Sparse Differential Privacy Regression via Priority Queue Optimization
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Solution Overview
Problem
Current differentially private machine learning algorithms are impractical for sparse high-dimensional datasets due to high training complexity and inability to scale, particularly with existing Frank-Wolfe algorithms that require O(D) complexity and produce dense solution vectors, limiting their scalability and effectiveness.
Innovation Solution
A method that uses the Frank-Wolfe algorithm to train a machine learning model on sparse datasets by converting sparse data into a matrix of data coordinates, generating a priority queue, iteratively selecting and updating data coordinates to avoid zero values, and adjusting weights, while maintaining sparsity and convergence, thereby reducing computational complexity and improving scalability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Frank-Wolfe algorithm is used for DP regression, then L1 constrained optimization is achieved, but training complexity becomes O(TD) which is impractical for large D
Solution Approach 1:
The algorithm segments the feature space by maintaining a priority queue of candidate features ranked by their potential contribution to the objective function. Instead of considering all D features at each iteration, the algorithm focuses on a small subset of promising features, reducing the per-iteration complexity from O(D) to O(log D) for queue operations plus O(k) for processing k candidate features.
Solution Approach 2:
The algorithm performs preliminary sorting and ranking of features by computing their potential contribution scores before the main optimization loop. This preliminary action organizes features in a priority queue structure, so that during each Frank-Wolfe iteration, only the top-k candidate features need to be evaluated, avoiding the need to scan all D features.
2Reliability
If noise is added to each variable for DP, then privacy is protected, but exploration of sparse datasets is limited
Solution Approach 1:
The algorithm applies differential privacy noise selectively rather than uniformly across all features. By focusing computational effort on a small priority queue of candidate features with the highest potential contribution, the algorithm adds noise only where necessary for privacy while maintaining the ability to effectively explore the sparse dataset structure through intelligent feature selection.
3Reliability
If L-BFGS is used for convex optimization, then DP is maintained, but solution vectors become completely dense with O(D) complexity for sparse data
Solution Approach 1:
The algorithm dynamically maintains sparsity by using a priority queue that adapts to the evolving solution. At each iteration, the priority queue is updated based on new gradient information, automatically focusing on features that are most likely to be non-zero in the final solution. This dynamic adaptation preserves sparsity without requiring post-processing thresholding that L-BFGS would need.
Solution Approach 2:
The algorithm changes the optimization approach from L-BFGS's dense parameter updates to a sparse parameter selection mechanism. By modifying how parameters are selected and updated—using priority queue-based candidate selection instead of full Hessian approximation—the algorithm maintains differential privacy while preserving the sparse structure of the solution vector.
4Productivity
If column sub-sampling is used to mitigate Frank-Wolfe dependency on sparse data, then scalability is partially improved, but results become suspect and non-scalable
Solution Approach 1:
Instead of sub-sampling columns during training, the algorithm performs preliminary organization of all features into a priority queue based on their potential contribution. This preliminary action allows the algorithm to efficiently identify and focus on relevant features without arbitrary sub-sampling, ensuring that all important features are considered while maintaining scalability through the priority queue structure.
Data Source
AI summary
Exemplary systems and methods are directed to training a machine learning model and for preventing leakage of training data by the machine learning model subsequent to training. A processor is configured to convert a sparse dataset into a matrix of plural data coordinates, generate a priority queue populated with the plural data coordinates, and iteratively select a data coordinate from the priority queue. Plural model values are calculated such that any zero value in the sparse dataset is avoided while maintaining a same result. A next feature is selected, and its weight is altered. Plural variables of the matrix are updated based on the altered weight value, and the priority queue is updated to adjust a priority of the data coordinates based on the update to the plural variables. The process is repeated for each next data coordinate until the model converges to a solution based on the model weights.