Machine learning improves official statistics but needs rigorous validation.
problem Lack of methodological robustness in machine learning for official statistics.
method Total Machine Learning Error (TMLE) framework to validate ML models.
result TMLE addresses representativeness and measurement errors in ML models.
RealStats detects fake images rigorously, combining multiple detectors for robustness.
problem Detecting AI-generated images remains challenging due to evolving generative models.
method Combines training-free statistics to compute p-values and aggregate them for a unified real-image distribution.
result Framework produces interpretable probability scores for robust fake image detection.
Spofe bridges statistical rigor and interpretability in feature extraction from tabular data.
problem Ensuring statistical rigor and interpretability in feature extraction from complex tabular data.
method Spofe combines kernel principal components and sparse polynomial functions with a multi-objective knockoff selection procedure.
result Spofe consistently outperforms other methods in feature selection for regression and classification tasks.
We rigorously prove statistical physics predictions for non-convex GLMs in high dimensions.
problem Analyzing high-dimensional optimization problems in non-convex Generalized Linear Models.
method Developed a systematic framework using the Gaussian Min-Max Theorem and AMP to rigorously prove replica-symmetric formulas.
result Validated statistical physics predictions for non-convex GLMs, aligning with physicist's conjectures.
In simulations of some economic gas-like models, the asymptotic regime shows an exponential wealth distribution, independently of the initial wealth distribution given to the system. The appearance of this statistical equilibrium for this type of gas-like models is explained in a rigorous analytical way.
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.
Machine learning should incorporate maximum likelihood for better estimation.
problem Lack of rigorous foundational theory in machine learning.
method Integrate maximum likelihood estimation into machine learning models.
result Foundationally rigorous machine learning models have greater practical impact.
We give a rigorous analysis of the statistical behavior of gradients in a randomly initialized fully connected network N with ReLU activations. Our results show that the empirical variance of the squares of the entries in the input-output Jacobian of N is exponential in a simple architecture-dependent constant beta, gi…
A framework integrates machine learning with robust control for safer, more reliable systems.
problem Combining machine learning with robust control for systems with stringent safety and reliability requirements.
method Integrates Gaussian Process Regression and state-of-the-art robust controller synthesis within a framework that provides rigorous guarantees.
result Demonstrated improved performance with more data while maintaining rigorous guarantees.
In these notes we describe heuristics to predict computational-to-statistical gaps in certain statistical problems. These are regimes in which the underlying statistical problem is information-theoretically possible although no efficient algorithm exists, rendering the problem essentially unsolvable for large instances…
A textbook on statistical machine learning for astronomy.
problem Uncertainty quantification in astronomical data analysis.
method Bayesian inference and classical statistical methods.
result Unified framework connecting modern and traditional methods.
A statistical toolbox for analyzing model performance in medical imaging.
problem Analyzing model performance by patient and recording properties, especially in medical imaging.
method Selection of appropriate performance metrics, correction of multiple comparisons, and finding interesting subgroups.
result Enables rigorous assessment of model performance for potential subgroup disparities.
FSR efficiently discovers significant patterns with few resampled datasets.
problem Mining significant patterns in transactional data, especially subgroups.
method FSR uses resampling to bound the supremum deviation of quality statistics, providing rigorous guarantees on false discoveries.
result FSR effectively discovers significant subgroups with a small number of resampled datasets.
Rigorous uncertainty quantification of probabilistic AI weather forecasts with conformal prediction
problem Calibrated uncertainty quantification in probabilistic weather forecasts
method Conformal prediction
result Calibrated uncertainty at no expense to other probabilistic metrics
STAND-DA improves AD in DA target domains with limited data.
problem Statistical validity of AD after DA with limited data.
method Selective Inference framework for GPU-accelerated p-value computation. result Valid p-values and controlled false positive rate. New framework formalizes estimating valid transport maps, revealing their statistical limits.
problem Estimating valid transport maps in generative modeling.
method Formalized a minimax framework for estimating valid transport maps.
result Estimating any valid transport map is as hard as estimating the optimal transport map under standard stability assumptions.
It has been known for a long time that the classical spherical perceptrons can be used as storage memories. Seminal work of Gardner, \cite{Gar88}, started an analytical study of perceptrons storage abilities. Many of the Gardner's predictions obtained through statistical mechanics tools have been rigorously justified. …
Benchmark assesses LLMs' causal inference skills, revealing significant limitations.
problem Lack of rigorous evaluation of LLMs' causal inference capabilities.
method CausalPitfalls benchmark with structured challenges and grading rubrics.
result Significant limitations in current LLMs' statistical causal inference.
Efficient algorithm for clustering and classification using MBO scheme.
problem Data clustering and classification tasks.
method Introduces constraints on cluster size leading to a linear integer problem, proving it's induced by a novel order statistic. Develops exact and efficient algorithms based on variational viewpoint connecting to volume-preserving mean curvature flow.
result Estimates computational complexity better than state-of-the-art, proving rigorous analysis.
Stock markets are complex systems exhibiting collective phenomena and particular features such as synchronization, fluctuations distributed as power-laws, non-random structures and similarity to neural networks. Such specific properties suggest that markets operate at a very special point. Financial markets are believe…
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.
Perceptrons have been known for a long time as a promising tool within the neural networks theory. The analytical treatment for a special class of perceptrons started in seminal work of Gardner \cite{Gar88}. Techniques initially employed to characterize perceptrons relied on a statistical mechanics approach. Many of su…
Lasso proves consistent model selection for high-dimensional Ising models.
problem Model selection consistency of Lasso for high-dimensional Ising models.
method Theoretical analysis of Lasso with and without post-thresholding for Ising models.
result Lasso without post-thresholding is model selection consistent in the whole paramagnetic phase with n=Ω(d3logp). We initiate the rigorous study of classification in quasi-metric spaces. These are point sets endowed with a distance function that is non-negative and also satisfies the triangle inequality, but is asymmetric. We develop and refine a learning algorithm for quasi-metrics based on sample compression and nearest neighbor…
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.
This work provides statistical guarantees for GANs that are invariant to certain group symmetries.
problem Learning group-invariant distributions efficiently.
method Study of group-invariant GANs and their performance guarantees.
result Group-invariant GANs require fewer samples and have a reduced discriminator approximation error.
Flexible framework for bounding high-loss predictions using quantiles.
problem Need for rigorous guarantees in risk-sensitive applications.
method Order statistics of loss values, flexible quantile-based metrics.
result Ability to rigorously control loss quantiles on real-world datasets.
Paper proposes a sequential statistical test for comparing imitation learning policies with near-optimal stopping.
problem Challenges in rigorously comparing imitation learning policies due to small sample sizes and potential p-hacking.
method Sequential statistical test that adapts the number of trials based on intermediate results, achieving near-optimal stopping.
result Reduces the number of evaluation trials by up to 32% compared to state-of-the-art baselines, saving significant time and effort.
This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators' to a distribution over the true error. The variance of this distribution can be…
New method estimates shape distance in neural representations with limited data.
problem Measuring geometric similarity between high-dimensional network representations.
method Method-of-moments estimator with tunable bias-variance tradeoff.
result New estimator achieves lower bias than standard methods in high-dimensional settings.
Statistical learning theory provides bounds of the generalization gap, using in particular the Vapnik-Chervonenkis dimension and the Rademacher complexity. An alternative approach, mainly studied in the statistical physics literature, is the study of generalization in simple synthetic-data models. Here we discuss the c…
This paper examines various definitions of adversarial risk and their implications.
problem Quantifying the performance of classifiers under adversarial perturbations.
method Optimal transport, robust statistics, functional analysis, and game theory.
result Generalization of Strassen's theorem and new connections to Choquet capacities and game theory.
This thesis improves practical reinforcement learning methods with robustness, scalability, and efficiency.
problem Improving reinforcement learning methods for practical applications.
method Analyzes and develops robust, scalable, and efficient reinforcement learning algorithms.
result Proves the efficiency and robustness of new RL methods.
Kulldorff's (1997) seminal paper on spatial scan statistics (SSS) has led to many methods considering different regions of interest, different statistical models, and different approximations while also having numerous applications in epidemiology, environmental monitoring, and homeland security. SSS provides a way to …
Bayesian framework proves thresholds for multi-graph alignment feasibility.
problem Determining when multi-graph alignment is statistically possible.
method Developed a Bayesian estimation framework over metric spaces.
result Identified thresholds for Gaussian and sparse Erdős-Rényi models.
Unified framework for statistical inference in gradient boosting regression.
problem Challenges in statistical inference and uncertainty quantification for gradient boosting.
method Integrates dropout or parallel training with regularization for CLT in boosting.
result Increasing dropout rate and parallel trees enhances signal recovery and performance.
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 method for rigorous confidence intervals in off-policy evaluation.
problem Evaluate new policies from off-policy data without executing them.
method Variational framework using kernel Bellman loss.
result Efficient method for tight confidence intervals in various settings.
The study explains transformer scaling laws using statistical and approximation theories.
problem Understanding why transformer scaling laws exist for large models trained on low-dimensional data.
method Established statistical estimation and mathematical approximation theories for transformers on low-dimensional manifolds.
result Predicted a power law between generalization error and model and data sizes, with power depending on intrinsic data dimension.
This paper identifies the salient factors that characterize the inequality income distribution for Romania. Data analysis is rigorously carried out using sophisticated techniques borrowed from classical statistics (Theil). Decomposition of the inequalities measured by the Theil index is also performed. This study relie…
Study on Bayesian deep linear networks with multiple outputs and convolutional layers.
problem Characterize feature learning in finite-width Bayesian deep linear networks.
method Exact and analytical formulas for joint and posterior distributions, using large deviation theory.
result Quantitative description of feature learning in infinite-width regime.
This paper introduces differentially private permutation tests for hypothesis testing.
problem Privacy concerns in sensitive data analysis.
method Differentially private permutation tests for kernel methods.
result Proposes dpMMD and dpHSIC for two-sample and independence testing, achieving optimal power.
We show that a large class of Estimation of Distribution Algorithms, including, but not limited to, Covariance Matrix Adaption, can be written as a Monte Carlo Expectation-Maximization algorithm, and as exact EM in the limit of infinite samples. Because EM sits on a rigorous statistical foundation and has been thorough…
Extreme value theory enhances statistical learning extrapolation for rare events.
problem Challenges in traditional machine learning methods for extreme data.
method Asymptotic theory and statistical tools for tail behavior.
result Effective extrapolation methods for extreme quantiles and anomalies.
New bounds on neural network capacity for treelike sign perceptrons using RDT.
problem Determining the capacity of treelike sign perceptrons neural networks.
method Random Duality Theory (RDT) to establish upper bounds.
result Mathematically rigorous bounds on network capacity for any number of neurons.
This paper analyzes MFVBI for GMM using statistical mechanics.
problem Approximate fast computation of Gaussian Mixture Model.
method Statistical mechanics and MFVBI applied to GMM.
result Rigorous analysis and mathematical foundation for MFVBI applied to GMM.
New data improves market impact estimation methods.
problem Improving efficiency of market impact estimation.
method Investigates the use of price trajectory data for market impact estimation.
result Estimation methods using early trade prices outperform established methods asymptotically.
Framework tests group fairness in machine learning models.
problem Detecting biases in machine learning classifiers.
method Optimal transport projections to audit group fairness.
result Statistical test for various fairness notions efficiently computed.