Symmetric matrix perturbation for differentially-private principal component analysis

Imtiaz, Hafiz; Sarwate, Anand D.

doi:10.1109/icassp.2016.7472095

Cited by 12 publications

(11 citation statements)

References 10 publications

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“…Dwork et al [13] provided the algorithms for (ε, δ)-DP, adding Gaussian noise to the original sample covariance matrix. Inspired by Dwork, Imtiaz et al [14,15] and Jiang et al [2] designed their algorithms for (ε, 0)-DP. Both of them added Wishart noise with parameters chosen to have a better utility bound.…”

Section: Related Workmentioning

confidence: 99%

Laplace Input and Output Perturbation for Differentially Private Principal Components Analysis

Yang

Bai

2019

Security and Communication Networks

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With the widespread application of big data, privacy-preserving data analysis has become a topic of increasing significance. The current research studies mainly focus on privacy-preserving classification and regression. However, principal component analysis (PCA) is also an effective data analysis method which can be used to reduce the data dimensionality, commonly used in data processing, machine learning, and data mining. In order to implement approximate PCA while preserving data privacy, we apply the Laplace mechanism to propose two differential privacy principal component analysis algorithms: Laplace input perturbation (LIP) and Laplace output perturbation (LOP). We evaluate the performance of LIP and LOP in terms of noise magnitude and approximation error theoretically and experimentally. In addition, we explore the variation of performance of the two algorithms with different parameters such as number of samples, target dimension, and privacy parameter. Theoretical and experimental results show that algorithm LIP adds less noise and has lower approximation error than LOP. To verify the effectiveness of algorithm LIP, we compare our LIP with other algorithms. The experimental results show that algorithm LIP can provide strong privacy guarantee and good data utility.

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Section: Related Workmentioning

confidence: 99%

Laplace Input and Output Perturbation for Differentially Private Principal Components Analysis

Yang

Bai

2019

Security and Communication Networks

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“…This serves as a preprocessing step to standardize the data prior to djICA, also without communicating full data sets outside of local sites. We replace the LocalPCA and GlobalPCA algorithms in djICA by a ϵ-differentially private PCA algorithm [13]. The DP-PCA algorithm provides an ϵ-differentially private approximation to the data second-moment matrix C = XX ⊤ .…”

Section: B Differentially-private Dpca Algorithmsmentioning

confidence: 99%

“…Unfortunately, communicating a function of the local data may not save in the sense of differential privacy; our algorithmic contribution is to replace the PCA computations with differentially private PCA algorithms. In particular, we use a recently proposed SN algorithm [13] which is a fast and efficient algorithm for ϵ-differentially private PCA. The end result is a differentially private version of djICA.…”

Section: A Decentralized Joint Icamentioning

confidence: 99%

Privacy-preserving source separation for distributed data using independent component analysis

Imtiaz

Silva

Baker

et al. 2016

2016 Annual Conference on Information Science and Systems (CISS)

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Building good feature representations and learning hidden source models typically requires large sample sizes. In many applications, however, the size of the sample at an individual data holder may not be sufficient. One such application is neuroimaging analyses for mental health disorders -there are many individual research groups, each with a moderate number of subjects. Pooling such data can enable efficient feature learning, but privacy concerns prevent sharing the underlying data. We propose a model for private feature learning in which the data holders share differentially private views of their respective datasets to enable collaborative learning of a joint feature map. We give an example of such an algorithm for independent component analysis (ICA) -a popular blind source separation algorithm used in neuroimaging analyses. Our algorithm is a differentially private version of the recently proposed distributed joint ICA algorithm. We evaluate the performance of this method on simulated functional magnetic resonance imaging (fMRI) data.

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“…A random perturbation is drawn according to a distribution calibrated using a user-defined quality measure, and added to the output. It has been used with success for PCA, perturbing either the covariance [14,30,29] or directly the eigenvectors of the covariance [31,1], and with genetic algorithms for k-means [60]. Such algorithms depend strongly on the quality measure of the output, which must be chosen carefully.…”

Section: Related Workmentioning

confidence: 99%

“…we have NSR X = 0. Utility is then preserved provided that NSR ≤ NSR max , which according to (29) translates to the condition ≥ √ 1000 / . Recall that we also need ≥ 2 as shown in Section 6.1.…”

Section: Choice Of the Sketch Sizementioning

confidence: 99%

Compressive learning with privacy guarantees

Chatalic¹,

Schellekens²,

Houssiau

et al. 2021

Information and Inference: A Journal of the IMA

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This work addresses the problem of learning from large collections of data with privacy guarantees. The compressive learning framework proposes to deal with the large scale of datasets by compressing them into a single vector of generalized random moments, called a sketch vector, from which the learning task is then performed. We provide sharp bounds on the so-called sensitivity of this sketching mechanism. This allows us to leverage standard techniques to ensure differential privacy—a well-established formalism for defining and quantifying the privacy of a random mechanism—by adding Laplace of Gaussian noise to the sketch. We combine these standard mechanisms with a new feature subsampling mechanism, which reduces the computational cost without damaging privacy. The overall framework is applied to the tasks of Gaussian modeling, k-means clustering and principal component analysis, for which sharp privacy bounds are derived. Empirically, the quality (for subsequent learning) of the compressed representation produced by our mechanism is strongly related with the induced noise level, for which we give analytical expressions.

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Symmetric matrix perturbation for differentially-private principal component analysis

Cited by 12 publications

References 10 publications

Laplace Input and Output Perturbation for Differentially Private Principal Components Analysis

Laplace Input and Output Perturbation for Differentially Private Principal Components Analysis

Privacy-preserving source separation for distributed data using independent component analysis

Compressive learning with privacy guarantees

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