The paper proves statistical consistency and fairness guarantees for a plug-in algorithm.
problem Establishing statistical guarantees for fairness-aware binary classification.
method Proves statistical consistency and derives finite sample guarantees for the plug-in algorithm.
result The plug-in algorithm is statistically consistent and guarantees fairness and differential privacy.
New gossip algorithms improve robustness of rank-based statistics in decentralized systems.
problem Ensuring robustness in decentralized AI and edge intelligence systems, especially in the presence of corrupted or adversarial data.
method Developed asynchronous gossip algorithms for computing rank-based statistics.
result First convergence rate bound for asynchronous gossip-based rank estimation.
New bandit algorithms focus on extreme values, outperforming existing methods.
problem Optimizing decisions based on extreme values rather than expected values.
method Robust statistics-based algorithms with vanishing extremal regret.
result The proposed algorithms achieve superior performance compared to existing methods.
Optimum-statistical collaboration improves black-box optimization efficiency.
problem Improving black-box optimization efficiency through better statistical collaboration.
method Introducing optimum-statistical collaboration framework for hierarchical bandits-based optimization.
result Demonstrated improved regret bounds and better performance in experiments.
Replicable clustering algorithms for k-medians, k-means, and k-centers are proposed.
problem Designing clustering algorithms that produce the same partition on repeated runs under the same distribution.
method Utilizing approximation routines for combinatorial clustering problems in a black-box manner.
result Replicable algorithms for statistical k-medians, k-means, and k-centers with specified approximation and sample complexities. Bandit algorithms struggle with consistent performance and robustness.
problem Achieving consistent and robust performance in stochastic multi-armed bandit settings.
method Analyzing regret minimization trade-offs and proposing distribution-oblivious algorithms.
result Logarithmic regret is inconsistent and super-logarithmic regret is necessary for consistent learning.
Paper tackles reinforcement learning with complex observations and simple latent dynamics.
problem Understanding reinforcement learning with complex observations and simple latent dynamics.
method Statistical and algorithmic analysis of reinforcement learning under general latent dynamics.
result Identifies latent pushforward coverability as a condition for statistical tractability.
Efficient streaming algorithms for robust statistics with near-optimal memory.
problem High-dimensional robust statistics tasks in streaming model.
method First efficient streaming algorithms with near-optimal memory requirements.
result Near-optimal error guarantees and space complexity nearly-linear in the dimension for robust mean estimation.
Improved computational complexity in statistical models using second-order information.
problem Polynomial convergence of gradient descent in singular statistical models.
method Normalized Gradient Descent (NormGD) algorithm with second-order information.
result NormGD reaches final statistical radius in logarithmic iterations of n. Statistical query algorithms and low-degree tests are nearly equivalent in high-dimensional hypothesis testing.
problem High-dimensional hypothesis testing and information-computation gaps.
method Analysis of statistical query framework and low-degree polynomials.
result Statistical query algorithms and low-degree polynomials are almost equivalent in power under mild conditions.
Learning in the presence of outliers is a fundamental problem in statistics. Until recently, all known efficient unsupervised learning algorithms were very sensitive to outliers in high dimensions. In particular, even for the task of robust mean estimation under natural distributional assumptions, no efficient algorith…
New DP EM algorithm with statistical guarantees for mixture models.
problem Preserving privacy in EM algorithms for mixture models.
method Proposed a DP EM algorithm with statistical guarantees.
result Near optimal estimation error for GMM in DP model.
This paper enhances privacy in statistical model checking of cyber-physical systems.
problem Privacy concerns in consumer-level applications due to statistical model checking.
method Proposes expected differential privacy and a new exponential mechanism for sequential algorithms.
result Demonstrates a novel mechanism to preserve privacy in statistical model checking.
Proposes an exponentially increasing step-size for faster parameter estimation in statistical models.
problem Slow convergence of gradient descent in locally convex loss functions.
method Exponentially increasing step-size in gradient descent algorithm.
result Converges linearly to optimal solution under homogeneous assumptions.
Paper develops efficient algorithms for robust distributed learning with statistical guarantees.
problem Limited communication power and adversarial node behaviors in distributed learning.
method Surrogate likelihood framework and median/trimmed mean operations.
result Provable robustness against Byzantine failures and optimal statistical rates.
New framework connects online learning to statistical learning for better generalization bounds.
problem Deriving generalization bounds for statistical learning algorithms.
method Constructing an online learning game and showing a connection to statistical learning.
result Established a connection between online and statistical learning, leading to new generalization bounds.
This article provides the role of big idea statisticians in future of Big Data Science. We describe the `United Statistical Algorithms' framework for comprehensive unification of traditional and novel statistical methods for modeling Small Data and Big Data, especially mixed data (discrete, continuous).
We consider statistical and algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. Prior results show that, from an \emph{algorithmic perspective}, when using sketching matrices constructed from random projections and leverage-score sampling, if the number of sampl…
This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning where objective functions are estimated from available data. We show that these alg…
Study uses online bootstrap for RL inference, showing effectiveness.
problem Statistical inference for RL parameters in online settings.
method Online bootstrap method applied to TD and GTD algorithms in RL.
result Method is distributionally consistent for policy evaluation inference.
Paper reproduces a kernel-based scan B-statistic for online change-point detection.
problem Continuous detection of distribution changes in online data streams.
method Efficient kernel-based scan B-statistic for online change-point detection.
result Scan B-statistic outperforms parametric methods in challenging scenarios.
We present a unifying framework for designing and analysing distributional reinforcement learning (DRL) algorithms in terms of recursively estimating statistics of the return distribution. Our key insight is that DRL algorithms can be decomposed as the combination of some statistical estimator and a method for imputing…
This paper advances FL algorithms for composite optimization and statistical recovery.
problem Federated learning optimization and statistical recovery in composite settings.
method Proposes Fast Federated Dual Averaging for strongly convex and smooth loss, and Multi-stage Federated Dual Averaging for restricted strongly convex and smooth loss.
result Establishes state-of-the-art iteration and communication complexity, and high probability complexity bound with linear speedup.
Survey of robust statistical methods for efficient computation.
problem Efficient robust statistical methods for various forms of data contamination and heavy-tailed distributions.
method Survey and technical connections between robustness forms, showing efficient algorithms.
result Same algorithmic ideas lead to efficient estimators for robustness in different settings.
Paper introduces a new gradient statistic to improve deep learning convergence.
problem Fluctuation effect of gradient updates between iterations.
method Introduces an unbiased stratified statistic \(\bar{G}_{mst}\) and a new algorithm MSSG.
result MSSG algorithm outperforms other sgd-like algorithms in training deep models.
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form solutions of proximal operators and envelope representations based on the Moreau, Fo…
Paper proposes a statistical test for feature selection pipelines using selective inference.
problem Assessing the significance of feature selection pipelines in data analysis.
method Selective inference technique applied to feature selection pipelines composed of various algorithms.
result The proposed statistical test controls false positive feature selection probabilities.
AdaStop improves statistical testing for Deep RL algorithm comparisons.
problem Statistical reproducibility issues in Deep RL.
method AdaStop, a new statistical test based on multiple group sequential tests.
result AdaStop ensures theoretically sound comparisons of Deep RL algorithms.
Study replicability in high-dimensional statistics, resolving open problems.
problem Ensuring consistent results in high-dimensional statistical tasks.
method Introduced replicable learning algorithms and established computational and statistical equivalence with high-dimensional isoperimetric tilings.
result Matching sample complexity upper and lower bounds for replicable mean estimation and coin problem.
We consider statistical as well as algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. For a LS problem with input data (X,Y)∈Rn×p×Rn, sketching algorithms use a sketching matrix, S∈Rr×n with $r \…
The study analyzes the performance of statistical estimators under stability and computational efficiency.
problem Understanding the performance of statistical estimators in relation to stability and computational efficiency.
method Developed a framework to bound statistical accuracy based on the interplay between algorithm convergence rates and stability.
result Unstable algorithms can achieve the same statistical accuracy as stable ones in fewer steps.
We provide sharp empirical estimates of expectation, variance and normal approximation for a class of statistics whose variation in any argument does not change too much when another argument is modified. Examples of such weak interactions are furnished by U- and V-statistics, Lipschitz L-statistics and various error f…
The paper optimizes private data sharing by selecting statistics and using MCMC for Bayesian inference.
problem Optimizing private data sharing by selecting statistics and performing Bayesian inference.
method Promotes Fisher information for statistic selection and proposes MCMC algorithms for inference.
result The Fisher information of the privatized statistic predicts the relative performance of the statistic in Bayesian estimation.
New algorithm improves clustering accuracy without sacrificing scalability.
problem Improving clustering accuracy for large datasets.
method Nonnegative low-rank semidefinite programming with Burer-Monteiro factorization.
result Significantly smaller mis-clustering errors compared to existing methods.
This paper simplifies computing higher-order U-statistics efficiently.
problem The inefficiency of computing higher-order U-statistics in practice. method Decomposition, connection to Einstein summation, and treewidth-based complexity estimate.
result A new, more efficient algorithm to compute U-statistics. This chapter reviews statistical tools for reinforcement learning.
problem Applying RL algorithms in healthcare and ride-sharing platforms.
method Statistical inference tools for RL, including hypothesis testing and confidence interval construction.
result Highlighting the value of statistical inference in RL for both communities.
Unified online tensor learning algorithm reduces computational and memory costs.
problem Efficiently learning from large tensors with minimal data storage and timely predictions.
method oRGrad algorithm for online tensor learning.
result oRGrad achieves optimal O(T1/2) regret and O(logT) adaptive regret. The paper analyzes Karcher means on restricted PSD matrices with statistical guarantees.
problem Statistical analysis of non-linear manifolds in machine learning.
method Intrinsic mean model on restricted PSD matrices, Karcher mean analysis, extrinsic signal-plus-noise model.
result Non-asymptotic statistical analysis of Karcher means with deterministic error bounds.
Database theory and database practice are typically the domain of computer scientists who adopt what may be termed an algorithmic perspective on their data. This perspective is very different than the more statistical perspective adopted by statisticians, scientific computers, machine learners, and other who work on wh…
Linear regression models contaminated by Gaussian noise (inlier) and possibly unbounded sparse outliers are common in many signal processing applications. Sparse recovery inspired robust regression (SRIRR) techniques are shown to deliver high quality estimation performance in such regression models. Unfortunately, most…
Paper develops PAC verification for hypothesis classes and statistical algorithms.
problem Verifying machine learning models interactively.
method Develops interactive proof for PAC verification, proves lower bounds, and introduces a generalization.
result Improved protocol for verifying unions of intervals and statistical query algorithms.
Extends JKO scheme for iterative algorithms with unknown parameters.
problem Computational and statistical analysis of iterative algorithms with unknown parameters.
method Develops statistical methods to estimate unknown parameters and adapts JKO scheme.
result Establishes asymptotic theory for the statistical JKO scheme.
Clustering is a fundamental problem in statistics and machine learning. Lloyd's algorithm, proposed in 1957, is still possibly the most widely used clustering algorithm in practice due to its simplicity and empirical performance. However, there has been little theoretical investigation on the statistical and computatio…
Develops a high-dimensional differentially-private EM algorithm with near-optimal statistical guarantees.
problem Designing differentially-private EM algorithms for high-dimensional latent variable models.
method Noisy iterative hard-thresholding, statistical guarantees, near-optimal convergence rates.
result Near-optimal statistical guarantees and minimax rate optimality in high-dimensional settings.
New algorithm balances user reward and statistical inference by mixing TS with UR based on difference size.
problem Combining statistical inference with user reward in adaptive experiments.
method TS-PostDiff algorithm that uses UR when differences are small and TS when large.
result TS-PostDiff reduces false positives and increases statistical power for small differences, while maximizing reward for large ones.
New algorithm for robust high-dimensional linear regression is both fast and statistically optimal.
problem Challenges in high-dimensional linear regression under heavy-tailed noise or outliers.
method Projected sub-gradient descent algorithm for sparse and low-rank regression problems.
result Algorithm achieves linear convergence and statistical optimality under various noise conditions.
In large-scale distributed learning, security issues have become increasingly important. Particularly in a decentralized environment, some computing units may behave abnormally, or even exhibit Byzantine failures -- arbitrary and potentially adversarial behavior. In this paper, we develop distributed learning algorithm…
MM (majorization--minimization) algorithms are an increasingly popular tool for solving optimization problems in machine learning and statistical estimation. This article introduces the MM algorithm framework in general and via three popular example applications: Gaussian mixture regressions, multinomial logistic regre…