arXiv subjects

Borja Balle

Publications and source records attributed to Borja Balle.

At least 55 records · Page 3Linked to original sources

arXiv2019

Privacy- and Utility-Preserving Textual Analysis via Calibrated Multivariate Perturbations

Accurately learning from user data while providing quantifiable privacy guarantees provides an opportunity to build better ML models while maintaining user trust. This paper presents a formal approach to carrying out privacy preserving text perturbation using the notion of dx-privacy designed to achieve geo-indistinguishability in location data. Our approach applies carefully calibrated noise to vector representation of words in a high dimension space as defined by word embedding models. We present a privacy proof that satisfies dx-privacy where the privacy parameter epsilon provides guarantees with respect to a distance metric defined by the word embedding space. We demonstrate how epsilon can be selected by analyzing plausible deniability statistics backed up by large scale analysis on GloVe and fastText embeddings. We conduct privacy audit experiments against 2 baseline models and utility experiments on 3 datasets to demonstrate the tradeoff between privacy and utility for varying values of epsilon on different task types. Our results demonstrate practical utility (< 2% utility loss for training binary classifiers) while providing better privacy guarantees than baseline models.

cs.LG↗

arXiv2019

Actor Critic with Differentially Private Critic

Reinforcement learning algorithms are known to be sample inefficient, and often performance on one task can be substantially improved by leveraging information (e.g., via pre-training) on other related tasks. In this work, we propose a technique to achieve such knowledge transfer in cases where agent trajectories contain sensitive or private information, such as in the healthcare domain. Our approach leverages a differentially private policy evaluation algorithm to initialize an actor-critic model and improve the effectiveness of learning in downstream tasks. We empirically show this technique increases sample efficiency in resource-constrained control problems while preserving the privacy of trajectories collected in an upstream task.

cs.LG↗

arXiv2019

Hypothesis Testing Interpretations and Renyi Differential Privacy

Differential privacy is a de facto standard in data privacy, with applications in the public and private sectors. A way to explain differential privacy, which is particularly appealing to statistician and social scientists is by means of its statistical hypothesis testing interpretation. Informally, one cannot effectively test whether a specific individual has contributed her data by observing the output of a private mechanism---any test cannot have both high significance and high power. In this paper, we identify some conditions under which a privacy definition given in terms of a statistical divergence satisfies a similar interpretation. These conditions are useful to analyze the distinguishability power of divergences and we use them to study the hypothesis testing interpretation of some relaxations of differential privacy based on Renyi divergence. This analysis also results in an improved conversion rule between these definitions and differential privacy.

cs.LG↗

arXiv2019

Improved Summation from Shuffling

A protocol by Ishai et al.\ (FOCS 2006) showing how to implement distributed $n$-party summation from secure shuffling has regained relevance in the context of the recently proposed \emph{shuffle model} of differential privacy, as it allows to attain the accuracy levels of the curator model at a moderate communication cost. To achieve statistical security $2^{-σ}$, the protocol by Ishai et al.\ requires the number of messages sent by each party to {\em grow} logarithmically with $n$ as $O(\log n + σ)$. In this note we give an improved analysis achieving a dependency of the form $O(1+σ/\log n)$. Conceptually, this addresses the intuitive question left open by Ishai et al.\ of whether the shuffling step in their protocol provides a "hiding in the crowd" amplification effect as $n$ increases. From a practical perspective, our analysis provides explicit constants and shows, for example, that the method of Ishai et al.\ applied to summation of $32$-bit numbers from $n=10^4$ parties sending $12$ messages each provides statistical security $2^{-40}$.

cs.CR↗

arXiv2019

Differentially Private Summation with Multi-Message Shuffling

In recent work, Cheu et al. (Eurocrypt 2019) proposed a protocol for $n$-party real summation in the shuffle model of differential privacy with $O_{ε, δ}(1)$ error and $Θ(ε\sqrt{n})$ one-bit messages per party. In contrast, every local model protocol for real summation must incur error $Ω(1/\sqrt{n})$, and there exist protocols matching this lower bound which require just one bit of communication per party. Whether this gap in number of messages is necessary was left open by Cheu et al. In this note we show a protocol with $O(1/ε)$ error and $O(\log(n/δ))$ messages of size $O(\log(n))$ per party. This protocol is based on the work of Ishai et al.\ (FOCS 2006) showing how to implement distributed summation from secure shuffling, and the observation that this allows simulating the Laplace mechanism in the shuffle model.

cs.CR↗

arXiv2019

The Privacy Blanket of the Shuffle Model

This work studies differential privacy in the context of the recently proposed shuffle model. Unlike in the local model, where the server collecting privatized data from users can track back an input to a specific user, in the shuffle model users submit their privatized inputs to a server anonymously. This setup yields a trust model which sits in between the classical curator and local models for differential privacy. The shuffle model is the core idea in the Encode, Shuffle, Analyze (ESA) model introduced by Bittau et al. (SOPS 2017). Recent work by Cheu et al. (EUROCRYPT 2019) analyzes the differential privacy properties of the shuffle model and shows that in some cases shuffled protocols provide strictly better accuracy than local protocols. Additionally, Erlingsson et al. (SODA 2019) provide a privacy amplification bound quantifying the level of curator differential privacy achieved by the shuffle model in terms of the local differential privacy of the randomizer used by each user. In this context, we make three contributions. First, we provide an optimal single message protocol for summation of real numbers in the shuffle model. Our protocol is very simple and has better accuracy and communication than the protocols for this same problem proposed by Cheu et al. Optimality of this protocol follows from our second contribution, a new lower bound for the accuracy of private protocols for summation of real numbers in the shuffle model. The third contribution is a new amplification bound for analyzing the privacy of protocols in the shuffle model in terms of the privacy provided by the corresponding local randomizer. Our amplification bound generalizes the results by Erlingsson et al. to a wider range of parameters, and provides a whole family of methods to analyze privacy amplification in the shuffle model.

cs.LG↗

arXiv2019

Singular value automata and approximate minimization

The present paper uses spectral theory of linear operators to construct approximately minimal realizations of weighted languages. Our new contributions are: (i) a new algorithm for the SVD decomposition of infinite Hankel matrices based on their representation in terms of weighted automata, (ii) a new canonical form for weighted automata arising from the SVD of its corresponding Hankel matrix and (iii) an algorithm to construct approximate minimizations of given weighted automata by truncating the canonical form. We give bounds on the quality of our approximation.

cs.FL↗

arXiv2019

Privacy-preserving Active Learning on Sensitive Data for User Intent Classification

Active learning holds promise of significantly reducing data annotation costs while maintaining reasonable model performance. However, it requires sending data to annotators for labeling. This presents a possible privacy leak when the training set includes sensitive user data. In this paper, we describe an approach for carrying out privacy preserving active learning with quantifiable guarantees. We evaluate our approach by showing the tradeoff between privacy, utility and annotation budget on a binary classification task in a active learning setting.

cs.LG↗

arXiv2019

Continual Learning in Practice

This paper describes a reference architecture for self-maintaining systems that can learn continually, as data arrives. In environments where data evolves, we need architectures that manage Machine Learning (ML) models in production, adapt to shifting data distributions, cope with outliers, retrain when necessary, and adapt to new tasks. This represents continual AutoML or Automatically Adaptive Machine Learning. We describe the challenges and proposes a reference architecture.

stat.ML↗

arXiv2018

Subsampled Rényi Differential Privacy and Analytical Moments Accountant

We study the problem of subsampling in differential privacy (DP), a question that is the centerpiece behind many successful differentially private machine learning algorithms. Specifically, we provide a tight upper bound on the Rényi Differential Privacy (RDP) (Mironov, 2017) parameters for algorithms that: (1) subsample the dataset, and then (2) applies a randomized mechanism M to the subsample, in terms of the RDP parameters of M and the subsampling probability parameter. Our results generalize the moments accounting technique, developed by Abadi et al. (2016) for the Gaussian mechanism, to any subsampled RDP mechanism.

cs.LG↗

arXiv2018

Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences

Differential privacy comes equipped with multiple analytical tools for the design of private data analyses. One important tool is the so-called "privacy amplification by subsampling" principle, which ensures that a differentially private mechanism run on a random subsample of a population provides higher privacy guarantees than when run on the entire population. Several instances of this principle have been studied for different random subsampling methods, each with an ad-hoc analysis. In this paper we present a general method that recovers and improves prior analyses, yields lower bounds and derives new instances of privacy amplification by subsampling. Our method leverages a characterization of differential privacy as a divergence which emerged in the program verification community. Furthermore, it introduces new tools, including advanced joint convexity and privacy profiles, which might be of independent interest.

cs.LG↗

arXiv2018

Hierarchical Methods of Moments

Spectral methods of moments provide a powerful tool for learning the parameters of latent variable models. Despite their theoretical appeal, the applicability of these methods to real data is still limited due to a lack of robustness to model misspecification. In this paper we present a hierarchical approach to methods of moments to circumvent such limitations. Our method is based on replacing the tensor decomposition step used in previous algorithms with approximate joint diagonalization. Experiments on topic modeling show that our method outperforms previous tensor decomposition methods in terms of speed and model quality.

stat.ML↗

arXiv2018

Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising

The Gaussian mechanism is an essential building block used in multitude of differentially private data analysis algorithms. In this paper we revisit the Gaussian mechanism and show that the original analysis has several important limitations. Our analysis reveals that the variance formula for the original mechanism is far from tight in the high privacy regime ($\varepsilon \to 0$) and it cannot be extended to the low privacy regime ($\varepsilon \to \infty$). We address these limitations by developing an optimal Gaussian mechanism whose variance is calibrated directly using the Gaussian cumulative density function instead of a tail bound approximation. We also propose to equip the Gaussian mechanism with a post-processing step based on adaptive estimation techniques by leveraging that the distribution of the perturbation is known. Our experiments show that analytical calibration removes at least a third of the variance of the noise compared to the classical Gaussian mechanism, and that denoising dramatically improves the accuracy of the Gaussian mechanism in the high-dimensional regime.

cs.LG↗

arXiv2017

Bisimulation Metrics for Weighted Automata

We develop a new bisimulation (pseudo)metric for weighted finite automata (WFA) that generalizes Boreale's linear bisimulation relation. Our metrics are induced by seminorms on the state space of WFA. Our development is based on spectral properties of sets of linear operators. In particular, the joint spectral radius of the transition matrices of WFA plays a central role. We also study continuity properties of the bisimulation pseudometric, establish an undecidability result for computing the metric, and give a preliminary account of applications to spectral learning of weighted automata.

cs.FL↗

arXiv2016

Generalization Bounds for Weighted Automata

This paper studies the problem of learning weighted automata from a finite labeled training sample. We consider several general families of weighted automata defined in terms of three different measures: the norm of an automaton's weights, the norm of the function computed by an automaton, or the norm of the corresponding Hankel matrix. We present new data-dependent generalization guarantees for learning weighted automata expressed in terms of the Rademacher complexity of these families. We further present upper bounds on these Rademacher complexities, which reveal key new data-dependent terms related to the complexity of learning weighted automata.

cs.LG↗

arXiv2016

Differentially Private Policy Evaluation

We present the first differentially private algorithms for reinforcement learning, which apply to the task of evaluating a fixed policy. We establish two approaches for achieving differential privacy, provide a theoretical analysis of the privacy and utility of the two algorithms, and show promising results on simple empirical examples.

cs.LG↗

arXiv2015

Low-Rank Approximation of Weighted Tree Automata

We describe a technique to minimize weighted tree automata (WTA), a powerful formalisms that subsumes probabilistic context-free grammars (PCFGs) and latent-variable PCFGs. Our method relies on a singular value decomposition of the underlying Hankel matrix defined by the WTA. Our main theoretical result is an efficient algorithm for computing the SVD of an infinite Hankel matrix implicitly represented as a WTA. We provide an analysis of the approximation error induced by the minimization, and we evaluate our method on real-world data originating in newswire treebank. We show that the model achieves lower perplexity than previous methods for PCFG minimization, and also is much more stable due to the absence of local optima.

cs.LG↗

arXiv2015

Diameter and Stationary Distribution of Random $r$-out Digraphs

Let $D(n,r)$ be a random $r$-out regular directed multigraph on the set of vertices $\{1,\ldots,n\}$. In this work, we establish that for every $r \ge 2$, there exists $η_r>0$ such that $\text{diam}(D(n,r))=(1+η_r+o(1))\log_r{n}$. Our techniques also allow us to bound some extremal quantities related to the stationary distribution of a simple random walk on $D(n,r)$. In particular, we determine the asymptotic behaviour of $π_{\max}$ and $π_{\min}$, the maximum and the minimum values of the stationary distribution. We show that with high probability $π_{\max} = n^{-1+o(1)}$ and $π_{\min}=n^{-(1+η_r)+o(1)}$. Our proof shows that the vertices with $π(v)$ near to $π_{\min}$ lie at the top of "narrow, slippery towers", such vertices are also responsible for increasing the diameter from $(1+o(1))\log_r n$ to $(1+η_r+o(1))\log_r{n}$.

math.PR↗