Local Differential Privacy

The parameter epsilon (ε) quantifies the privacy loss. A smaller ε (e.g., 0.1) provides stronger privacy by adding more noise, while a larger ε (e.g., 10) provides weaker privacy but higher accuracy.

• ε = 0: Perfect privacy, zero utility.
• ε = 0.1–1: High privacy, suitable for sensitive genomic data.
• ε = 1–10: Moderate privacy, used for aggregate statistics.
• Composition: Privacy loss accumulates additively across multiple queries.

The foundational LDP technique where a user's true answer is flipped according to a known probability before transmission. For a binary attribute, the user tells the truth with probability p and lies with probability 1-p.

• Plausible Deniability: The curator cannot distinguish a true from a flipped response.
• Unbiased Estimation: The true population proportion is recoverable by correcting for the known noise injection rate.
• Genomic Application: Protects individual variant presence when querying allele frequencies across a cohort.

For numerical queries (e.g., gene expression levels), the Laplace mechanism adds noise drawn from a Laplace distribution calibrated to the query's sensitivity and the privacy budget ε.

• Sensitivity: The maximum change in the query output if a single individual's data is modified.
• Scale Parameter: Noise scale = sensitivity / ε.
• Local Application: Each device independently perturbs its numeric value before uploading, ensuring the raw measurement never leaves the device.

Unlike central differential privacy, LDP operates under a zero-trust server model. The data curator, aggregator, or cloud infrastructure is assumed to be potentially malicious or compromised.

• No Trusted Intermediary: Eliminates the need for a trusted data curator required in the central model.
• Client-Side Guarantee: Privacy protection is enforced cryptographically and statistically on the device.
• Genomic Relevance: Critical for direct-to-consumer genetic testing where the platform itself may be an adversary.

LDP imposes a stricter privacy model than central DP, resulting in a fundamental accuracy penalty for the same ε value. Achieving useful aggregate statistics requires a significantly larger user population.

• Sample Size Dependency: Error decreases as O(1/√n) in the number of participants.
• Genomic Implication: Rare variant analysis requires massive cohorts to overcome the injected noise.
• Amplification by Shuffling: A hybrid model where a trusted shuffler permutes messages to amplify privacy guarantees.

Advanced LDP protocols designed for categorical data (e.g., nucleotide bases A, C, G, T) that optimize the accuracy of frequency estimation under a given privacy budget.

• Unary Encoding: Each value is encoded as a bit vector with randomized bits.
• Optimized Local Hashing: Hashes the input into a smaller domain before applying randomized response, reducing communication cost.
• Hadamard Response: Uses a Hadamard matrix to achieve near-optimal accuracy for frequency estimation in large alphabets.

The mathematical framework that provides a provable guarantee of privacy. It ensures that the output of a computation is statistically indistinguishable whether or not any single individual's data is included. The key parameter ε (epsilon) quantifies the privacy loss budget—lower values mean stronger privacy. LDP is a specific instantiation where the guarantee is enforced locally, before data leaves the device.

A cryptographic protocol that allows a central server to compute the sum of model updates from multiple clients without inspecting any individual contribution. In a genomic federated learning system, LDP noise is added locally, and secure aggregation ensures the server only sees the noisy, aggregated result, never the raw or individually-noised updates. This provides defense-in-depth against an honest-but-curious server.

The systematic tracking of cumulative ε expenditure over multiple queries or training rounds. Each time a genomic data point is accessed, the privacy budget is debited. Key concepts include:

• Composition theorems: How ε adds up across sequential queries
• Privacy accountants: Software modules that track and enforce a total budget ceiling
• Budget exhaustion: The point at which data must be locked to prevent leakage

The canonical mechanism for implementing LDP on categorical data. A user flips a biased coin to decide whether to answer a sensitive question truthfully or give a random response. For genomic variant presence/absence queries, this allows researchers to estimate population allele frequencies without ever knowing any individual's true genotype. The noise is calibrated to achieve a target ε guarantee.

A fundamental LDP technique for numeric queries that adds noise drawn from a Laplace distribution calibrated to the query's sensitivity—the maximum change in output caused by a single individual's data. In genomic contexts, this is used to privatize continuous values like gene expression counts or polygenic risk scores before transmission. The scale parameter is set to Δf/ε, where Δf is sensitivity.

A hybrid privacy architecture that inserts a trusted shuffler between clients and the server. Clients add a small amount of local noise, and the shuffler randomly permutes all messages before forwarding them. This breaks the link between a report and its source, amplifying the privacy guarantee. The shuffler model achieves central-DP-level accuracy with LDP-level trust assumptions, making it ideal for multi-institutional genomic consortia.