New mechanisms improve differential privacy for scalar queries.
problem Improving differential privacy for scalar, real-valued query functions.
method Mixing multiple Gaussian distributions to satisfy differential privacy.
result Mechanisms yield lower noise amplitudes and variances compared to the analytic Gaussian mechanism.
The Gaussian mechanism is an essential building block used in multitude of differentially private data analysis algorithms. In this paper we revisit the Gaussian mechanism and show that the original analysis has several important limitations. Our analysis reveals that the variance formula for the original mechanism is …
Expands differential privacy mechanisms to include the Generalized Gaussian mechanism for improved private machine learning.
problem Improving privacy in machine learning algorithms while maintaining utility.
method Introduces and analyzes the Generalized Gaussian (GG) mechanism for differential privacy.
result The GG mechanism provides better performance than the Laplace and Gaussian mechanisms across various values of β.
A new Gaussian mechanism for differential privacy in the shuffle model is introduced.
problem Improving differential privacy in distributed learning environments.
method Characterization and upper-bounding of Rényi differential privacy (RDP) for the shuffle Gaussian mechanism.
result The shuffle Gaussian mechanism provides improved privacy guarantees compared to existing methods.
This paper assesses Gaussian and Exponential mechanisms for certifying adversarial robustness.
problem Certifying adversarial robustness using randomized smoothing mechanisms.
method Proposes a generic framework to assess the appropriateness of randomized smoothing mechanisms.
result Gaussian mechanism is an appropriate option for certifying both ℓ2-norm and ℓ∞-norm robustness. Optimal Gaussian noise mechanisms achieve nearly optimal error in unbiased mean estimation.
problem Efficiently estimating the mean of high-dimensional data while preserving privacy.
method Differential privacy mechanisms with Gaussian noise, focusing on optimal covariance.
result Gaussian noise mechanisms achieve nearly optimal error among all private unbiased mean estimation mechanisms.
The paper improves privacy accounting for discrete-valued mechanisms and the subsampled Gaussian mechanism.
problem Improving the accuracy and efficiency of differential privacy accounting for discrete outputs.
method Uses fast Fourier transform (FFT) for rigorous error analysis and accounting of privacy loss.
result Provides strict lower and upper bounds for (ε,δ)-values, demonstrating up to 75% reduction in noise variance. The Sampled Gaussian Mechanism's noise level decreases with larger subsampling rates, improving privacy-utility trade-offs.
problem Improving privacy-utility trade-offs in differentially private stochastic optimization.
method Proof of a conjecture about the Sampled Gaussian Mechanism's noise level and subsampling rate relationship.
result A rigorous proof of the conjecture, completing the proof of Theorem 6.2 in the original paper.
PACE-GGM uses Gaussian mechanism for private covariance estimation.
problem Private estimation of covariance matrices in high dimensions.
method Data-adaptive selection of entries, Gaussian mechanism, maximum-entropy reconstruction.
result Consistent improvements in estimation error compared to Gaussian mechanism and baselines.
Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it for…
Study symmetry breaking in quantum mechanics to understand many-body physics.
problem Understanding many-body physics from quantum mechanics.
method Analyzing potentials with unstable critical points and local minima.
result Emergence of many-body physics from spontaneous symmetry breaking.
Proposes a Gaussian process model for constrained dynamics learning.
problem Challenges in identifying constrained dynamics of mechanical systems.
method Combines analytical mechanics with Gaussian process regression.
result Improves data efficiency and constraint integrity in predictions.
The Sampled Gaussian Mechanism (SGM)---a composition of subsampling and the additive Gaussian noise---has been successfully used in a number of machine learning applications. The mechanism's unexpected power is derived from privacy amplification by sampling where the privacy cost of a single evaluation diminishes quadr…
This paper analyzes MFVBI for GMM using statistical mechanics.
problem Approximate fast computation of Gaussian Mixture Model.
method Statistical mechanics and MFVBI applied to GMM.
result Rigorous analysis and mathematical foundation for MFVBI applied to GMM.
Transformers can solve complex filtering problems for non-Gaussian signals.
problem Non-linear and non-Markovian filtering problems for conditionally Gaussian signals.
method Continuous-time transformer models called filterformers.
result Filterformers can approximate the conditional law of non-Markovian and conditionally Gaussian signal processes.
Paper introduces a Gaussian Process for operator learning in computational mechanics.
problem Efficient and accurate solutions for large datasets with reliable uncertainty quantification.
method Gaussian Process (GP) embedded in a neural operator framework with stochastic dual descent (SDD) algorithm.
result Improves GP resolution independence and scalability for high-dimensional and non-linear systems.
Improved bound for Gaussian mechanism in differential privacy.
problem Finding tighter bounds for Gaussian mechanism in differential privacy.
method Presented a new closed form bound for (ε,δ)-differential privacy using zero mean Gaussian noise. result The new bound is always lower and valid for all ε>0. Complex analysis techniques link Gaussian RBF kernels to quantum mechanics.
problem Understanding the Gaussian RBF kernel in machine learning and SVMs.
method Using Fock space and Segal-Bargmann theories in complex analysis.
result Proves connections between Gaussian RBF kernels and quantum mechanics operators.
Quantum model captures rare financial events not seen by Gaussian statistics.
problem Underestimation of rare financial events by Gaussian statistics.
method Quantum Bohmian Mechanics applied to multifractal random walk (MRW) models.
result Rare financial events generate a potential barrier in quantum potentials.
Paper explores Bayes rule for Gaussian mixtures with missing data, outperforming supervised classifiers.
problem Improving classification accuracy in partially classified samples with missing data.
method Generative model framework with missing-data mechanism, Bayes rule allocation.
result Bayes rule classifier with missing-data mechanism outperforms fully supervised classifiers in various conditions.
Exact 1-Wasserstein distance between location-scale distributions derived, with privacy effects studied.
problem Calculating the 1-Wasserstein distance between location-scale distributions and its impact on differential privacy.
method Exact expressions and special functions for 1-Wasserstein distance, new upper bounds, and asymptotic analysis.
result New linear upper bound and detailed asymptotic bounds for Gaussian case, effect of differential privacy studied.
A new discrete privacy mechanism for federated learning.
problem Differentially private federated learning with communication constraints.
method Skellam mechanism based on Poisson distributions.
result Skellam mechanism provides similar privacy-accuracy trade-offs as Gaussian mechanism.
CAG method predicts nonlinear solid mechanics responses in real-time with high accuracy and efficiency.
problem Real-time prediction of nonlinear solid mechanics responses.
method Clustering adaptive Gaussian process regression (CAG) method.
result Offers predictions within a second with high precision using only 20 samples.
Novel compression method preserves privacy while reducing communication costs.
problem Reducing communication costs in differential privacy mechanisms.
method Poisson private representation (PPR) for compressing and simulating local randomizers.
result Achieves compression within a logarithmic gap from theoretical lower bound.
New mechanism protects neural network weights from privacy attacks during self-supervised learning.
problem Privacy risks during fine-tuning stage of self-supervised learning.
method Proposes a novel differential privacy mechanism using additive logistic noise.
result Reduces membership inference attack accuracy to 50% while maintaining below 5% performance loss.
A new method for semi-supervised learning with missing data using GMM and margin confidence.
problem Handling missing data in semi-supervised learning with classification uncertainty.
method Explicitly models missingness mechanism, uses margin confidence and Aranda Ordaz function, develops ECM algorithm.
result Effective reduction of bias and robustness in semi-supervised learning with substantial missing labels.
New privacy mechanism reduces error in query results.
problem Achieving privacy while minimizing noise in query results.
method Extended sufficient and necessary condition for (ε,δ)-differential privacy for symmetric and log-concave noise densities. result Significantly lower mean squared errors than Laplace and Gaussian mechanisms.
A new mechanism for differentially private Fréchet mean on SPD matrices.
problem Privacy-preserving statistical summaries for SPD matrices.
method Tangent Gaussian mechanism for log-Euclidean metric.
result Significantly better utility and computational efficiency.
Scales attention for long contexts in LLMs.
problem Development of attention mechanisms for long context inference.
method Scale-invariant total attention and sparsity conditions, with a position-dependent transformation of logits.
result Scale-invariant attention scheme improves validation loss and long-context retrieval.
Interactive privacy mechanisms improve spectral density estimation under local differential privacy.
problem Estimating spectral density of Gaussian time series with local differential privacy constraints.
method Two-stage process: Laplace mechanism followed by privatized sample analysis.
result Interactive mechanisms achieve faster rates for spectral density estimation.
As increasing amounts of sensitive personal information is aggregated into data repositories, it has become important to develop mechanisms for processing the data without revealing information about individual data instances. The differential privacy model provides a framework for the development and theoretical analy…
Local laGPR speeds up multiscale mechanics simulations without neural networks.
problem High computational costs in multiscale mechanics simulations.
method Local approximate Gaussian process regression (laGPR) combined with FE schemes.
result laGPR offers better accuracy than neural networks for stress predictions.
The paper provides stability guarantees for non-parametric maximum likelihood estimation using statistical mechanics.
problem Non-parametric maximum likelihood estimation and Gaussian mixture models.
method Statistical mechanics analysis to establish stability guarantees for NPMLE.
result High probability upper bounds on the Kullback-Leibler divergence between NPMLE estimators and the true density.
Proposes a privacy-preserving recommendation system using matrix factorization and differential privacy.
problem Privacy leakage in recommendation systems when anonymizing user data is not sufficient.
method Uses matrix factorization and differential privacy via the Gaussian mechanism.
result Demonstrates excellent utility for privacy-preserving recommendation systems.
A new privacy accountant for Gaussian differential privacy measures individual privacy losses.
problem Bounding differential privacy loss for each participant in data analysis.
method Developed a privacy accountant for adaptive compositions of randomised mechanisms using Gaussian differential privacy.
result Provided optimal bounds for the Gaussian mechanism and constructed an approximative individual privacy accountant.
We extend Gaussian Differential Privacy to curved Riemannian manifolds.
problem Extending Gaussian Differential Privacy to curved spaces.
method Developed a Riemannian Gaussian distribution using the Bishop-Gromov theorem and a MCMC-based algorithm.
result Achieved Gaussian Differential Privacy on general Riemannian manifolds with bounded Ricci curvature.
The paper introduces a differentially private method for optimization on Riemannian manifolds.
problem Differential privacy in optimization constrained to Riemannian manifolds.
method Adding Gaussian noise to the Riemannian gradient on the tangent space, with privacy and utility guarantees.
result Privacy and utility guarantees for differentially private Riemannian optimization.
Sparse Gaussian process quantile regression tackles computational challenges in Bayesian quantile regression.
problem Nonconjugacy and computational cost in Gaussian process quantile regression.
method Sparse Gaussian process framework with Laplace approximation, adaptive inducing-input placement, and sequential data acquisition.
result Accuracy of Laplace approximation and effectiveness of adaptive mechanisms in reducing predictive uncertainty.
Paper proposes mechanism learning to reverse causal inference in ML.
problem Machine learning models learn associational, not causal, relationships.
method Causally weighted Gaussian mixture models (CW-GMMs).
result CW-GMMs can deconfound observational data for reverse causal inference.
Attention mechanisms in deep learning become Gaussian process-like as the number of heads increases.
problem Understanding the behavior of attention mechanisms in deep learning models.
method Extending the equivalence between wide neural networks and Gaussian processes to attention architectures.
result Multi-head attention architectures behave as Gaussian processes as the number of heads tends to infinity.
Multi-output Gaussian processes have received increasing attention during the last few years as a natural mechanism to extend the powerful flexibility of Gaussian processes to the setup of multiple output variables. The key point here is the ability to design kernel functions that allow exploiting the correlations betw…
A new method for approximating softmax and Gaussian kernels with reduced error.
problem Approximating softmax and Gaussian kernels with low error.
method Simplex Random Features (SimRFs) and SimRFs+.
result SimRFs provide the smallest MSE among weight-independent geometrically-coupled PRF mechanisms.
Paper develops physics-informed, boundary-constrained Gaussian process for fluid flow field reconstruction.
problem Reconstructing fluid flow fields from limited data.
method Physics-informed, boundary-constrained Gaussian process regression.
result Derives physics-informed kernels for simulating incompressible flows.
Unified framework improves robust causal inference, overcoming Gaussian barriers and optimization issues.
problem Improving robust causal inference in non-Gaussian settings.
method Combines gamma-Divergence, GNC, and Gatekeeper mechanism.
result Enhanced robustness and global optimization in causal effect estimation.
ICA reveals deep learning's feature learning mechanisms from non-Gaussian data.
problem Understanding feature learning from non-Gaussian inputs in deep neural networks.
method Investigates ICA and SGD on synthetic and real data.
result FastICA requires n≳d4 samples for single non-Gaussian direction recovery, while SGD outperforms and optimised SGD reaches n≳d2. Engle's ARCH algorithm is a generator of stochastic time series for financial returns (and similar quantities) characterized by a time-dependent variance. It involves a memory parameter b (b=0 corresponds to {\it no memory}), and the noise is currently chosen to be Gaussian. We assume here a generalized noise, name…
We study the problem of subsampling in differential privacy (DP), a question that is the centerpiece behind many successful differentially private machine learning algorithms. Specifically, we provide a tight upper bound on the Rényi Differential Privacy (RDP) (Mironov, 2017) parameters for algorithms that: (1) subsamp…
New acquisition function for extreme rewards in bandits.
problem Online decision making with extreme payoffs in multi-armed bandits.
method Modeling payoffs as Gaussian processes and using a novel UCB acquisition function.
result Demonstrated benefits across synthetic and real-world benchmarks.