arXiv subjects

Mijung Park

Publications and source records attributed to Mijung Park.

33 records · Page 2Linked to original sources

arXiv2021

ABCDP: Approximate Bayesian Computation with Differential Privacy

We develop a novel approximate Bayesian computation (ABC) framework, ABCDP, that produces differentially private (DP) and approximate posterior samples. Our framework takes advantage of the Sparse Vector Technique (SVT), widely studied in the differential privacy literature. SVT incurs the privacy cost only when a condition (whether a quantity of interest is above/below a threshold) is met. If the condition is met sparsely during the repeated queries, SVT can drastically reduces the cumulative privacy loss, unlike the usual case where every query incurs the privacy loss. In ABC, the quantity of interest is the distance between observed and simulated data, and only when the distance is below a threshold, we take the corresponding prior sample as a posterior sample. Hence, applying SVT to ABC is an organic way to transform an ABC algorithm to a privacy-preserving variant with minimal modification, but yields the posterior samples with a high privacy level. We theoretically analyze the interplay between the noise added for privacy and the accuracy of the posterior samples.

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arXiv2020

Interpretable and Differentially Private Predictions

Interpretable predictions, where it is clear why a machine learning model has made a particular decision, can compromise privacy by revealing the characteristics of individual data points. This raises the central question addressed in this paper: Can models be interpretable without compromising privacy? For complex big data fit by correspondingly rich models, balancing privacy and explainability is particularly challenging, such that this question has remained largely unexplored. In this paper, we propose a family of simple models in the aim of approximating complex models using several locally linear maps per class to provide high classification accuracy, as well as differentially private explanations on the classification. We illustrate the usefulness of our approach on several image benchmark datasets as well as a medical dataset.

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arXiv2019

Privacy-Preserving Causal Inference via Inverse Probability Weighting

The use of inverse probability weighting (IPW) methods to estimate the causal effect of treatments from observational studies is widespread in econometrics, medicine and social sciences. Although these studies often involve sensitive information, thus far there has been no work on privacy-preserving IPW methods. We address this by providing a novel framework for privacy-preserving IPW (PP-IPW) methods. We include a theoretical analysis of the effects of our proposed privatisation procedure on the estimated average treatment effect, and evaluate our PP-IPW framework on synthetic, semi-synthetic and real datasets. The empirical results are consistent with our theoretical findings.

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arXiv2019

DP-MAC: The Differentially Private Method of Auxiliary Coordinates for Deep Learning

Developing a differentially private deep learning algorithm is challenging, due to the difficulty in analyzing the sensitivity of objective functions that are typically used to train deep neural networks. Many existing methods resort to the stochastic gradient descent algorithm and apply a pre-defined sensitivity to the gradients for privatizing weights. However, their slow convergence typically yields a high cumulative privacy loss. Here, we take a different route by employing the method of auxiliary coordinates, which allows us to independently update the weights per layer by optimizing a per-layer objective function. This objective function can be well approximated by a low-order Taylor's expansion, in which sensitivity analysis becomes tractable. We perturb the coefficients of the expansion for privacy, which we optimize using more advanced optimization routines than SGD for faster convergence. We empirically show that our algorithm provides a decent trained model quality under a modest privacy budget.

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arXiv2019

Neuron ranking -- an informed way to condense convolutional neural networks architecture

Convolutional neural networks (CNNs) in recent years have made a dramatic impact in science, technology and industry, yet the theoretical mechanism of CNN architecture design remains surprisingly vague. The CNN neurons, including its distinctive element, convolutional filters, are known to be learnable features, yet their individual role in producing the output is rather unclear. The thesis of this work is that not all neurons are equally important and some of them contain more useful information to perform a given task . Consequently, we quantify the significance of each filter and rank its importance in describing input to produce the desired output. This work presents two different methods: (1) a game theoretical approach based on Shapley value which computes the marginal contribution of each filter; and (2) a probabilistic approach based on what-we-call, the Importance switch using variational inference. Strikingly, these two vastly different methods produce similar experimental results, confirming the general theory that some of the filters are inherently more important that the others. The learned ranks can be readily useable for network compression and interpretability.

cs.LG↗

arXiv2019

Radial and Directional Posteriors for Bayesian Neural Networks

We propose a new variational family for Bayesian neural networks. We decompose the variational posterior into two components, where the radial component captures the strength of each neuron in terms of its magnitude; while the directional component captures the statistical dependencies among the weight parameters. The dependencies learned via the directional density provide better modeling performance compared to the widely-used Gaussian mean-field-type variational family. In addition, the strength of input and output neurons learned via the radial density provides a structured way to compress neural networks. Indeed, experiments show that our variational family improves predictive performance and yields compressed networks simultaneously.

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arXiv2018

Private Topic Modeling

We develop a privatised stochastic variational inference method for Latent Dirichlet Allocation (LDA). The iterative nature of stochastic variational inference presents challenges: multiple iterations are required to obtain accurate posterior distributions, yet each iteration increases the amount of noise that must be added to achieve a reasonable degree of privacy. We propose a practical algorithm that overcomes this challenge by combining: (1) an improved composition method for differential privacy, called the moments accountant, which provides a tight bound on the privacy cost of multiple variational inference iterations and thus significantly decreases the amount of additive noise; and (2) privacy amplification resulting from subsampling of large-scale data. Focusing on conjugate exponential family models, in our private variational inference, all the posterior distributions will be privatised by simply perturbing expected sufficient statistics. Using Wikipedia data, we illustrate the effectiveness of our algorithm for large-scale data.

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arXiv2018

Variational Bayes In Private Settings (VIPS)

Many applications of Bayesian data analysis involve sensitive information, motivating methods which ensure that privacy is protected. We introduce a general privacy-preserving framework for Variational Bayes (VB), a widely used optimization-based Bayesian inference method. Our framework respects differential privacy, the gold-standard privacy criterion, and encompasses a large class of probabilistic models, called the Conjugate Exponential (CE) family. We observe that we can straightforwardly privatise VB's approximate posterior distributions for models in the CE family, by perturbing the expected sufficient statistics of the complete-data likelihood. For a broadly-used class of non-CE models, those with binomial likelihoods, we show how to bring such models into the CE family, such that inferences in the modified model resemble the private variational Bayes algorithm as closely as possible, using the Polya-Gamma data augmentation scheme. The iterative nature of variational Bayes presents a further challenge since iterations increase the amount of noise needed. We overcome this by combining: (1) an improved composition method for differential privacy, called the moments accountant, which provides a tight bound on the privacy cost of multiple VB iterations and thus significantly decreases the amount of additive noise; and (2) the privacy amplification effect of subsampling mini-batches from large-scale data in stochastic learning. We empirically demonstrate the effectiveness of our method in CE and non-CE models including latent Dirichlet allocation, Bayesian logistic regression, and sigmoid belief networks, evaluated on real-world datasets.

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arXiv2018

A Differentially Private Kernel Two-Sample Test

Kernel two-sample testing is a useful statistical tool in determining whether data samples arise from different distributions without imposing any parametric assumptions on those distributions. However, raw data samples can expose sensitive information about individuals who participate in scientific studies, which makes the current tests vulnerable to privacy breaches. Hence, we design a new framework for kernel two-sample testing conforming to differential privacy constraints, in order to guarantee the privacy of subjects in the data. Unlike existing differentially private parametric tests that simply add noise to data, kernel-based testing imposes a challenge due to a complex dependence of test statistics on the raw data, as these statistics correspond to estimators of distances between representations of probability measures in Hilbert spaces. Our approach considers finite dimensional approximations to those representations. As a result, a simple chi-squared test is obtained, where a test statistic depends on a mean and covariance of empirical differences between the samples, which we perturb for a privacy guarantee. We investigate the utility of our framework in two realistic settings and conclude that our method requires only a relatively modest increase in sample size to achieve a similar level of power to the non-private tests in both settings.

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arXiv2016

DP-EM: Differentially Private Expectation Maximization

The iterative nature of the expectation maximization (EM) algorithm presents a challenge for privacy-preserving estimation, as each iteration increases the amount of noise needed. We propose a practical private EM algorithm that overcomes this challenge using two innovations: (1) a novel moment perturbation formulation for differentially private EM (DP-EM), and (2) the use of two recently developed composition methods to bound the privacy "cost" of multiple EM iterations: the moments accountant (MA) and zero-mean concentrated differential privacy (zCDP). Both MA and zCDP bound the moment generating function of the privacy loss random variable and achieve a refined tail bound, which effectively decrease the amount of additive noise. We present empirical results showing the benefits of our approach, as well as similar performance between these two composition methods in the DP-EM setting for Gaussian mixture models. Our approach can be readily extended to many iterative learning algorithms, opening up various exciting future directions.

cs.LG↗

arXiv2016

A note on privacy preserving iteratively reweighted least squares

Iteratively reweighted least squares (IRLS) is a widely-used method in machine learning to estimate the parameters in the generalised linear models. In particular, IRLS for L1 minimisation under the linear model provides a closed-form solution in each step, which is a simple multiplication between the inverse of the weighted second moment matrix and the weighted first moment vector. When dealing with privacy sensitive data, however, developing a privacy preserving IRLS algorithm faces two challenges. First, due to the inversion of the second moment matrix, the usual sensitivity analysis in differential privacy incorporating a single datapoint perturbation gets complicated and often requires unrealistic assumptions. Second, due to its iterative nature, a significant cumulative privacy loss occurs. However, adding a high level of noise to compensate for the privacy loss hinders from getting accurate estimates. Here, we develop a practical algorithm that overcomes these challenges and outputs privatised and accurate IRLS solutions. In our method, we analyse the sensitivity of each moments separately and treat the matrix inversion and multiplication as a post-processing step, which simplifies the sensitivity analysis. Furthermore, we apply the {\it{concentrated differential privacy}} formalism, a more relaxed version of differential privacy, which requires adding a significantly less amount of noise for the same level of privacy guarantee, compared to the conventional and advanced compositions of differentially private mechanisms.

cs.CR↗

arXiv2015

K2-ABC: Approximate Bayesian Computation with Kernel Embeddings

Complicated generative models often result in a situation where computing the likelihood of observed data is intractable, while simulating from the conditional density given a parameter value is relatively easy. Approximate Bayesian Computation (ABC) is a paradigm that enables simulation-based posterior inference in such cases by measuring the similarity between simulated and observed data in terms of a chosen set of summary statistics. However, there is no general rule to construct sufficient summary statistics for complex models. Insufficient summary statistics will "leak" information, which leads to ABC algorithms yielding samples from an incorrect (partial) posterior. In this paper, we propose a fully nonparametric ABC paradigm which circumvents the need for manually selecting summary statistics. Our approach, K2-ABC, uses maximum mean discrepancy (MMD) as a dissimilarity measure between the distributions over observed and simulated data. MMD is easily estimated as the squared difference between their empirical kernel embeddings. Experiments on a simulated scenario and a real-world biological problem illustrate the effectiveness of the proposed algorithm.

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arXiv2015

Bayesian Manifold Learning: The Locally Linear Latent Variable Model (LL-LVM)

We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variational optimisation of the posterior distribution on coordinates and locally linear maps from the latent space to the observation space given the data. Thus, the LL-LVM encapsulates the local-geometry preserving intuitions that underlie non-probabilistic methods such as locally linear embedding (LLE). Its probabilistic semantics make it easy to evaluate the quality of hypothesised neighbourhood relationships, select the intrinsic dimensionality of the manifold, construct out-of-sample extensions and to combine the manifold model with additional probabilistic models that capture the structure of coordinates within the manifold.

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arXiv2014

Hierarchical models for neural population dynamics in the presence of non-stationarity

Neural population activity often exhibits rich variability and temporal structure. This variability is thought to arise from single-neuron stochasticity, neural dynamics on short time-scales, as well as from modulations of neural firing properties on long time-scales, often referred to as "non-stationarity". To better understand the nature of co-variability in neural circuits and their impact on cortical information processing, we need statistical models that are able to capture multiple sources of variability on different time-scales. Here, we introduce a hierarchical statistical model of neural population activity which models both neural population dynamics as well as inter-trial modulations in firing rates. In addition, we extend the model to allow us to capture non-stationarities in the population dynamics itself (i.e., correlations across neurons). We develop variational inference methods for learning model parameters, and demonstrate that the method can recover non-stationarities in both average firing rates and correlation structure. Applied to neural population recordings from anesthetized macaque primary visual cortex, our models provide a better account of the structure of neural firing than stationary dynamics models.

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arXiv2012

Active Bayesian Optimization: Minimizing Minimizer Entropy

The ultimate goal of optimization is to find the minimizer of a target function.However, typical criteria for active optimization often ignore the uncertainty about the minimizer. We propose a novel criterion for global optimization and an associated sequential active learning strategy using Gaussian processes.Our criterion is the reduction of uncertainty in the posterior distribution of the function minimizer. It can also flexibly incorporate multiple global minimizers. We implement a tractable approximation of the criterion and demonstrate that it obtains the global minimizer accurately compared to conventional Bayesian optimization criteria.

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