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SoK: A Review of Differentially Private Linear Models For High-Dimensional Data
Apr 01, 2024
Linear models are ubiquitous in data science, but are particularly prone to overfitting and data memorization in high dimensions. To guarantee the privacy of training data, differential privacy can be used. Many papers have proposed optimization techniques for high-dimensional differentially private linear models, but a systematic comparison between these methods does not exist. We close this gap by providing a comprehensive review of optimization methods for private high-dimensional linear models. Empirical tests on all methods demonstrate robust and coordinate-optimized algorithms perform best, which can inform future research. Code for implementing all methods is released online.
Comprehensive OOD Detection Improvements
Jan 18, 2024As machine learning becomes increasingly prevalent in impactful decisions, recognizing when inference data is outside the model's expected input distribution is paramount for giving context to predictions. Out-of-distribution (OOD) detection methods have been created for this task. Such methods can be split into representation-based or logit-based methods from whether they respectively utilize the model's embeddings or predictions for OOD detection. In contrast to most papers which solely focus on one such group, we address both. We employ dimensionality reduction on feature embeddings in representation-based methods for both time speedups and improved performance. Additionally, we propose DICE-COL, a modification of the popular logit-based method Directed Sparsification (DICE) that resolves an unnoticed flaw. We demonstrate the effectiveness of our methods on the OpenOODv1.5 benchmark framework, where they significantly improve performance and set state-of-the-art results.
Scaling Up Differentially Private LASSO Regularized Logistic Regression via Faster Frank-Wolfe Iterations
Oct 30, 2023
To the best of our knowledge, there are no methods today for training differentially private regression models on sparse input data. To remedy this, we adapt the Frank-Wolfe algorithm for $L_1$ penalized linear regression to be aware of sparse inputs and to use them effectively. In doing so, we reduce the training time of the algorithm from $\mathcal{O}( T D S + T N S)$ to $\mathcal{O}(N S + T \sqrt{D} \log{D} + T S^2)$, where $T$ is the number of iterations and a sparsity rate $S$ of a dataset with $N$ rows and $D$ features. Our results demonstrate that this procedure can reduce runtime by a factor of up to $2,200\times$, depending on the value of the privacy parameter $\epsilon$ and the sparsity of the dataset.
Sparse Private LASSO Logistic Regression
Apr 29, 2023
LASSO regularized logistic regression is particularly useful for its built-in feature selection, allowing coefficients to be removed from deployment and producing sparse solutions. Differentially private versions of LASSO logistic regression have been developed, but generally produce dense solutions, reducing the intrinsic utility of the LASSO penalty. In this paper, we present a differentially private method for sparse logistic regression that maintains hard zeros. Our key insight is to first train a non-private LASSO logistic regression model to determine an appropriate privatized number of non-zero coefficients to use in final model selection. To demonstrate our method's performance, we run experiments on synthetic and real-world datasets.
The Challenge of Differentially Private Screening Rules
Mar 18, 2023
Linear $L_1$-regularized models have remained one of the simplest and most effective tools in data analysis, especially in information retrieval problems where n-grams over text with TF-IDF or Okapi feature values are a strong and easy baseline. Over the past decade, screening rules have risen in popularity as a way to reduce the runtime for producing the sparse regression weights of $L_1$ models. However, despite the increasing need of privacy-preserving models in information retrieval, to the best of our knoweledge, no differentially private screening rule exists. In this paper, we develop the first differentially private screening rule for linear and logistic regression. In doing so, we discover difficulties in the task of making a useful private screening rule due to the amount of noise added to ensure privacy. We provide theoretical arguments and experimental evidence that this difficulty arises from the screening step itself and not the private optimizer. Based on our results, we highlight that developing an effective private $L_1$ screening method is an open problem in the differential privacy literature.