Abstract: Data privacy is very essential in this modern era where everyone, including scientists, rely ever more on results from data in making decisions. In conducting research, the privacy of individuals involved in a study must be guaranteed. How can
we include this privacy in a machine learning algorithm?
Key Words: Differential privacy, pliable lasso, multinomial, classification, interaction
models.
Supervisors: Theophilus Quachie Asenso, Manuela Zucknick
Project description
Big data analysis has become one of the greatest concerns for statisticians. Often,
such data, such as electronic health records, genetic screening data, account informa-
tion, web search history, etc., include personal information, which have been stored in
databases for future references (Chaudhuri, Monteleoni, & Sarwate, 2011). These data sets are exposed to a lot of risk when they fall into the hands of an adversary (Dwork & Roth, 2014).
Cynthia Dwork (Dwork, 2006) proposed a quantitative measure of the privacy risk
associated in processing data that contain sensitive information. This is known as
differential privacy and it is independent of background information. An algorithm is
said to satisfy ε differential privacy if changing an individual data point does not affect
the output distribution much. The definition of differential privacy can formally be
stated as follows:
Definition 1.1. A random algorithm \(\mathcal{A}\) with domain Xn is (ε, δ)-differentially private
if for all \(\mathcal{O}\) ⊆ Range(A) and for all pairs of adjacent data sets S, S′ ∈ Xn:
Pr[\(\mathcal{A}\)(S) ∈ \(\mathcal{O}\)] ≤ exp(ε) Pr[A(S′) ∈ \(\mathcal{O}\)] + δ,
where the probability space is over the coin flips of the algorithm \(\mathcal{A}\).
For the student working on this project the goal will be to train a classification
model while protecting sensitive information of the individuals involved in a study in
precision cancer medicine, where we aim to predict whether a patient will respond
to a certain cancer treatment based on genomic information about the tumour. The
model for consideration is the pliable lasso which was proposed by Robert Tibshirani
and Jerome Friedman (Tibshirani & Friedman, 2020) to model interaction terms in a
high-dimensional context. The project work will involve the following aspects:
(1) development of a differential privacy pliable lasso model;
(2) application of the proposed method to a penalised logistic regression setup, for
binary classification;
(3) demonstration of the gain of privacy in an application to a real data set from
precision cancer medicine, comparing the privacy model to the original model
(without privacy).
References
- Chaudhuri, K., Monteleoni, C., & Sarwate, A. (2011). Differentially private empirical risk minimization. Journal of machine learning research : JMLR, 12 , 1069-1109.
- Dwork, C. (2006). Differential privacy. In M. Bugliesi, B. Preneel, V. Sassone, & I. Wegener (Eds.), Automata, languages and programming (p. 1-12). Berlin, Heidelberg: Springer Berlin Heidelberg.
- Dwork, C., & Roth, A. (2014). The algorithmic foundations of differential privacy. Foundations and Trends® in Theoretical Computer Science, 9 (3–4), 211-407. Retrieved from http://dx.doi.org/10.1561/0400000042 doi:
- Tibshirani, R., & Friedman, J. (2020). A pliable lasso. Journal of Computational and Graphical Statistics, 29 (1), 215-225, DOI: 10.1080/10618600.2019.1648271. Retrieved from https://doi.org/10.1080/10618600.2019.1648271 doi