a low k-degree Bayesian network over the high-dimensional dataset via exponential mechanism in differential privacy, where the score function is optimized to reduce the sensitivity using mutual information, equivalence classes in maximum joint distribution and dynamic programming; (ii)studying the algorithm to compute a set of noisy conditional distributions from joint distributions in the subspace of Bayesian network, via the Laplace mechanism of differential privacy. (iii)exploring how to generate synthetic data from the differentially private Bayesian network and conditional distributions, without explicitly materializing the noisy global distribution. The proposed solution may have theoretical and technical significance for synthetic data generation with differential privacy on business prospects. IC 0.0659
( ) differentialprivacyisthestateoftheartgoalfortheproblemofprivacypreservingdatarelease andprivacypreservingdataminingexistingtechniquesusingdifferentialprivacyhoweverca nnoteffectivelyhandlethepublicationofhighdimensionaldatainparticularwhentheinputd atasetcontainsalargenumberofattributesexistingmethodsincurhighercomputingcomple xityandlowerinformationtonoiseratiowhichrendersthepublisheddatanexttouselessthisp roposalaimstoreducecomputingcomplexityandsignaltonoiseratiothestartingpointistoap proximatethefulldistributionofhighdimensionaldatasetwithasetoflowdimensionalmargi naldistributionsviaoptimizingscorefunctionandreducingsensitivityinwhichgenerationof noisyconditionaldistributionswithdifferentialprivacyiscomputedinasetoflowdimensiona lsubspacesandthenthesampletuplesfromthenoisyapproximationdistributionareusedto generateandreleasethesyntheticdatasetsomecrucialscienceproblemswouldbeinvestiga tedbelowiconstructingalowkdegreebayesiannetworkoverthehighdimensionaldatasetvi aexponentialmechanismindifferentialprivacywherethescorefunctionisoptimizedtoredu cethesensitivityusingmutualinformationequivalenceclassesinmaximumjointdistributio nanddynamicprogrammingiistudyingthealgorithmtocomputeasetofnoisyconditionaldis tributionsfromjointdistributionsinthesubspaceofbayesiannetworkviathelaplacemechan ismofdifferentialprivacyiiiexploringhowtogeneratesyntheticdatafromthedifferentiallypr ivatebayesiannetworkandconditionaldistributionswithoutexplicitlymaterializingthenois yglobaldistributiontheproposedsolutionmayhavetheoreticalandtechnicalsignificancefo rsyntheticdatagenerationwithdifferentialprivacyonbusinessprospects
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step1 (1) 2 IC (2) 3 IC (3) n IC d , IC 0.065 Virginia d
Example: ciphertext2 2 IC=0.0419
Example: ciphertext3 3 IC=0.0419
Example: ciphertext7 1 lvqbmzwwxxqziimivqvanikmbqvxbqvliiplkavncabkmbxizivbpatibazimukqqvbbxbfpqbqvlebqv qbwxvnvcvbkivviqanqiuvtvammutbgqlcmommaqmzkzeqotavlivwpmtbwtqnqimzqbbmagcn witvuqblxubbzkiwltjnvqacwqwpkvqbdmvombnlvxjvsltjembzvqiqbwcgmikakzboqlvqjak vgiubgeoeearapegtavvryleriqhvtfneernbnhngguhevyavgbvegvgbfbvqcbgtbvnbbvrfvtfnvbzna eagthnpflugbqyojsnpcnbfhfacrunzvghrnnlpghvbbanbgtrlrivaqiazfsnpgrbvbgvhgbaynzwfvlev huvbfvvqhegovosnerrvsvnktrfvevgenanvqhvkyvtfyoufgubyuvnfvrbvgihcg knfjklyqnjlqidafjlvswumhkjqgtmnyybnysqryjntwhsjisnntjmxfzyurzzrdsntwnfrkytmnyykjqfnxn xssnnnlnnniznjqdzxbngfyqxjufxnxssxsixhjgzaybwfljyjlxfnjjrjqdmksrwmyxzwjjxftytstsijyrjxynyt izsxgspqrxkfhumsdhtknndjsynyyudfydizjjnfwfslsdhssknfxwx 2 3 7 gtuvchthaxcgxufkvjwhkcxqvcgcjgnrnvvvpgqdkgpjwoagoqcetdfvgrntqizuqcuiuqvfwjgnvgfqiuk qkgqfgkkthqptpkvxqkhgnejcrouzpdtqvngvueurugkgpkmdpmgocgrcpkvxtqvrfepvopkxekwfwf eouiqqgppckuktpuguyvccfpkkkqvgcggagctpckuvkgkqdtprncjegnkqgcvjgtpug 7 IC=0.0657
IC 1 2 3 4 5 6 7 IC IC IC IC IC IC IC IC 1 1609 0.0419 0.0419 2 805 0.0427 804 0.0411 0.0419 3 537 0.0417 536 0.0417 536 0.0424 0.0419 4 403 0.0425 402 0.0.98 402 0.0424 402 0.0427 0.0419 5 322 0.0417 322 0.0414 322 0.0418 322 0.0413 321 0.0411 0.0415 6 269 0.0402 268 0.0397 268 0.0441 268 0.0432 268 0.0419 268 0.0416 0.0418 7 230 0.0674 230 0.0677 230 0.0621 230 0.0584 230 0.0744 230 0.0666 229 0.0634 0.0657 8 0.0422 IC 0.065, IC IC 0.065 d=7.
step2 (1) Virginia , i(i=1 d) key i 26 26 ( ) Virginia (2 1 d
n i pi(i=1 n) Cj( j=1 d) Cj ni,j j fi,j f n = i , = = i j * , 1 M p j d j i n 1 , i j
Example: 326 3 3 3 knfjklyqnjlqidafjlvswumhkjqgtmnyybnysqryjntwhsjisnntjmxfzyurzzrdsntwnf rkytmnyykjqfnxnxssnnnlnnniznjqdzxbngfyqxjufxnxssxsixhjgzaybwfljyjlxfnjjrj qdmksrwmyxzwjjxftytstsijyrjxynytizsxgspqrxkfhumsdhtknndjsynyyudfydizjjn fwfslsdhssknfxwx 1(b) 0.0387 14 0.0326 2(c) 0.0325 15 0.0348 3(d) 0.0324 16 0.0416 4(e) 0.0368 17 0.0392 26 26 0.0332 20 0.0461 Virginia f 3 5 (f) 0.0615 18 0.0405 6 0.0433 19 0.0361 7 8 0.0279 21 0.0386 9 0.0468 22 0.0356 7 Virginia 10 0.0384 23 0.0313 11 0.0365 infosec 24 0.0364 12 0.0356 25 0.0429 13 0.0368 26(a) 0.0340
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