Improved sampling from Gaussian distributions with privacy constraints.
problem Sampling from unbounded Gaussian distributions with differential privacy.
method First $\widetilde{\mathcal{O}}\left(d
ight)$ -sample algorithm for unbounded Gaussians under $\left(\varepsilon, δ
ight)$ -differential privacy.
result A quadratic improvement over previous results, settling an open question.
Improved sample efficiency for private learning of Gaussian mixtures.
problem Learning mixtures of Gaussians with differential privacy.
method Inverse sensitivity mechanism, sample compression, sumset volume bounds.
result Proved optimal sample complexity for private learning of mixtures of Gaussians.
Estimates Gaussian mixtures from weighted samples efficiently.
problem Estimating Gaussian mixtures from weighted samples with correct weight treatment.
method Density interpretation and expectation-maximization method considering weights.
result Correctly estimates Gaussian mixtures with weighted samples.
A simple algorithm for Gaussian mean testing with optimal sample complexity.
problem Distinguishing between standard Gaussian and other Gaussian distributions with unknown mean and covariance.
method An extremely simple algorithm with a one-page analysis.
result Optimal sample complexity of Θ(√d/ε^2) with sample linear time.
Improved sample complexity for Gaussian process approximations.
problem Efficiently approximating Gaussian processes with sparse spectrum.
method Improved sample complexity analysis and auto-encoding algorithm.
result Gaussian process predictions and model evidence can be well-approximated with low sample complexity.
Optimal sample complexity for learning Gaussian DAG models established.
problem Learning the structure of Gaussian DAG models from observational data.
method Established minimax optimal sample complexity for two settings: equal variances without ordering knowledge and general linear models with ordering knowledge.
result Optimal sample complexity n ≍ q log ( d / q ) n\asymp q\log(d/q) n ≍ q log ( d / q ) for both settings, matching undirected graphical models under equal variances. The paper shows how to efficiently generate large Gaussian process samples with reliability guarantees.
problem Generating large-scale Gaussian process samples efficiently and with reliability.
method Demonstrates scaling data generation to large \(n\) while providing high probability guarantees.
result Efficiently generates large Gaussian process samples with reliability guarantees.
Improved sample efficiency in reinforcement learning with deep Gaussian processes.
problem Efficiently learn to control actions with limited interaction data.
method Deep Gaussian processes that simulate dynamics with depth and prior knowledge.
result Significantly improved early sample efficiency across various tasks, including half-cheetah control.
Algorithm samples composite logconcave densities efficiently.
problem Sampling from composite logconcave densities efficiently.
method Uses a restricted Gaussian oracle and gradient queries.
result Achieves strong total variation distance guarantees.
New algorithm reduces regret in multi-armed bandit problems with Gaussian rewards.
problem Optimizing decisions in multi-armed bandit problems with Gaussian rewards.
method Proposed TSCG and UTSCG algorithms using Thompson Sampling with Gaussian prior.
result Achieved lower regret bounds for optimal arm selection.
Improved sample complexity for Gaussian Mixture Models using Pair Correlation Factor.
problem Understanding the sample complexity of Gaussian Mixture Models.
method Introducing Pair Correlation Factor (PCF) to measure clustering of component means and improving sample complexity bounds.
result The Pair Correlation Factor (PCF) more accurately determines the difficulty of parameter recovery in Gaussian Mixture Models.
Scalable algorithm for sampling Gaussian processes using sparse grids and preconditioners.
problem Generating high-dimensional Gaussian random vectors for GP sampling is computationally challenging.
method Proposes a scalable algorithm using inducing points approximation with sparse grids and additive Schwarz preconditioners.
result Demonstrates the efficacy and accuracy of the proposed method through experiments and comparisons.
Optimal algorithm learns Gaussian under halfspace truncation with minimal samples.
problem Learning a Gaussian distribution truncated to an unknown halfspace.
method Efficient algorithm using n = i l d e O ( d 2 / ε 2 ) n = ilde{O}(d^2/\varepsilon^2) n = i l d e O ( d 2 / ε 2 ) samples and runtime dominated by empirical covariance matrix computation. result Optimal sample and time complexity bounds for learning a Gaussian under halfspace truncation.
Polynomial-time DP algorithm for learning Gaussians with matching sample complexity.
problem Learning Gaussian distributions while maintaining privacy.
method General framework for reducing DP estimation to non-private, polynomial-time algorithm for Gaussian learning.
result Matching sample complexity to information-theoretic upper bound for Gaussian learning.
Improves Bayesian optimization using Gaussian process Thompson sampling.
problem Global optimization of Gaussian process posterior samples.
method Carefully selects starting points for gradient-based multi-start optimizers, identifies all local optima via univariate global rootfinding, and optimizes the posterior sample.
result Dramatic improvements in overall performance of Bayesian optimization.
This work introduces efficient sampling methods for Gaussian processes by focusing on pathwise conditioning.
problem Intractable mathematical expressions in Gaussian process posteriors limit practical applications.
method Investigates a pathwise interpretation of conditioning to derive efficient sampling methods.
result Derives a general family of approximations that allow for efficient sampling of Gaussian process posteriors.
Study shows private learning of mixtures of Gaussians is possible with polynomial samples.
problem Estimating mixtures of Gaussians under differential privacy constraints.
method Developed a new framework for privately learning mixtures of Gaussians without structural assumptions.
result Polynomial number of samples (poly(k,d,1/α,1/ε,log(1/δ))) sufficient for estimation up to total variation distance α with (ε, δ)-DP.
Efficiently learns Gaussian tree models with near-optimal sample complexity.
problem Learning tree-structured Gaussian distributions efficiently.
method Conditional mutual information tester for Gaussian variables, near-optimal sample complexity.
result Near-optimal sample complexity for structure learning of Gaussian tree models.
This study approximates distances between Gaussian processes and covariance operators using RKHS.
problem Approximating distances between Gaussian processes and covariance operators from finite samples.
method Using reproducing kernel Hilbert space (RKHS) covariance and cross-covariance operators, the study shows how to consistently and efficiently estimate Sinkhorn divergence from finite samples.
result Convergence rates are dimension-independent and of the same order as Hilbert-Schmidt distance.
This paper optimizes Gaussian mixture model learning with optimal sampling complexity.
problem Learning the number of components and mixing distribution in 1D Gaussian mixtures.
method Fourier-based approach to estimate model order and mixing distribution.
result The proposed method matches the optimal sampling complexity and outperforms conventional techniques.
New study shows Gaussian samplers struggle with heavy-tailed targets, while stable samplers excel.
problem The difficulty of sampling from heavy-tailed distributions using Gaussian versus stable oracles.
method Comparison of Gaussian and stable oracles for proximal samplers.
result Gaussian samplers have a fundamental barrier for high-accuracy guarantees in heavy-tailed sampling, while stable samplers excel.
The paper integrates multiple Gaussian process predictions using Monte Carlo sampling.
problem Accurate prediction of variables using multiple models.
method Log-linear pooling of Gaussian process predictions, combined with Monte Carlo sampling.
result The log-linear pooling method improves prediction accuracy compared to linear pooling.
HMC improves Gaussian sampling efficiency with long, random steps.
problem Efficiently sampling from high-dimensional Gaussian distributions.
method Hamiltonian Monte Carlo with long and random integration times.
result HMC achieves ε \varepsilon ε -closeness in total variation distance with O ~ ( κ d 1 / 4 log ( 1 / ε ) ) \widetilde{O}(\sqrt{\kappa} d^{1/4} \log(1/\varepsilon)) O ( κ d 1/4 log ( 1/ ε )) gradient queries. Differential privacy of Gaussian process posterior sampling
problem Privacy of posterior sample paths from Gaussian process
method Intrinsic randomness yields DP guarantees
result Intrinsic randomness yields DP guarantees
Study learns Gaussian mixtures from censored data.
problem Learning Gaussian mixtures with incomplete data.
method Proposes an algorithm to estimate weights and means with minimal samples.
result Achieves accurate estimation with very few samples.
Elliptical slice sampling converges geometrically, providing reliable sampling for Bayesian learning.
problem Sampling from posterior distributions in Bayesian learning.
method Elliptical slice sampling, geometric ergodicity.
result Elliptical slice sampling yields geometric convergence guarantees under weak regularity assumptions.
This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian Processes (GP), and to states represented as a weighted sum of Gaussians. The key attr…
New bounds for private learning of high-dimensional Gaussian distributions.
problem Learning high-dimensional Gaussian distributions under differential privacy constraints.
method Analytic tools for constructing global covers from local covers, modified hypothesis selection techniques.
result Near-optimal sample complexity bounds for general Gaussians, conjectured to be near-optimal in the general case.
Improves GP models with known bounds for sampling and optimization.
problem Functions with known upper and lower bounds.
method Transforms GP models with bounds for posterior sampling and BO.
result Bounded entropy search (BES) selects points satisfying constraints.
Proposes sampling from reverse diffusion posteriors for contextual bandits.
problem Complex distributions in contextual bandits.
method Approximate posterior sampling with a diffusion model prior using Laplace approximation.
result Empirically consistent and efficient approximations for contextual bandits.
New sampling methods improve statistical efficiency for intractable targets.
problem Sampling from complex, intractable probability distributions.
method Gaussian invariant versions of RWM, MALA, and Hessian MALA.
result Gaussian invariant sampling leads to improved statistical efficiency.
The Gaussian process (GP) is a popular way to specify dependencies between random variables in a probabilistic model. In the Bayesian framework the covariance structure can be specified using unknown hyperparameters. Integrating over these hyperparameters considers different possible explanations for the data when maki…
Study provides bounds for estimating intrinsic dimension using Gaussian kernels.
problem Estimating intrinsic dimension from data.
method Finite-sample concentration and anti-concentration bounds for Gaussian kernel sums.
result Explicit dependence on sample size, bandwidth, and geometric parameters.
Motivated by a sampling problem basic to computational statistical inference, we develop a nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical analysis. Given an n × n n\times n n × n SDDM matrix M {\bf \mathbf{M}} M , and a constant − 1 ≤ p ≤ 1 -1 \leq p \leq 1 − 1 ≤ p ≤ 1 , our algorithm gives efficient access to a…
Thompson Sampling bounds for contextual bandits with sub-Gaussian rewards.
problem Improving the performance of Thompson Sampling in contextual bandits with sub-Gaussian rewards.
method Proved comprehensive bounds on Thompson Sampling expected cumulative regret based on mutual information and lifted information ratio for sub-Gaussian rewards.
result Explicit regret bounds for various contextual bandit scenarios.
New algorithms estimate parameters of Gaussian and non-Gaussian distributions from truncated samples.
problem Estimating distributional parameters from truncated samples.
method Polynomial time algorithms for exponential families and simple sets.
result Efficient algorithms for estimating parameters of various distributions from truncated samples.
Study on learning sparse fixed-structure Gaussian Bayesian networks with near-optimal sample complexity.
problem Learning a fixed-structure Gaussian Bayesian network up to a bounded error in total variation distance.
method Analysis of node-wise least squares regression and introduction of BatchAvgLeastSquares and CauchyEst algorithms.
result BatchAvgLeastSquares and CauchyEstTree have near-optimal sample complexity.
pmsims R package uses Gaussian process for flexible sample size estimation in clinical models.
problem Determining adequate sample size for clinical prediction models.
method Simulation-based Gaussian process search for flexible sample size estimation.
result Gaussian process-based method produces more stable sample size estimates, especially in challenging settings.
Two algorithms learn Gaussian graphical models from Glauber dynamics trajectories.
problem Learning Gaussian graphical models from dependent data.
method Two complementary approaches: local edge-testing and burn-in/thinning reduction.
result Both approaches provide finite-sample recovery guarantees and empirical comparisons.
ERTS uses Thompson sampling for Gaussian entropic risk bandits, achieving regret bounds.
problem Risk in decision making complicates reward maximization in MAB problems.
method ERTS (Entropic Risk Thompson Sampling) using Thompson sampling with an entropic risk measure.
result Regret bounds for ERTS under entropic risk measure provided.
Unified sampling approach for Bayesian imaging problems.
problem Sampling from complex prior and posterior distributions in Bayesian imaging.
method Gaussian latent machine model for efficient prior and posterior sampling.
result Unified and generalized sampling algorithms for various imaging problems.
This study tackles Gaussian process regression with summarized data.
problem Learning and inference with summarized data (summary statistics, counts) in spatial modeling.
method Sample quasi-likelihood approach to Gaussian process regression.
result Approximation performance of the method is influenced by data granularity and covariance function length scale.
VOGP efficiently identifies Pareto optimal solutions in black-box vector optimization.
problem Black-box vector optimization with incomplete order relations.
method VOGP is an adaptive elimination algorithm using Gaussian process bandits.
result VOGP achieves theoretical guarantees with sample complexity bounds.
Near-optimal algorithms for mean estimation and linear regression with Gaussian covariates and Huber contamination.
problem Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination.
method Near-optimal algorithms with optimal error guarantees, achieving sample complexity n = i l d e O ( d / ε 2 ) n = ilde{O}(d/ε^2) n = i l d e O ( d / ε 2 ) and almost linear runtime. result First sample near-optimal and almost linear-time algorithms with optimal error guarantees for both problems.
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of larger frameworks, wherein quantities of interest are ultimately defined by integ…
Nonparametric Thompson Sampling achieves optimal regret for risk-averse bandits with sub-Gaussian rewards.
problem Optimizing risk-averse bandit problems with sub-Gaussian rewards.
method Anchor-free nonparametric Thompson Sampling algorithm ρ e x t − N P T S S G ρ ext{-}NPTS_{\mathrm{SG}} ρ e x t − N P T S SG . result Achieves regret matching the instance-dependent lower bound to leading order in log n \log n log n . A new strategy for identifying the best arm in Gaussian bandits with improved exploration.
problem Best-arm identification for Gaussian bandits with bounded means and unit variance.
method Exploration-Biased Sampling, a non-asymptotic approach with improved exploration behavior.
result Improved exploration behavior makes the strategy more stable and interpretable.
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.