Unified framework for DRL algorithms using statistical estimation.
problem Designing and analyzing DRL algorithms in terms of return distribution statistics.
method Decompose DRL algorithms into statistical estimation and return distribution imputation.
result Improved analyses and a new algorithm (EDRL) based on expectiles.
Two EM algorithms estimate prior distributions in mixture of linear regressions.
problem Estimating prior distributions in mixture of linear regressions.
method Two EM algorithms: one for continuous priors, one for discrete priors.
result Both algorithms accurately estimate prior distributions and the number of clusters.
Private KL distribution estimation improved with instance-optimality.
problem Minimizing KL divergence between true and estimated distributions.
method Construct minimax optimal private estimators, then focus on instance-optimality.
result Achieved instance-optimality up to constant factors for KL estimation.
This paper tackles distributed estimation of the top-L eigenspace in PCA for large data sets.
problem Challenges in estimating the top-L eigenspace in principal component analysis for large data sets.
method Proposes a novel multi-round algorithm using shift-and-invert preconditioning and convex optimization.
result Achieves a fast convergence rate and covers the targeted top-L eigenspace without explicit eigengap assumption.
In this paper we develop an Expectation Maximization(EM) algorithm to estimate the parameter of a Yule-Simon distribution. The Yule-Simon distribution exhibits the "rich get richer" effect whereby an 80-20 type of rule tends to dominate. These distributions are ubiquitous in industrial settings. The EM algorithm presen…
EDAs are shown to be a type of EM algorithm.
problem Understanding and improving Estimation of Distribution Algorithms.
method Connecting EDAs to Expectation-Maximization (EM) framework.
result EDAs can be understood as a special case of EM.
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important characteristic for large distributed systems. We establish connections between performance of…
New efficient algorithm for approximate PML distribution.
problem Computing the profile maximum likelihood (PML) distribution efficiently.
method Exploiting sparsity structure and new matrix rounding algorithm.
result First provable computationally efficient implementation of PseudoPML.
New path-gradient estimator for continuous normalizing flows.
problem Limitation of simple Gaussian variational distributions in complex applications.
method Proposed a path-gradient estimator for continuous normalizing flows.
result Empirical evidence of superior performance of the new estimator.
Paper explores Elliptical Wishart distributions in signal processing and machine learning.
problem Estimating parameters of Elliptical Wishart distributions.
method Proposes fixed point and Riemannian optimization algorithms for maximum likelihood estimation.
result Characterizes existence, uniqueness, and convergence of the MLE.
Private density estimation in Wasserstein distance for geographic populations.
problem Private estimation of population density distributions.
method Differentially private algorithms for Wasserstein distance, instance-optimal.
result Uniformly achievable instance-optimal rates in both 1D and 2D.
We investigate an existing distributed algorithm for learning sparse signals or data over networks. The algorithm is iterative and exchanges intermediate estimates of a sparse signal over a network. This learning strategy using exchange of intermediate estimates over the network requires a limited communication overhea…
Introduces LDM to estimate machine learning algorithm capacity.
problem Estimating the performance of supervised learning algorithms.
method Characterizes algorithm flexibility using the diversity of possible outputs.
result LDM provides valuable insight into algorithm prediction behavior.
New algorithm efficiently estimates symmetric properties using approximate PML.
problem Estimating symmetric properties of a distribution efficiently.
method Developed an algorithm to compute an approximate PML distribution in nearly linear time.
result Achieved nearly linear time universal plug-in estimator for all symmetric functions.
Unified meta algorithms estimate various distribution functionals in infinite-armed bandits.
problem Estimating various distribution functionals in infinite-armed bandits.
method Unified meta algorithms for offline and online settings, achieving optimal sample complexities.
result Online estimation offers significant advantage for certain distribution functionals.
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…
ULA estimates covariance of log-concave distributions efficiently.
problem Estimating covariance matrices of log-concave distributions efficiently.
method Unadjusted Langevin algorithm (ULA) for sampling and covariance estimation.
result Sample complexity of single-chain ULA is smaller than that of parallel ULA by a logarithmic factor.
Proves subgaussian distributions are SoS-certifiably subgaussian, enabling efficient algorithms for various statistical tasks.
problem Efficiently learning from subgaussian distributions in high dimensions.
method Universal constant C and polynomial sum of squares (SoS) approach. result Proves subgaussian distributions are SoS-certifiably subgaussian.
In this paper is proposed a new heuristic approach belonging to the field of evolutionary Estimation of Distribution Algorithms (EDAs). EDAs builds a probability model and a set of solutions is sampled from the model which characterizes the distribution of such solutions. The main framework of the proposed method is an…
SURF simplifies distribution estimation with simple, robust, and fast algorithms.
problem Efficient and accurate distribution estimation in statistics and machine learning.
method Piecewise polynomial approximation using empirical probability interpolation and divide-and-conquer merging.
result Surpassing state-of-the-art algorithms in efficiency and accuracy, SURF estimates distributions robustly and quickly.
Profile entropy measures learnability and compressibility of discrete distributions.
problem Understanding the learnability and compressibility of discrete distributions.
method Investigates profile entropy, showing its role in estimation, inference, and compression.
result Profile entropy is a fundamental measure unifying estimation, inference, and compression.
Efficiently estimates distributed mean with side information, near-optimal and universal.
problem Distributed mean estimation with side information in communication constrained settings.
method Wyner-Ziv estimators for communication and computation efficiency.
result Near-optimal and universal recovery guarantees for distributed optimization and compression.
New algorithm reduces communication in distributed eigenspace estimation.
problem Efficiently estimating eigenspaces in distributed settings without excessive communication.
method Communication-efficient distributed algorithm using Procrustean alignment.
result Achieves similar error rate to centralized estimator for PCA.
New RESK distributions improve robust clustering of skewed data.
problem Robustly clustering non-symmetric, heavy-tailed data clusters.
method Proposes RESK distributions and an EM algorithm with robust skew-Huber M-estimator.
result Numerical experiments confirm the effectiveness of the proposed methods.
New algorithm estimates eigenspace with faulty nodes, matching performance of existing methods.
problem Estimating eigenspace in distributed systems with node failures.
method Develops an eigenspace estimation algorithm for distributed environments with arbitrary node failures.
result Matches performance of existing non-robust estimator up to an additive error.
OPAA estimates probability densities using functional analysis.
problem Estimating probability density functions efficiently and accurately.
method OPAA uses a parallelizable algorithm based on functional analysis to estimate probability distributions.
result OPAA provides an efficient method to estimate probability density functions and normalizing weights.
Efficiently estimates sparse mean from heavy-tailed data.
problem Robustly estimating sparse mean from heavy-tailed distributions.
method Stability-based approach adapted for heavy-tailed data.
result Optimal sample complexity with logarithmic dependence on dimension.
Paper tackles moment estimation under covariate shift with a two-stage algorithm.
problem Estimating moments under covariate shift when source and target distributions differ.
method Proposes a two-stage algorithm: first, an optimal estimator for the source distribution; second, likelihood ratio reweighting for calibration.
result Achieves minimax optimal bound for moment estimation.
New collaborative algorithm improves personalized mean estimation in online settings.
problem Online estimation of means from multiple, possibly overlapping distributions.
method Novel collaborative strategy for active querying and mean estimation.
result Algorithm improves mean estimates through communication among agents.
Efficiently estimates Gaussian distributions privately and robustly.
problem Private and robust estimation of Gaussian distributions.
method Efficient algorithms for pure and approximate differential privacy models.
result Optimal sample complexity in both pure and approximate differential privacy settings.
New mixture models for clustering and density estimation of unknown distributions.
problem Clustering and density estimation of data with unknown distributions.
method Two fitting methods: EM algorithm and Bayesian non-parametric method using Gibbs sampler.
result Effective clustering and density estimation of data with unknown distributions.
Paper proposes a new method for better estimating continuous distributions in RL.
problem Challenges in parameterizing estimated distributions for better approximation of true continuous distribution.
method Proposes fully parameterized quantile function with fraction and value networks.
result Significantly outperforms existing distributional RL algorithms on 55 Atari Games.
New method for robust learning from batches, even adversarial ones.
problem Learning from batches that may be corrupt or adversarial.
method General framework for robust learning, derived from optimal robust algorithms.
result First robust agnostic learning algorithms for various distributions.
New algorithm identifies near-optimal policies in adversarial distributed RL settings.
problem Adversarial agents in distributed RL settings that can collude and report arbitrary data.
method Weighted-Clique algorithm for robust mean estimation from batches, combined with novel distributed algorithms.
result Achieves superior robustness guarantees and near-optimal sample complexities in both offline and online settings.
We quantify uncertainty in Oja's algorithm's leading eigenvector estimation.
problem Estimating the error of Oja's algorithm's leading eigenvector from streaming data.
method Combining U-statistics, high-dimensional central limit theorems, and multiplier bootstrap.
result Established a weighted χ² approximation for the error between the eigenvector and algorithm output.
Develops a novel stochastic algorithm for diagonal estimation of large matrices.
problem Efficient diagonal estimation for large or implicit matrices.
method Adaptive parameter selection in a stochastic algorithm.
result Lower bound on random query vectors needed for estimation.
Paper improves statistical efficiency of median-of-means estimator for Byzantine robust distributed inference.
problem Byzantine robustness in distributed learning systems.
method Variance reduced median-of-means (VRMOM) estimator for Byzantine robust distributed inference.
result Achieves a fast convergence rate with only a constant number of rounds of communications.
Two novel distributed VB algorithms improve Bayesian inference in sensor networks.
problem Efficient inference in Bayesian frameworks for sensor networks.
method Two novel distributed VB algorithms for general Bayesian inference, using stochastic natural gradient and ADMM.
result Distributed algorithms perform nearly as well as centralized ones, demonstrating excellent performance.
Distributed learning method for multi-agent reinforcement learning with policy coordination.
problem Solving multi-agent reinforcement learning problems with coordination.
method Distributed off-policy actor critic with policy consensus.
result The proposed algorithm achieves asymptotic agreement on the global optimal policy function.
Estimating statistical models within sensor networks requires distributed algorithms, in which both data and computation are distributed across the nodes of the network. We propose a general approach for distributed learning based on combining local estimators defined by pseudo-likelihood components, encompassing a num…
New method estimates Gaussian copulas with missing data using EM algorithm.
problem Estimating Gaussian copulas with missing data and prior assumptions.
method Rigorous application of the Expectation Maximization (EM) algorithm for marginal distributions and dependence structure.
result Joint distribution learned is closer to the underlying distribution.
Efficiently estimates covariance matrix for elliptical distributions under strong contamination.
problem Robust estimation of covariance matrix in the presence of adversarial corruptions.
method Proposes an algorithm that uses spatial sign of elliptical distributions and spectral covariance filtering.
result Achieves nearly optimal error guarantee for various elliptical distributions.
Paper introduces DQPOPE for estimating return distributions in reinforcement learning.
problem Estimating the entire return distribution from off-policy data.
method Deep quantile process regression for distributional off-policy evaluation.
result DQPOPE achieves statistical advantages by estimating full return distribution with same sample size.
Faster algorithms estimate robust covariance in high dimensions.
problem Estimating covariance in corrupted high-dimensional data.
method Developed faster algorithms with nearly optimal error guarantees.
result Running time nearly matches computing the empirical covariance.
Paper proposes a privacy-preserving method for estimating complex models.
problem Lack of flexibility in existing model classes for approximating data-generating processes.
method Privacy-preserving distributed estimation of generalized additive mixed models using component-wise gradient boosting.
result Proposed algorithm yields equivalent model estimates as component-wise gradient boosting on pooled data.
Polynomial-time private algorithm for robust estimation of mean and covariance in the presence of outliers.
problem Estimating mean and covariance in the presence of adversarial outliers.
method Stabilizing convex relaxations using a new estimate-dependent noise injection mechanism.
result First efficient private robust estimation algorithm for covariance without condition-number assumptions.
New algorithm learns changing discrete distributions with minimal drift error.
problem Learning discrete distributions that change over time with limited past samples.
method Adaptive algorithm using data-dependent bounds to balance statistical and drift errors.
result Tighter statistical error bounds for drifting distributions with or without finite support.
Efficient algorithm for estimating target mean under known sampling distribution.
problem Statistical estimation under known sampling distribution without distributional assumptions.
method Worst-case analysis of weighted combination of sample values.
result Worst-case expected error is at most a π/2 factor worse than optimal.