Score attack method provides a lower bound on privacy-constrained minimax risk.
problem Characterizing the optimality of privacy-constrained statistical models.
method Score attack based on tracing attack concept.
result Optimally lower bounds the minimax risk of estimating unknown model parameters.
Optimized Franz-Parisi criterion matches SQ lower bounds for various statistical models.
problem Understanding computational hardness in statistical inference.
method Proposed and refined Franz-Parisi criterion, established equivalence with SQ lower bounds.
result Optimized Franz-Parisi criterion is equivalent to Statistical Query (SQ) lower bounds.
Study on statistical estimation over Gaussian MAC, comparing analog and digital schemes.
problem Distributed minimax statistical estimation over a Gaussian MAC.
method Developed analog joint estimation-communication schemes and derived information-theoretic lower bounds.
result Achieved risk within a logarithmic factor of information-theoretic lower bounds.
We study the fundamental tradeoffs between computational tractability and statistical accuracy for a general family of hypothesis testing problems with combinatorial structures. Based upon an oracle model of computation, which captures the interactions between algorithms and data, we establish a general lower bound tha…
Paper studies statistical-computational trade-offs in tensor PCA and related problems.
problem Statistical-computational gap in tensor PCA estimation.
method Derives computational lower bounds using communication complexity.
result Lower bounds specify trade-off among passes, sample size, and memory.
Statistical Query lower bound shows difficulty in list-decodable linear regression.
problem List-decodable linear regression with adversarial corruption.
method Statistical Query (SQ) lower bound analysis.
result Lower bound of dpoly(1/α) for list-decodable linear regression. The paper introduces gapped scale-sensitive dimensions to improve learning rate bounds.
problem Improving lower bounds on rates of convergence in statistical and online learning.
method Introducing and analyzing gapped scale-sensitive dimensions for function classes.
result Gapped dimensions lead to stronger lower bounds on offset Rademacher averages.
Paper proves first non-trivial PTF testing lower bounds for NGCA.
problem Proving lower bounds against PTF tests is challenging.
method Developed tools to prove PTF testing lower bounds for NGCA.
result First non-trivial PTF testing lower bounds for NGCA.
Develops high-probability minimax quantile bounds for statistical problems.
problem Statistical procedures often lose information about tail behavior when reduced to expectations.
method Introduces minimax quantiles, develops high-probability variants of minimax methods, and converts risk lower bounds to quantile lower bounds.
result Obtains high-probability minimax quantile lower bounds for various statistical problems.
In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an information-theoretic setting, it is known that Fano's inequality typically doe…
A new method uses randomized trials to estimate the strength of unobserved confounding.
problem Unobserved confounding compromises causal conclusions from non-randomized studies.
method Designs a statistical test to detect unobserved confounding strength and estimates a lower bound.
result Estimates an asymptotically valid lower bound on unobserved confounding strength.
New computational lower bounds for clustering and related problems.
problem Statistical-computational gaps in high-dimensional clustering problems.
method Investigation of low-degree polynomials in latent space models to derive lower bounds.
result New and sharper computational lower bounds for clustering, sparse clustering, and biclustering.
New SQ lower bounds show learning mixtures of bounded covariance Gaussians is hard.
problem Learning mixtures of Gaussians with bounded covariance matrices is hard.
method Statistical Query (SQ) lower bounds.
result Any SQ algorithm requires complexity at least dΩ(1/ε) for learning mixtures of bounded covariance Gaussians. New bounds show complex neural networks need many queries to learn.
problem Learning non-polynomial activation functions with Gaussian marginals.
method Gradient boosting procedure to amplify lower bounds on SQ dimension of neural networks.
result Statistical-query lower bounds for ReLU regression with 2ncε queries. The paper extends statistical estimation techniques under differential privacy.
problem Establishing sample complexity bounds for estimation tasks under differential privacy.
method Proposes analogues of Le Cam's method, Fano's inequality, and Assouad's lemma under central differential privacy.
result Optimal sample complexity bounds for discrete distribution estimation under total variation and ℓ2 distances. New lower bounds for private covariance estimation of Gaussian distributions are proven.
problem Proving tight lower bounds for private estimation tasks under differential privacy.
method Generalized fingerprinting method for exponential families and private Assouad method.
result Tight lower bounds for private covariance estimation in Frobenius and spectral norms.
The paper explores the trade-off between bias and variance in high-dimensional models.
problem Understanding the unavoidable trade-off between bias and variance in high-dimensional statistical models.
method Proposes a general strategy to obtain lower bounds on the variance of estimators with a specified bias, and applies it to various statistical models.
result Shows the extent to which the bias-variance trade-off is unavoidable and quantifies the performance loss for methods that do not balance it.
Sum-of-Squares lower bound shows NGCA requires more samples than known algorithms.
problem Finding a non-Gaussian direction in a high-dimensional dataset.
method Sum-of-Squares (SoS) framework to prove lower bounds.
result First super-constant degree SoS lower bound for NGCA.
New method uses almost orthonormal bases to prove low-degree lower bounds in complex statistical models.
problem Proving statistical-computational gaps in high-dimensional models with planted structures.
method Constructing an almost orthonormal polynomial basis under the planted distribution.
result Established new low-degree lower bounds for various complex models.
Proves SQ lower bounds for learning two-hidden-layer neural networks.
problem Learning two-hidden-layer ReLU networks with Gaussian inputs.
method Refined lifting procedure to reduce Boolean PAC learning to Gaussian.
result Superpolynomial SQ lower bounds for Gaussian inputs.
Unified framework for lower bounds in interactive decision making.
problem Challenges in interactive decision making, especially bandits and reinforcement learning.
method Interactive Fano method and Fractional Covering Number.
result Unified characterization of learnability for stochastic bandit problems and tight lower bounds for interactive decision making.
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.
Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this paper, we investigate the tradeoff between statistical accuracy and privacy in mean estimation and linear regression, under both the …
Optimal SQ bounds for learning binary product distributions and Ising models.
problem Learning binary product distributions and Ising models robustly.
method Statistical Query (SQ) lower bounds for robust learning.
result Optimal SQ lower bounds match known algorithm error guarantees.
New algorithms for private GLM estimation with minimax lower bounds.
problem Privacy in generalized linear models.
method Differentially private algorithms using projected gradient descent.
result Nearly rate-optimal performance with privacy-constrained minimax lower bounds.
Variational inference (VI) is a widely used framework in Bayesian estimation. For most of the non-Gaussian statistical models, it is infeasible to find an analytically tractable solution to estimate the posterior distributions of the parameters. Recently, an improved framework, namely the extended variational inference…
New SQ lower bound shows complexity nearly matches known upper bound for smoothed agnostic learning.
problem Smoothed agnostic learning of halfspaces under subgaussian distributions.
method Statistical Query (SQ) lower bound using moment-matching hard distribution and linear programming duality.
result First non-trivial lower bound on complexity nearly matches known upper bound.
Paper solves k-sparse parity problem with sign SGD, matching SQ lower bound.
problem Solving k-sparse parity problems efficiently.
method Sign stochastic gradient descent on neural networks.
result Matches Statistical Query lower bound for solving k-sparse parity problems.
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.
Study near-optimal bounds for learning Gaussian halfspaces with random noise.
problem Learning general halfspaces with Gaussian distribution and random classification noise.
method Established nearly-matching algorithmic and SQ lower bounds, developed a computationally efficient learning algorithm.
result Sample complexity of learning algorithm is O(d/ε+d/(max{p,ε})2), SQ lower bound is Ω(d1/2/(max{p,ε})2). Study on conditions for achieving optimal robustness in statistical estimators.
problem Achieving the optimal robustness of estimators in statistical models.
method Developed a Wasserstein analogue of the Cramer-Rao inequality and investigated conditions for achieving the Wasserstein-Cramer-Rao lower bound.
result Conditions for the existence of asymptotically efficient estimators in one-parameter models and location-scale families.
New SQ lower bounds for NGCA without requiring chi-squared condition.
problem Proving SQ hardness for NGCA under moment-matching conditions.
method General SQ lower bound methodology applied to NGCA under moment-matching conditions.
result Proved near-optimal SQ lower bounds for NGCA without chi-squared condition.
New complexity measure for interactive learning reduces regret to near-optimal levels.
problem Challenges in sample-efficient, adaptive learning algorithms for interactive decision making.
method Introduces the Decision-Estimation Coefficient and the Estimation-to-Decisions (E2D) principle.
result Unified algorithm design principle E2D achieves optimal sample-efficient learning.
Lower bounds show density estimation requires linear samples or query time.
problem Statistical-computational trade-offs in density estimation.
method Lower bound analysis on data structures.
result Lower bounds demonstrate statistical-computational trade-offs for density estimation.
The study establishes SQ lower bounds for learning halfspaces and ReLUs under Gaussian marginals.
problem Agnostically learning halfspaces and ReLUs under Gaussian marginals.
method Statistical Query (SQ) lower bounds analysis.
result Proves SQ lower bounds of dpoly(1/ε) for both problems. Gradient descent fails to learn simple neural networks efficiently.
problem Learning one-layer neural networks efficiently using gradient descent.
method Gradient descent and statistical query algorithms.
result Superpolynomial lower bounds for learning one-layer neural networks.
Paper connects free-energy and low-degree hardness in high-dimensional statistics.
problem High-dimensional statistical inference problems are computationally hard.
method Defines a free-energy criterion and connects it to low-degree hardness.
result Establishes connection between free-energy and low-degree hardness for Gaussian models.
Automating statistical modelling is a challenging problem in artificial intelligence. The Automatic Statistician takes a first step in this direction, by employing a kernel search algorithm with Gaussian Processes (GP) to provide interpretable statistical models for regression problems. However this does not scale due …
Paper tackles sparse recovery with shuffled labels, establishing statistical and computational limits.
problem Sparse recovery with shuffled labels, focusing on permutation matrix and sparse signal reconstruction.
method Statistical and computational analysis, including minimax lower bounds and exhaustive-search based estimator.
result Established statistical and computational limits for correct recovery of permutation matrix and support set.
New bounds on learning shared representations improve model performance and efficiency.
problem Improving model performance and efficiency through shared representations across clients.
method Established new upper and lower bounds on statistical error, designed a spectral estimator for non-convex least-squares solutions.
result Optimal statistical rate achieved when shared representation is well covered across clients.
Du, Kakade, Wang, and Yang recently established intriguing lower bounds on sample complexity, which suggest that reinforcement learning with a misspecified representation is intractable. Another line of work, which centers around a statistic called the eluder dimension, establishes tractability of problems similar to t…
In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency. We measure the performance of a test by the smallest signal strength that it can detect and we propose a computationally efficient method based on semidefinite prog…
We study the information-theoretic lower bound of the sample complexity of the correct recovery of diffusion network structures. We introduce a discrete-time diffusion model based on the Independent Cascade model for which we obtain a lower bound of order Ω(klogp), for directed graphs of p nodes, and at most k…
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.
Measuring mutual information from finite data is difficult. Recent work has considered variational methods maximizing a lower bound. In this paper, we prove that serious statistical limitations are inherent to any method of measuring mutual information. More specifically, we show that any distribution-free high-confide…
The study sets limits on how well halfspaces can be learned when labels are corrupted.
problem Learning halfspaces in the presence of Massart noise.
method Statistical query (SQ) lower bounds.
result No SQ algorithm can achieve misclassification error better than the corruption rate η with superpolynomial accuracy or a superpolynomial number of queries. We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured model -- an actively studied topic in statistics and machine learning. In the noi…
Survey on statistical inference under memory constraints.
problem Effect of memory limitations on statistical inference performance.
method Review of state-of-the-art in several canonical problems.
result Identification of fundamental building blocks and useful techniques.