Solla discusses neural processing using statistical physics and Bayesian methods.
problem Understanding neural information processing through statistical physics.
method Bayesian inference, Gibbs description, Generalized Linear Models, dimensionality reduction.
result Connection between neural processing and statistical physics.
Paper introduces data-dependent SSP for private linear and logistic regression.
problem Private linear and logistic regression with better performance.
method Data-dependent sufficient statistic perturbation (SSP) for linear and logistic regression.
result Data-dependent SSP outperforms state-of-the-art methods for linear and logistic regression.
A novel Bayesian framework for private linear regression with MCMC.
problem Private linear regression in a distributed setting.
method Generative statistical model, MCMC algorithms, fast Bayesian estimation.
result The proposed methods provide well-rounded estimation and prediction.
Study on distributional TD learning with linear approximations for better return estimation.
problem Estimating the return distribution of a policy in reinforcement learning.
method Finite-sample analysis of distributional TD learning with linear function approximation, using the linear-categorical Bellman equation and exponential stability arguments for products of random matrices.
result Sample complexity of linear distributional TD learning matches that of classic linear TD learning, indicating similar difficulty in estimating return distribution versus its expectation.
Survey on statistical learning theory for control, focusing on linear systems.
problem Applying machine learning techniques to control systems, especially linear ones.
method Adapting tools from modern high-dimensional statistics and learning theory.
result Recent advances in statistical learning theory for control, particularly for linear systems.
Improved estimator reduces bias in statistical learning models.
problem Asymptotic bias in classic WDRO estimator.
method Adjusted Wasserstein distributionally robust estimator.
result Asymptotic unbiased estimator with smaller MSE.
New algorithms improve distributional TD learning with linear approximations.
problem Estimating return distributions in reinforcement learning.
method Fine-grained analysis of linear-categorical Bellman equation, variance reduction techniques.
result Tight sample complexity bounds for distributional TD learning with linear approximations.
The paper addresses statistical estimation in MDPs with confounders using instrumental variables.
problem Statistical estimation of value functions in MDPs with unobservable confounders.
method Two-stage estimator based on instrumental variables for confounded linear MDPs.
result Established statistical properties of the two-stage estimator, including error bounds and asymptotic normality.
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.
SAR evaluates ML-based linear regression models for statistical significance.
problem Lack of formal statistical significance in ML-based regression models.
method Statistical Agnostic Regression (SAR) using concentration inequalities and worst-case scenario analysis.
result SAR provides a threshold for statistical significance without assuming underlying assumptions.
Study reward-free RL in non-linear settings, improving efficiency and removing assumptions.
problem Improving sample efficiency in reward-free reinforcement learning for non-linear function approximation.
method Proposed RFOLIVE algorithm for minimal structural assumptions, analyzed hardness results for reward-free and reward-aware exploration.
result Statistical efficiency and hardness results under various structural assumptions, no need for reachability or explorability assumptions.
Gradient descent with random weights in linear regression analyzed for various noise types.
problem Analyzing the impact of random noise on gradient descent in linear regression.
method Gradient descent with randomly weighted data points, various weighting distributions, geometric moment contraction.
result Characterization of implicit regularization and non-asymptotic convergence bounds.
Optimal algorithms for non-linear ridge bandits reduce burn-in cost.
problem Non-linear models introduce a burn-in period with fixed cost.
method Two-stage algorithm: find initial action, then treat locally linear.
result Two-stage algorithm is statistically optimal.
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.
Unified framework for statistical inference of low-rank tensors.
problem Statistical inference for tensors in high-dimensional data.
method Unified framework using debiasing and tangent space projection.
result Achieves asymptotic normality and minimax-optimal confidence intervals.
Paper proposes a statistical test for transfer learning in linear regression.
problem Theoretical framework for parameter transfer in linear regression.
method Developed a statistical test to predict transfer quality.
result The test can predict if a fine-tuned model has lower prediction risk.
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 d p o l y ( 1 / α ) d^{\mathrm{poly}(1/α)} d poly ( 1/ α ) for list-decodable linear regression. Improved texture synthesis using wavelet-based statistics with rectifier non-linearity.
problem Improving texture synthesis quality using wavelet representations.
method Proposes a family of statistics based on non-linear wavelet representations with a generalized rectifier non-linearity.
result Significantly improves visual quality of texture synthesis compared to classical wavelet-based models.
Paper uses SGD for solving linear inverse problems, improving empirical performance.
problem Solving statistical inverse problems in science and engineering.
method Stochastic Gradient Descent (SGD) for linear inverse problems, with smoothing techniques.
result Consistency and finite sample bounds for excess risk demonstrated.
Lecture notes on advanced linear regression methods.
problem Understanding the properties of linear regression estimators in high dimensions.
method Proposition-proof exploration of least squares, ridgeless, ridge, and lasso estimators.
result Detailed analysis of the existence, uniqueness, relations, computation, and non-asymptotic properties of these estimators.
In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution. However, no finite sample statistical guarantees and no computationally efficient o…
Efficient algorithm for near-optimal online learning with generalized linear functions.
problem Exponential gap between statistically optimal regret and efficient regret for some function classes.
method Computational efficient algorithm for realizable K-wise linear classification and over-parameterized polynomial featurization.
result First algorithm with log(T/σ) regret for realizable K-wise linear classification.
New method distinguishes feature relevance in non-linear contexts.
problem Finding relevant features with preserved redundancies.
method Random forest models and statistical methods.
result Distinguishes strong from weak feature relevance in non-linear problems.
Paper connects GLM and LRM for better classification performance.
problem Improving classification performance using statistical inference.
method Derives a statistical test based on SVM and permutation analysis.
result MLE-based inference provides better parameter estimation.
Study smooth linear statistics on random covers of hyperbolic surfaces, showing central limit and variance results.
problem Analyzing fluctuations and energy variance of random covers of compact hyperbolic surfaces.
method Examining fluctuations in a small energy window around a fixed energy level, considering the variance of a typical surface, using a double limit where n n n and L L L go to infinity. result Distribution of fluctuations tends to a Gaussian with variance of GOE/GUE, and energy variance of a typical random n n n -cover is that of GOE/GUE. Paper studies PSGD for constrained optimization problems and its statistical properties.
problem Online inference for constrained optimization problems.
method Stochastic gradient descent with projection (PSGD) for constrained optimization.
result Limiting distribution of PSGD-based estimates under linear-equality constraints.
Linear cost method approximates Gaussian Matérn processes with exponentially convergent accuracy.
problem High computational cost for Gaussian process inference and prediction.
method Optimal rational approximation of spectral density for Gaussian processes on bounded intervals.
result Exponential decrease in covariance error with increasing order of approximation.
Learning to control linear systems is statistically hard, especially for underactuated systems.
problem Statistical difficulty of learning to control linear systems, especially underactuated ones.
method Utilized minimax lower bounds and structural assumptions to prove learning complexity can be exponential.
result Learning complexity can be at most exponential with the controllability index of the system.
The paper explores when linear system identification is hard or easy, especially for under-actuated systems.
problem Statistical hardness of learning linear systems, especially under-actuated or under-excited systems.
method Using tools from minimax theory and recent statistical tools for finite sample analysis of system identification.
result The controllability index of linear systems affects the sample complexity of identification, making some systems hard to learn.
Improves survey sampling with unbiased machine learning methods.
problem Design-consistent model-assisted estimation lacks a general theory for machine learning.
method Proposes a subsampling Rao-Blackwell method for design-unbiased estimation.
result Yields efficiency gains over standard methods while ensuring valid estimation.
National statistical systems are the enterprises tasked with collecting, validating and reporting societal attributes. These data serve many purposes - they allow governments to improve services, economic actors to traverse markets, and academics to assess social theories. National statistical systems vary in quality, …
We tackle permutation in linear regression with a new inference framework.
problem Statistical investigation of permutation in linear regression models.
method Localization step followed by conditional Monte Carlo test and coefficient inference.
result Valid statistical inference procedures for permutation and regression coefficients.
Proposes a method for differentially private linear regression and synthetic data generation.
problem Lack of valid inference and synthetic data generation methods for small-scale datasets in privacy-aware settings.
method Gaussian differentially private linear regression with bias-corrected estimator and SDG procedure.
result Improves accuracy and provides valid confidence intervals for downstream tasks.
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation, and noisy matrix completion. We propose computationally feasible conv…
New algorithm learns linear dynamical systems from measurements.
problem Learning system dynamics from linear measurements efficiently and accurately.
method Method of moments estimator to directly estimate Markov parameters.
result First polynomial time algorithm for learning linear dynamical systems.
Paper proposes a statistical model for detecting mu-suppression in EEG signals.
problem Detecting mu-suppression in motor imagery EEG signals.
method Proposes a statistical model based on the generalized extreme value distribution (GEV) and a linear classifier.
result Preliminary results show good classification accuracy in detecting mu-suppression and distinguishing EEG events.
The study uncovers universality laws for Gaussian mixtures in generalized linear models.
problem Understanding the asymptotic behavior of estimators in Gaussian mixture models.
method Investigates the asymptotic joint statistics of generalized linear estimators from empirical risk minimization and Gibbs sampling.
result Characterizes conditions under which the joint statistics depend only on means and covariances of class conditional features.
Study compares dropout and l2 regularization in linear models.
problem Understanding the statistical behavior of dropout and l2 regularization in linear models.
method Derives non-asymptotic bounds for gradient descent iterates with dropout and compares them to l2 regularization.
result Indicates a more subtle relationship between dropout and l2 regularization, highlighting interactions between dynamics and randomness.
DiffKnock improves feature selection in neural networks with complex dependencies and non-linear associations.
problem Selecting important features in neural networks with complex dependencies and non-linear associations.
method DiffKnock uses diffusion models to generate knockoffs and neural network statistics to measure feature importance.
result DiffKnock outperforms existing methods in detecting non-linear associations and preserving feature dependencies.
Test assesses if a linear classifier is random or significant.
problem Determining if a linear classifier captures meaningful differences between classes.
method Proposes a homogeneity test related to linear separability, establishes upper bounds for p-values.
result Upper bounds for p-values are highly accurate for normally distributed samples.
New algorithm achieves nearly optimal regret with one-pass updates for GLB problems.
problem Generalized linear bandits with non-linear reward distributions.
method Jointly efficient algorithm using OMD estimator with one-pass updates.
result Nearly optimal regret bound with O ( 1 ) \mathcal{O}(1) O ( 1 ) time and space complexities per round. Paper uses SLT to improve model selection for SHM.
problem Model selection for SHM using data-based systems.
method Utilizes Statistical Learning Theory to rigorously estimate generalisation.
result Incorporating domain knowledge improves model generalisation.
Develops a new asymptotic efficiency theory for non-Euclidean parameter spaces.
problem Lack of a unified efficiency theory for non-Euclidean parameter spaces.
method Introduces a new theory for Riemannian manifolds with regularity conditions.
result Establishes efficiency bounds for non-Euclidean parameter spaces.
We study the competitive equilibrium of large random economies with linear activities using methods of statistical mechanics. We focus on economies with C C C commodities, N N N firms, each running a randomly drawn linear technology, and one consumer. We derive, in the limit N , C → ∞ N,C\to\infty N , C → ∞ with n = N / C n=N/C n = N / C fixed, a complete de…
Study improves statistical inference for CATEs using Lasso and DML.
problem Estimating and inferring CATEs in high-dimensional settings.
method Doubly robust estimator, Lasso regularization, debiased Lasso, DML.
result TDL (triple/debiased Lasso) achieves n \sqrt{n} n -consistency and confidence intervals. New algorithms improve Bayesian linear regression with spike-and-slab priors.
problem Efficiently sampling from Bayesian linear regression models with sparsity-inducing priors.
method Design of two sampling algorithms: Gibbs sampling and Stochastic Localization.
result Stochastic Localization sampler shows significant advantage for poorly designed data matrices.
Proposes statistical inference for dependency knowledge graphs from EHR data.
problem Statistical uncertainty in linking entities in EHR data.
method Dynamic log-linear topic model with singular value decomposition.
result Established asymptotic normality for sparse graph edge recovery.
Study compares forecasting methods for logistics time series.
problem Improving forecasting accuracy in logistics.
method Compared statistical and machine learning methods on simulated time series.
result Statistical methods outperformed machine learning in one-step forecasts.