Quantum algorithm estimates mean with sub-Gaussian error.
problem Estimating mean of quantum-computed random variables.
method Quantum mean estimation algorithm with sub-Gaussian error rate.
result Achieves nearly-optimal quadratic speedup over classical methods.
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.
New winsorized mean improves robustness to up to 50% contamination.
problem Improving robustness of mean estimation in the presence of outliers.
method Outlyingness-induced winsorized mean approach.
result Achieves up to 50% contamination robustness with sub-Gaussian performance.
Study on estimating Gaussian mean from coarse data, resolving identifiability and computational efficiency questions.
problem Estimating the mean of a Gaussian distribution from coarse data (sets containing true samples rather than exact values).
method Analyzes the conditions for mean identifiability and computable estimation under convex partitions.
result Resolves the identifiability and computational efficiency questions for Gaussian mean estimation from coarse data.
New study shows mean estimation algorithms can't beat sub-Gaussian rate in general.
problem Improving mean estimation beyond worst-case scenarios.
method Constructing counterexamples and introducing neighborhood optimality.
result No reasonable estimator can achieve better than sub-Gaussian error rate for any distribution.
New estimator accurately estimates mean of real-valued distributions without variance knowledge.
problem Estimating the mean of real-valued distributions without prior variance knowledge.
method Introduces a novel estimator that converges sub-Gaussian and works across distributions with bounded variance.
result The estimator achieves accuracy of σ·(1+o(1))√(2log(1/δ)/n) with parameters n, δ, and σ².
Improved median of means estimator with tighter bounds.
problem Improving the efficiency and reliability of median of means estimator.
method Modification of the median of means estimator with sub-Gaussian deviation bounds.
result Achieves nearly optimal constants under minimal assumptions.
New algorithm estimates Gaussian means and covariances efficiently and privately.
problem Estimating Gaussian parameters privately and efficiently.
method Differentially private preconditioner to transform arbitrary Gaussian samples.
result First polynomial-time, sample-efficient estimator for arbitrary Gaussian distributions.
Algorithm estimates common mean from Gaussian variables with unknown variances.
problem Estimating common mean from Gaussian variables with different unknown variances.
method Intuitive and efficient algorithm using Subset-of-Signals model as benchmark.
result Improved estimation error by polynomial factors compared to previous work.
Robust estimators for Gaussian sparse tasks with optimal error under contamination.
problem Robust mean estimation, PCA, and linear regression in the presence of Huber contamination.
method Novel multidimensional filtering method for sparse regime.
result Optimal error guarantees within constant factors for Gaussian robust k k k -sparse mean estimation. Study on efficient estimation of Gaussian mean with limited communication.
problem Estimating Gaussian mean under communication constraints.
method Decomposition into localization and refinement stages, development of communication-efficient and statistically optimal procedures.
result Established minimax rates of convergence and developed optimal procedures.
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.
New kriging method improves mean estimation and uncertainty.
problem Improving mean estimation and uncertainty in kriging.
method Proposes a rational kriging method using generalized least squares and Gaussian process.
result Generalized least squares estimate is more well-behaved than ordinary kriging.
Study on estimating Gaussian mean with missing data in high dimensions.
problem Estimating Gaussian mean in high dimensions with missing data due to realizable contamination.
method Statistical Query model, Low-Degree Polynomials, PTF tests, and algorithms.
result Established information-computation gap and developed efficient algorithms.
We study the problem of estimating the mean of a random vector X X X given a sample of N N N independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of X X X exists. The estimator is based on a novel concept of a…
New measure of robustness for estimators, with tight bounds for Gaussian mean estimation.
problem Developing robust statistical estimators for datasets with noise or outliers.
method Introducing empirical sensitivity as a new robustness measure and proving lower bounds for Gaussian mean estimation.
result Empirical sensitivity bounds for optimal estimators are tight, showing obstructions on mean and variance.
We consider the problem of estimating the mean and covariance of a distribution from iid samples in R n \mathbb{R}^n R n , in the presence of an η η η fraction of malicious noise; this is in contrast to much recent work where the noise itself is assumed to be from a distribution of known type. The agnostic problem includes many…
Optimizes sliding window approach for tracking Gaussian densities.
problem Improving tracking performance of Gaussian density estimation.
method Theoretical analysis of sliding window Gaussian Kernel Density Estimators.
result Empirical evidence shows improved tracking performance with optimal weight sequence.
We propose an estimator for the mean of a random vector in R d \mathbb{R}^d R d that can be computed in time O ( n 4 + n 2 d ) O(n^4+n^2d) O ( n 4 + n 2 d ) for n n n i.i.d.~samples and that has error bounds matching the sub-Gaussian case. The only assumptions we make about the data distribution are that it has finite mean and covariance; in particular, we mak…
This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition technique yields consistent parameter estimates from low-order observable moments, wit…
A new algorithm estimates mean adaptively to covariance, faster and more flexible than existing methods.
problem Estimating mean of a distribution with unknown covariance efficiently and privately.
method Adaptive differentially private algorithm with optimal convergence rates and near-linear sample complexity.
result Achieves optimal rates of convergence with respect to the Mahalanobis norm ∣ ∣ ⋅ ∣ ∣ Σ ||\cdot||_Σ ∣∣ ⋅ ∣ ∣ Σ . We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus on estimators based on median-of-means techniques but other methods such as the t…
Lower bound shows super-polynomial gap for estimating truncated Gaussian means.
problem Estimating mean of truncated Gaussian distribution with limited samples.
method Statistical Query (SQ) lower bounds for learning.
result Super-polynomial information-computation gap for the task.
Enhances deep neural networks with fixed-mean Gaussian processes for uncertainty estimation.
problem Post-hoc uncertainty estimation of pre-trained deep neural networks.
method Fixed-mean Gaussian processes with variational inference for efficient stochastic optimization.
result FMGP improves uncertainty estimation and computational efficiency compared to state-of-the-art methods.
Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adaptation to combination MCC and combination to adaptation MCC, are developed to deal with the distributed estimation over network in impulsive (long-tailed) noise environments. The cost functions used in distri…
Study non-asymptotic estimation bounds for LTI models with Gaussian noise.
problem Estimating parameters of LTI models with non-asymptotic error bounds.
method Sharp non-asymptotic lower bounds using Cramér-Rao and van Trees inequalities, concentration results, and differential geometric constructions.
result Sharp and rate-optimal lower bounds for mean square estimation risk.
Proposes a convex method to estimate GGMs with covariates.
problem Improving conditional independence structure estimation with covariates.
method Convex optimization framework for joint estimation of mean and precision matrix.
result Improved theoretical guarantees and practical utility demonstrated.
Study robust estimation under varying corruption probabilities in data.
problem Robust estimation in scenarios with heterogeneous corruption rates.
method Developed estimators for mean and regression under various corruption patterns.
result Optimal estimators can discard corrupted samples beyond a specific threshold.
This paper improves Gaussian process predictions by integrating prior knowledge.
problem Gaussian processes lack predictive power when prior information is ignored.
method Derive mean and covariance functions from previous data using weighted sums of basis functions.
result Integrating prior knowledge significantly increases look-ahead time and accuracy.
Paper extends multi-task Gaussian Cox processes for heterogeneous tasks.
problem Modeling multiple heterogeneous correlated tasks jointly.
method Data augmentation and mean-field approximation for non-conjugate Bayesian inference.
result Demonstrates improved performance and inference on synthetic and real data.
The stochastic multi-armed bandit problem is well understood when the reward distributions are sub-Gaussian. In this paper we examine the bandit problem under the weaker assumption that the distributions have moments of order 1+ε, for some ε ∈ ( 0 , 1 ] ε\in (0,1] ε ∈ ( 0 , 1 ] . Surprisingly, moments of order 2 (i.e., finite variance) are suffi…
Efficiently estimates mean in contaminated Gaussian data with near-optimal sample complexity.
problem Robust mean estimation in the presence of mean-shift contamination.
method First computationally efficient algorithm with near-optimal sample complexity and polynomial-time running.
result Approximates the target mean to any desired accuracy with constant fraction of outliers tolerated.
New method for robust linear regression in nearly linear time.
problem High-dimensional robust linear regression with adversarial corruption.
method Proposes estimators for two settings with near linear time complexity.
result Achieves optimal sample complexities and recovery guarantees.
The paper estimates common mean of entangled Gaussians with bounded variances.
problem Estimating common mean of entangled Gaussians with bounded variances.
method Iteratively averaging truncated samples.
result Achieves error $O \left(\frac{\sqrt{n\ln n}}{m}
ight)$ with high probability when m = Ω ( n ln n ) m=Ω(\sqrt{n\ln n}) m = Ω ( n ln n ) . A new method for uncertainty estimation in neural networks using Gaussian-softmax integration.
problem Quantifying uncertainty in neural network predictions.
method Proposes a single-model approach integrating Gaussian distribution with softmax outputs, using mean-field approximation.
result Competitive performance on uncertainty estimation tasks and outperforms many methods on out-of-distribution detection.
We tackle the problem of estimating a location parameter with differential privacy guarantees and sub-Gaussian deviations. Recent work in statistics has focused on the study of estimators that achieve sub-Gaussian type deviations even for heavy tailed data. We revisit some of these estimators through the lens of differ…
We develop time-uniform confidence spheres for estimating means of random vectors.
problem Sequential mean estimation in high-dimensional spaces.
method Derive time-uniform confidence sphere sequences (CSSs) for various types of random vectors.
result Optimal CSSs for log-concave, sub-Gaussian, and sub- ψ ψ ψ random vectors. Simple private estimators for mean and covariance outperform existing methods.
problem Private estimation of mean and covariance at small sample sizes.
method Differentially private estimators for multivariate sub-Gaussian data.
result Asymptotic error rates match theoretical bounds and outperform previous methods.
Gradient boosting can be seen as Gaussian process inference.
problem Improving uncertainty estimates in out-of-domain detection.
method Gradient boosting reformulated as a kernel method converging to Gaussian process inference.
result Gradient boosting can provide better uncertainty estimates through Monte-Carlo estimation of posterior variance.
We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian processes. The proposed method can also achieve high generalization performance fo…
Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical covariance estimator (and its modifications) is very sensitive to outliers in the da…
New algorithms reduce communication for sparse mean estimation in noisy distributed systems.
problem Sparse normal means estimation with limited communication in a distributed setting.
method Two distributed algorithms for estimating a sparse mean vector with sublinear communication.
result Correct support of the sparse mean can be recovered with significantly less communication than previously required.
Method estimates multiple related Gaussian distributions using Laplacian regularization.
problem Jointly estimate multiple related zero-mean Gaussian distributions.
method Laplacian regularized stratified model fitting with hyper-parameters to encourage covariance closeness.
result The method performs well, especially in low data regimes, as demonstrated in finance, radar, and weather.
This paper investigates a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from returns and expert opinions in the form of noisy signals about the current state of the drift arriving at the jump times of a homogeneous Poisson process. Dr…
Paper improves SDR estimation speed and conditions.
problem Improving sufficient dimension reduction for multi-index models.
method Estimating expected smoothed gradient outer product.
result Achieves fast parametric convergence rate of C d ⋅ n − 1 / 2 C_d \cdot n^{-1/2} C d ⋅ n − 1/2 . The mixture of Gaussian distributions, a soft version of k-means , is considered a state-of-the-art clustering algorithm. It is widely used in computer vision for selecting classes, e.g., color, texture, and shapes. In this algorithm, each class is described by a Gaussian distribution, defined by its mean and covarianc…
Corrected whitening restores orthogonality in high-dimensional spherical Gaussian mixtures.
problem In high-dimensional data, standard whitening fails to preserve orthogonality of mixture means.
method Derived exact limits for whitened means dot products using random matrix theory, constructed a corrected whitening matrix.
result Corrected whitening allows for improved estimation of spherical Gaussian mixtures in the large-dimensional regime.
Proposes variational Gaussian approximations for solving the Kushner equation.
problem Solving the Kushner equation for state estimation with observations.
method Tractable variational Gaussian approximations of proximal losses based on Wasserstein and Fisher metrics.
result The proposed method leads to a Gaussian flow consistent with Kalman-Bucy and Riccati flows.