New mechanism for pure differential privacy on functional summaries using Laplace-like process.
problem Challenges in achieving differential privacy for complex, structured functional summaries.
method Independent Component Laplace Process (ICLP) mechanism for infinite-dimensional Hilbert space.
result Effective enhancement of utility of private summaries through oversmoothing.
Paper develops privacy-preserving mechanisms for machine learning using wavelet transforms.
problem Improper data privacy methods compromise user data even with small preliminary knowledge.
method Three privacy-preserving mechanisms with discrete M-band wavelet transform.
result Successfully retains both differential privacy and learnability in various machine learning environments.
We design two mechanisms for the recommender system to collect user ratings. One is modified Laplace mechanism, and the other is randomized response mechanism. We prove that they are both differentially private and preserve the data utility.
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.
Paper introduces efficient top-k selection with differential privacy.
problem Efficiently selecting top-k elements with differential privacy.
method Oneshot Laplace mechanism, generalizing Report Noisy Max.
result Noise level of O(sqrt(k)/eps) for approximate differential privacy.
We consider the problem of obfuscating sensitive information while preserving utility, and we propose a machine learning approach inspired by the generative adversarial networks paradigm. The idea is to set up two nets: the generator, that tries to produce an optimal obfuscation mechanism to protect the data, and the c…
We investigate the problem of nodes clustering under privacy constraints when representing a dataset as a graph. Our contribution is threefold. First we formally define the concept of differential privacy for structured databases such as graphs, and give an alternative definition based on a new neighborhood notion betw…
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.
Two private algorithms estimate Jaccard similarity efficiently.
problem Estimating Jaccard similarity while preserving user privacy.
method Extends MinHash with Generalized Randomized Response and Laplace Mechanism.
result Achieves privacy-utility trade-off with theoretical bounds and experiments.
Enhances predictive performance in Bayesian deep learning via generalized Laplace approximation.
problem Inconsistency in Bayesian deep learning.
method Interprets posterior tempering as a correction for model misspecification and recalibration of priors. Introduces generalized Laplace approximation.
result Generalized Laplace approximation enhances predictive performance.
A new privacy-preserving mechanism for shapes on manifolds.
problem Privacy-preserving sanitization of shapes on curved manifolds.
method Developed a K-norm gradient mechanism on Riemannian manifolds.
result The K-norm gradient mechanism offers better control over sensitivity than the Laplace mechanism on positively curved manifolds.
Study spin chains and sigma models on flag manifolds, calculating spectra and geodesics.
problem Understanding the spectrum and geodesics of sigma models on flag manifolds.
method Connecting SU(n) spin chains to sigma models and calculating spectra and geodesics.
result Calculated the spectrum of the Laplace-Beltrami operator and geodesics for CP1 and F3. 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.
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.
We propose a new input perturbation mechanism for publishing a covariance matrix to achieve (ε,0)-differential privacy. Our mechanism uses a Wishart distribution to generate matrix noise. In particular, We apply this mechanism to principal component analysis. Our mechanism is able to keep the positive semi-definitene…
Improves privacy guarantees by analyzing randomness in privacy-preserving mechanisms.
problem Balancing user privacy and business constraints in privacy-preserving mechanisms.
method Analyzes explicit and implicit randomness in privacy mechanisms and proposes a probabilistic calibration method.
result Proposes privacy at risk, providing stronger privacy guarantees with quantifiable risks.
Quantum mechanics models for financial Black-Scholes model.
problem Modeling financial derivatives using quantum mechanics.
method Noncommutative quantum mechanics applied to specific mechanical systems.
result Generalized noncommutative quantum mechanics of financial models.
Private two-sample tests under LDP achieve minimax rates for multinomial and continuous data.
problem Achieving statistical utility while maintaining privacy in two-sample testing.
method Private permutation tests for multinomial data and adaptive tests for continuous data.
result Minimax optimal tests for private two-sample testing under LDP.
In this paper, we focus on developing a novel mechanism to preserve differential privacy in deep neural networks, such that: (1) The privacy budget consumption is totally independent of the number of training steps; (2) It has the ability to adaptively inject noise into features based on the contribution of each to the…
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…
Popular approaches to differential privacy, such as the Laplace and exponential mechanisms, calibrate randomised smoothing through global sensitivity of the target non-private function. Bounding such sensitivity is often a prohibitively complex analytic calculation. As an alternative, we propose a straightforward sampl…
Optimizes survey design for private mean estimation with reduced variance.
problem Minimizing variance in private mean estimation with privacy constraints.
method Formulates optimal survey design as an optimization problem, determining optimal subsampling sizes to minimize variance.
result Identifies the first privacy-aware stratified sampling scheme that minimizes variance under different privacy mechanisms.
The Dirichlet mechanism protects privacy while minimizing KL divergence.
problem Minimizing KL divergence while protecting sensitive data privacy.
method Using the exponential mechanism with the KL divergence loss function, resulting in the Dirichlet mechanism.
result Proved a probability tail bound on KL divergence and derived a lower bound for sample complexity.
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.
Efficiently transforms samples from various statistical models.
problem Approximately transforming samples from one statistical model to another without knowing the source model's parameters.
method Constructs computationally efficient procedures to reduce uniform, Erlang, and Laplace models to general target families.
result Establishes nonasymptotic reductions between canonical high-dimensional problems, such as mixtures of experts, phase retrieval, and signal denoising.
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.
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.
Following Feynman's prescription for constructing a path integral representation of the propagator of a quantum theory, a short-time approximation to the propagator for imaginary time, N=1 supersymmetric quantum mechanics on a compact, even-dimensional Riemannian manifold is constructed. The path integral is interprete…
Private variable selection method controls FDR with simulations showing reasonable power.
problem Performing variable selection with privacy constraints.
method Private knockoff filter using Gaussian and Laplace mechanisms.
result Achieves controlled false discovery rate (FDR) in variable selection.
The paper analyzes network models with binary values and sub-Gamma noise, deriving asymptotic properties.
problem Analyzing network models with binary values and sub-Gamma noise.
method Derives asymptotic properties of network models with binary values and sub-Gamma noise.
result Established asymptotic consistency and normality of parameter estimators in network models.
Dirichlet-Neumann duality for Riemannian submersions
problem Spectral geometry of Riemannian submersions
method Summation formula for reciprocal of basic Dirichlet eigenvalues
result Supersymmetric duality between basic Dirichlet and Neumann spectra
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum mechanical observables. In particular, previous studies constructed quantum grav…
Quantum systems on coadjoint orbits yield spectra matching Dolbeault and de Rham indices.
problem Finding exact spectra of generalized Laplace operators on coadjoint orbits.
method Truncation of 1D sigma models and nonlinear chiral multiplets.
result Exact spectra of spin chain Hamiltonians match Dolbeault and de Rham indices of target spaces.
Intuition drawn from quantum mechanics and geometric optics raises the following long-standing question: can the length spectrum of a closed Riemannian manifold be recovered from its Laplace spectrum? The Poisson relation states that for any closed Riemannian manifold (M,g) the singular support of the trace of its wa…
The Schroedinger operators on the Newtonian space-time are defined in a way which make them independent on the class of inertial observers. In this picture the Schroedinger operators act not on functions on the space-time but on sections of certain one-dimensional complex vector bundle -- the Schroedinger line bundle. …
Let x:M→Em be an isometric immersion of a Riemannian manifold M into a Euclidean m-space. Denote by Δ the Laplace operator of M. Then Δ gives rise to a differentiable map L:M→Em, called the Laplace map, defined by L(p)=(Δx)(p), p∈M. We call L(M) the Laplace image, and the transformat…
The paper examines special Q-nets that terminate after a finite number of Laplace steps.
problem Understanding the termination of Laplace sequences in Q-nets.
method Analyzing discrete Koenigs nets and their Laplace sequences.
result For certain Koenigs nets, Laplace sequences terminate after a finite number of steps.
Estimates eigenvalues of poly-Laplace operator on lattice subgraphs.
problem Estimating eigenvalues of poly-Laplace operator on subgraphs of lattice graphs.
method Introduced discrete poly-Laplace operator, derived upper and lower bounds for eigenvalues.
result Poly-Laplace eigenvalues are at least squares of lower-order poly-Laplace eigenvalues.
Introduces a new elliptic operator with positive eigenvalue.
problem None explicitly stated in the abstract.
method Introduces a new elliptic operator called the two-radical Laplace operator.
result The eigenvalue of the new operator is the positive square root of the Laplace operator's eigenvalue.
Revisits online Laplace methods for neural networks, showing they are sound under certain conditions.
problem Online Laplace methods violate the Laplace approximation's critical assumption.
method Re-derives online Laplace methods, showing they target a variational bound on a mode-corrected variant of the Laplace evidence.
result Online Laplace and its mode-corrected counterpart share stationary points that satisfy the Laplace method's assumption.
Trapezoids uniquely identified by their Dirichlet Laplace spectrum.
problem Identifying trapezoids based on their spectral properties.
method Analyzing the Dirichlet Laplace spectrum of non-obtuse trapezoids.
result Non-obtuse trapezoids are uniquely determined by their Dirichlet Laplace spectrum.
Formula derived for Laplace-Beltrami on Stiefel manifold.
problem Finding Laplace-Beltrami operator on Stiefel manifold.
method Using the general framework of Laplace operators on constraint manifolds, derived the explicit formula in terms of ambient Euclidean coordinates.
result Extended previously known formulas for sphere and special orthogonal group.
Study compares eigenvalues on spherically symmetric manifolds to Euclidean balls.
problem Comparing eigenvalues on spherically symmetric manifolds to Euclidean balls.
method Examines Dirichlet Laplace eigenvalues on balls of spherically symmetric manifolds and Euclidean space.
result Eigenvalues on spherically symmetric manifolds are smaller for small radii, but larger for hyperbolic spaces.
New methods improve Laplace approximations for deep neural networks by selecting key parameters.
problem Improving uncertainty quantification in deep neural networks using computationally feasible approximations.
method Gradient-Laplace and Greedy-Laplace methods for selecting parameters in sub-network Laplace approximations.
result Gradient-Laplace method outperforms existing heuristic approaches and provides formal optimality guarantees.
A new method combines Laplace and Variational Bayes for scalable inference.
problem Complex models and large datasets make exact inference infeasible.
method Low-Rank Variational Bayes Correction (VBC) using Laplace method and Variational Bayes correction in a lower dimension.
result The method ensures scalability in both model complexity and data size.
The paper studies graph Laplace operator behavior near isolated singularities.
problem Investigating asymptotics of graph Laplace operator near isolated singularities.
method Analyzing curvature growth and conformal modifications to understand operator behavior.
result The graph Laplace operator converges to a weighted Laplace-Beltrami operator as bandwidth decreases, or behaves like \(O(\frac{1}{\sqrt{t}})\) if curvature grows too fast.
Differential privacy provides strong privacy guarantees simultaneously enabling useful insights from sensitive datasets. However, it provides the same level of protection for all elements (individuals and attributes) in the data. There are practical scenarios where some data attributes need more/less protection than ot…
QLA improves Bayesian uncertainty estimation for DNNs without increasing computational cost.
problem Overconfident out-of-distribution predictions from DNNs.
method Proposes Quadratic Laplace Approximation (QLA) to improve Bayesian uncertainty quantification.
result QLA yields modest yet consistent uncertainty estimation improvements over Linearized Laplace Approximation (LLA) on five regression datasets.