Survey of statistical queries and their applications.
problem Understanding statistical queries and their applications.
method Exploration of statistical queries model, definitions, and connections to learnability.
result Connections to learnability and applications in optimization, evolvability, and differential privacy.
Paper proposes a method to use in silico experiments with foundation models to reduce sample size.
problem Costly and uncertain randomized experiments.
method Integrates predictions from multiple foundation models with experimental data.
result Estimator offers substantial precision gains, equivalent to a 20% reduction in sample size.
Enhanced TSFMs improve time series forecasting accuracy and reliability.
problem Variance, bias, and uncertainty in TSFMs' predictions on real data.
method Statistical and ensemble techniques including bagging, stacking, residual modeling, and prediction intervals.
result Hybrid models consistently outperform standalone TSFMs across multiple horizons.
Lecture notes on reinforcement learning using statistical methods.
problem Addressing the exploration-exploitation dilemma in decision making.
method Frequentist and Bayesian approaches, function approximation, neural networks.
result Unified framework for decision making and estimation.
InfoAtlas speeds up MI estimation for real-time data analysis.
problem Efficiently measuring statistical dependency between high-dimensional datasets.
method Directly infers mutual information in a single forward pass using a pretrained model.
result Matches state-of-the-art accuracy with 100x speedup.
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.
Foundation models alter medical data science workflow, challenging veridical data science principles.
problem Foundation models disrupt traditional data science practices in medicine.
method Critically examined the medical foundation model lifecycle and its deviation from veridical data science principles.
result Foundation models challenge veridical data science principles of predictability, computability, and stability.
We develop a statistical framework to benchmark and select large language models based on their risks.
problem Benchmarking and selecting large language models based on their associated risks.
method A distributional framework using first and second order stochastic dominance, linked to mean-risk models in finance.
result Formalizes a risk-aware approach for model selection, balancing risk and utility.
Introduces foundation priors for using model-generated data in empirical research.
problem Using model-generated data as real observations in empirical research.
method Introduces foundation priors as an exponential-tilted, generalized Bayesian update of the user's primitive prior.
result Synthetic data reflects both model patterns and user's priors, enabling principled use in empirical work.
Foundation models improve time series prediction reliability, especially with limited data.
problem Improving time series prediction reliability with limited data.
method Comparison of Time Series Foundation Models (TSFMs) with traditional methods in conformal prediction.
result TSFMs provide more reliable conformalized prediction intervals and more stable calibration with limited data.
PFNs pre-train models on simulated data to predict class probabilities.
problem Training machine learning models on large datasets.
method Pre-train a fixed model on small simulated datasets and use it to infer class probabilities in-context.
result PFNs achieve state-of-the-art performance and improve with larger inference data.
A model learns causal graphs from summary statistics of synthetic data.
problem Causal discovery algorithms are brittle with large sets of variables and limited data.
method A supervised model trained on synthetic data predicts causal graphs from summary statistics.
result The model generalizes well beyond its training set and runs on large graphs.
Foundation models leak sensitive data in synthetic tabular data generation, especially LLaMA 3.3 70B.
problem Privacy leakage in synthetic tabular data generation using foundation models.
method Benchmarked three foundation models (GPT-4o-mini, LLaMA 3.3 70B, TabPFN v2) against four baselines on 35 real-world tables.
result Foundation models, especially LLaMA 3.3 70B, have the highest privacy risk in synthetic tabular data generation.
ML reduces high-dimensional data to reveal its underlying structure.
problem Handling large, high-dimensional data sets.
method Non-linear dimension reduction techniques.
result Reveals the geometric shape of high-dimensional data.
GIFT-Eval benchmarks time series forecasting models across diverse datasets.
problem Lack of comprehensive benchmarks for evaluating time series foundation models.
method Developed GIFT-Eval, a benchmark with 23 datasets, 177 million data points, and 144,000 time series.
result Promotes evaluation of foundation models across various domains and frequencies.
Foundation models improve wage gap decomposition by capturing omitted career history factors.
problem Estimating wage disparities using incomplete career history data.
method Fine-tuning foundation models to mitigate omitted variable bias and estimate wage gaps.
result Foundation models can decompose gender wage gaps more accurately than traditional econometric methods.
Foundation models improve volatility forecasting in finance.
problem Improving volatility forecasting in financial markets.
method Evaluation of TimesFM model, incremental fine-tuning, comparison with econometric benchmarks.
result Incremental fine-tuning improves forecast accuracy and outperforms traditional models.
TSFMs embed non-stationary time series data, revealing specific types of changes.
problem Understanding non-stationarity in TSFMs' embedding spaces.
method Examined mean shifts, variance changes, linear trends, and persistence in TSFMs.
result Different TSFMs exhibit distinct failure modes in detecting non-stationarity.
We briefly review statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the agents in payment for goods and services. We focus on conceptual foundations for this …
A property, or statistical functional, is said to be elicitable if it minimizes expected loss for some loss function. The study of which properties are elicitable sheds light on the capabilities and limitations of point estimation and empirical risk minimization. While recent work asks which properties are elicitable, …
A permutation-based SW test achieves minimax-optimal power for two-sample testing.
problem Nonparametric two-sample testing using the sliced Wasserstein distance.
method Proposes a permutation-based SW test and analyzes its performance.
result Achieves minimax separation rate n−1/2 over multinomial and bounded-support alternatives. This paper provides theoretical foundations for using quantized actions in behavior cloning.
problem Applying autoregressive models to continuous control requires discretizing actions through quantization, which is poorly understood.
method The paper analyzes quantization error propagation and statistical sample complexity, and proposes model-based augmentation.
result Behavior cloning with quantized actions achieves optimal sample complexity, matching existing lower bounds.
Mathematical foundation for phylogenetic tree uncertainty quantification.
problem Uncertainty in evolutionary relationships between species.
method Introducing the Wald space as a subset of symmetric positive definite matrices, studying its topology and structure, and proposing a new numerical method for geodesics and curvature.
result Wald space has a topology of disjoint open cubes, is contractible, and is a Whitney stratified space of type (A).
AI model enhances grid monitoring with synchro-waveform tech.
problem Dynamic, stochastic, low-inertia future grids need advanced monitoring.
method AI Foundation Model with synchro-waveform tech.
result Significantly improved fault detection accuracy and speed.
This chapter tackles class imbalance in datasets to promote data democracy.
problem Class imbalance in datasets leading to biased decisions and policies.
method Statistical measures and data-level methods (oversampling, undersampling, etc.) applied to a real dataset.
result Popular data-level methods improve performance in handling class imbalance.
The problem of replicating the flexibility of human common-sense reasoning has captured the imagination of computer scientists since the early days of Alan Turing's foundational work on computation and the philosophy of artificial intelligence. In the intervening years, the idea of cognition as computation has emerged …
Paper proposes a probabilistic alignment method for domain adaptation.
problem Latent distribution mismatch and miscalibrated uncertainty in adapting large-scale models.
method Bayesian latent transport framework with PAC-Bayesian regularization.
result Reduction in latent manifold discrepancy and improved uncertainty calibration.
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.
Study identifies and analyzes three types of errors in learning Fourier operators.
problem Statistical, discretization, and truncation errors in learning Fourier operators.
method Analysis of a Discrete Fourier Transform (DFT) based least squares estimator.
result Established upper and lower bounds on statistical, discretization, and truncation errors.
Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this topic and a comprehensive experimental analysis of the most-known algorithms. We sta…
The article reviews scoring rules for estimating and evaluating forecasts.
problem Evaluating probabilistic forecasts and estimating probability distributions.
method Mathematical foundations and characterization of scoring rules.
result Important families of scoring rules and their applications in statistics and machine learning.
New theory uses probability sets for data variability, improving machine learning.
problem Variability in data distribution causes learning issues.
method Uses convex sets of probabilities (credal sets) to model data variability.
result Derives bounds for risk of models learned from multiple training sets.
Maximum mean discrepancy (MMD), also called energy distance or N-distance in statistics and Hilbert-Schmidt independence criterion (HSIC), specifically distance covariance in statistics, are among the most popular and successful approaches to quantify the difference and independence of random variables, respectively. T…
Chentsov's theorem characterizes the Fisher information metric on statistical models as essentially the only Riemannian metric that is invariant under sufficient statistics. This implies that each statistical model is naturally equipped with a geometry, so Chentsov's theorem explains why many statistical properties can…
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.
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…
Paper establishes statistical inference for pairwise comparison models.
problem Statistical inference for pairwise comparison models when the number of subjects diverges.
method Identifies Fisher information matrix as a weighted graph Laplacian for asymptotic normality.
result Near-optimal asymptotic normality result for maximum likelihood estimator.
Neural networks learn more efficiently with hidden factorial structures.
problem Challenges in high-dimensional statistical learning.
method Controlled experimental framework to test neural networks' ability to exploit hidden factorial structures.
result Neural networks can leverage hidden factorial structures to learn discrete distributions more efficiently.
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.
Paper introduces EnDKF for more accurate pose tracking.
problem Accurate pose tracking with directional uncertainty.
method EnDKF integrates unit-quaternion attitude representation for better directional uncertainty capture.
result Significant reduction in error compared to traditional methods.
The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures. In particular we will develop Markov networks (also known as Markov random field…
Bayesian nonparametrics adapt model complexity to diverse datasets.
problem Complex challenges across statistics, computer science, and engineering.
method Flexible Bayesian nonparametric models that adapt model complexity.
result Bayesian nonparametrics offer innovative solutions to multi-object tracking.
We investigate the problem of learning discrete, undirected graphical models in a differentially private way. We show that the approach of releasing noisy sufficient statistics using the Laplace mechanism achieves a good trade-off between privacy, utility, and practicality. A naive learning algorithm that uses the nois…
Introduces machine learning basics and algorithms.
problem Developing and analyzing machine learning algorithms.
method Mathematical foundations, optimization, statistical prediction, reproducing kernel theory, Hilbert space techniques, sampling methods, Markov chains, graphical models, variational methods, deep learning, clustering, factor analysis, manifold learning.
result Theoretical support and practical algorithms for machine learning.
The paper derives Einstein tensors for a family of α-connections on quasi-statistical manifolds.
problem Deriving Einstein tensors for a new family of connections.
method Developed mathematical foundations of statistical and quasi-statistical manifolds, including dual and equiaffine connections.
result Explicit expressions for curvatures and Einstein tensors of the α-connections.
These are the proceedings of the workshop "Math in the Black Forest", which brought together researchers in shape analysis to discuss promising new directions. Shape analysis is an inter-disciplinary area of research with theoretical foundations in infinite-dimensional Riemannian geometry, geometric statistics, and geo…
STOIC improves energy demand forecasting with reliable uncertainty estimates.
problem Accurate point forecasts alone are insufficient for energy systems; reliable uncertainty estimates are needed.
method Integrates graph-based forecasting with tabular foundation models for zero-shot calibration of spatial-temporal residuals.
result STOIC delivers more reliable and robust uncertainty estimates for complex graph-structured energy time series.
New statistical theory explains contrastive learning effectiveness.
problem Understanding why contrastive learning works well for representation extraction.
method Developed a new theoretical framework based on approximate sufficient statistics.
result Near-sufficient encoders derived from contrastive learning can be adapted for downstream tasks.