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- Moritz Hardt, Eric Price
- NIPS
- 2014

We provide a new robust convergence analysis of the well-known power method for computing the dominant singular vectors of a matrix that we call the noisy power method. Our result characterizes the convergence behavior of the algorithm when a significant amount noise is introduced after each matrix-vector multiplication. The noisy power method can be seen… (More)

- Moritz Hardt, Aaron Roth
- STOC
- 2013

We consider differentially private approximate singular vector computation. Known worst-case lower bounds show that the error of any differentially private algorithm must scale polynomially with the dimension of the singular vector. We are able to replace this dependence on the dimension by a natural parameter known as the <i>coherence</i> of the matrix… (More)

- Moritz Hardt, Kunal Talwar
- STOC
- 2010

We consider the noise complexity of differentially private mechanisms in the setting where the user asks d linear queries f:R<sup>n</sup> -> R non-adaptively. Here, the database is represented by a vector in R and proximity between databases is measured in the l<sub>1</sub>-metric. We show that the noise complexity is determined by two geometric… (More)

- Moritz Hardt, Guy N. Rothblum
- 2010 IEEE 51st Annual Symposium on Foundations of…
- 2010

We consider statistical data analysis in the interactive setting. In this setting a trusted curator maintains a database of sensitive information about individual participants, and releases privacy-preserving answers to queries as they arrive. Our primary contribution is a new differentially private multiplicative weights mechanism for answering a large… (More)

- Moritz Hardt, Benjamin Recht, Yoram Singer
- ICML
- 2016

We show that parametric models trained by a stochastic gradient method (SGM) with few iterations have vanishing generalization error. We prove our results by arguing that SGM is algo-rithmically stable in the sense of Bousquet and Elisseeff. Our analysis only employs elementary tools from convex and continuous optimization. We derive stability bounds for… (More)

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data… (More)

- Moritz Hardt, Aaron Roth
- STOC
- 2012

Computing accurate low rank approximations of large matrices is a fundamental data mining task. In many applications however the matrix contains sensitive information about individuals. In such case we would like to release a low rank approximation that satisfies a strong privacy guarantee such as differential privacy. Unfortunately, to date the best known… (More)

- Moritz Hardt, Katrina Ligett, Frank McSherry
- NIPS
- 2012

We present a new algorithm for differentially private data release, based on a simple combination of the Exponential Mechanism with the Multiplicative Weights update rule. Our MWEM algorithm achieves what are the best known and nearly optimal theoretical guarantees, while at the same time being simple to implement and experimentally more accurate on actual… (More)

We study <i>fairness in classification</i>, where individuals are classified, e.g., admitted to a university, and the goal is to prevent discrimination against individuals based on their membership in some group, while maintaining utility for the classifier (the university). The main conceptual contribution of this paper is a framework for fair… (More)

- Anupam Gupta, Moritz Hardt, Aaron Roth, Jonathan Ullman
- SIAM J. Comput.
- 2011

Suppose we would like to know all answers to a set of statistical queries C on a data set up to small error, but we can only access the data itself using statistical queries. A trivial solution is to exhaustively ask all queries in C. Can we do any better? We show that the number of statistical queries necessary and sufficient for this task is---up to… (More)