New method for fast, accurate Gaussian process regression with data guarantees.
problem Slow and unreliable GP inference methods for nonparametric regression.
method Developed a novel objective function (preconditioned Fisher divergence) for scalable approximate GP regression with finite-data guarantees.
result Minimizing the pF divergence provides pointwise mean and variance estimates with tight 2-Wasserstein distance bounds and comparable empirical performance to variational sparse GPs.
XGES improves GES by favoring early edge deletion, outperforming GES in finite data settings.
problem Learning directed acyclic graphs from finite data.
method Extremely Greedy Equivalent Search (XGES) improves GES by favoring early edge deletion.
result XGES consistently outperforms GES in recovering the correct graphs, and is 10 times faster.
PACC Discovery improves causal inference from limited data.
problem Inferring causal relationships from finite data.
method Extends PAC learning principles to causal inference.
result Theoretical guarantees for various causal methods.
Estimates causal effects in Gaussian Linear SCMs with finite data.
problem Estimating causal effects from observational data with latent confounders.
method Centralized Gaussian Linear SCMs (CGL-SCMs) and EM-based estimation algorithm.
result Learned CGL-SCM parameters accurately recover causal distributions from finite observational samples.
We identify linear models from nonlinear systems with initialization constraints.
problem Identifying linear models from nonlinear systems with initialization constraints.
method Multiple trajectories-based deterministic data acquisition algorithm followed by regularized least squares.
result We provide a finite sample error bound on the learned linearized dynamics.
The paper proves mutual information measurement is statistically limited.
problem Measuring mutual information from finite data is difficult.
method Proves statistical limitations on any method of measuring mutual information.
result Any distribution-free high-confidence lower bound on mutual information estimated from N samples cannot be larger than O(ln N ).
Feature selection aims to select the smallest subset of features for a specified level of performance. The optimal achievable classification performance on a feature subset is summarized by its Receiver Operating Curve (ROC). When infinite data is available, the Neyman- Pearson (NP) design procedure provides the most e…
Finite resources limit false discovery rate control in structured hypothesis spaces.
problem Controlling false discovery rate in hypothesis testing with finite data and structured hypothesis spaces.
method Framework for exact FDR control and adaptive power maximization.
result Exact FDR control and adaptive power maximization.
We consider 1-qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the average-variance-optimality (A-optimality) criterion, known in the classical theory of experimental design and applied here to quantum …
A mechanism to share risks and costs with guarantees against extreme outcomes.
problem Softening extreme individual burdens in risk sharing schemes.
method Formalizes Certified Allocation Problem; uses Conformal Risk Sharing with interpretable sharing policy and split conformal calibration.
result Reduces extreme obligations for high-risk agents while controlling harm to others.
New method reduces over-parametrization in neural networks, ensuring sparsity and finite network size.
problem Over-parametrization leads to too many active neurons in neural networks, especially with large data.
method Investigates a nonconvex regularization method for shallow ReLU networks.
result Locally optimal networks are finite even with infinite data, maintaining approximation guarantees and network size bounds.
Users of a personalised recommendation system face a dilemma: recommendations can be improved by learning from data, but only if the other users are willing to share their private information. Good personalised predictions are vitally important in precision medicine, but genomic information on which the predictions are…
Adversarial training can degrade standard accuracy even when optimal for robust accuracy.
problem Tradeoff between standard and robust accuracy in adversarial training.
method Analyzes adversarial training's impact on standard accuracy, even when optimal for robust accuracy.
result Even with optimal predictors, adversarial training can still degrade standard accuracy.
Improved neural network regression uncertainty estimation.
problem Neural networks lack classical uncertainty due to finite data.
method Bootstrapped Deep Ensembles, incorporating parametric bootstrap.
result Significantly improved uncertainty estimation compared to standard Deep Ensembles.
Improves Laplace approximation for Bayesian inference on Riemannian manifolds.
problem Inaccurate Gaussian approximations for complex targets and finite-data posteriors.
method Develops alternative variants of the Laplace approximation using a Riemannian metric.
result Exact approximations at the limit of infinite data, improving practical performance.
The paper finds Koopman invariant subspaces using personalized PageRank.
problem Selecting a finite dictionary of observables for Koopman-invariant span.
method Exploiting zero-block structure in EDMD matrices and applying PageRank.
result Personalized PageRank can detect Koopman invariant subspaces.
Study shows generative priors improve rank-one matrix recovery with optimal sample complexity.
problem Recovering a rank-one signal matrix from noisy data with additional prior information.
method Analysis of a nonlinear least squares objective with a favorable global optimization landscape.
result Established optimal sample complexity for generative priors in rank-one matrix recovery.
We introduce a new class of possibly noncompact n-dimensional manifolds without boundary associated to finite data which we call topological automata. This class is large enough to contain many interesting examples of open 2-dimensional and 3-dimensional manifolds of interest to low-dimensional topologists. Our main re…
The Bellman error is a poor proxy for value function accuracy, even with all state-action pairs.
problem The Bellman error is a poor proxy for the accuracy of the value function.
method Study of the Bellman equation as a surrogate objective for value prediction accuracy.
result The magnitude of the Bellman error is only weakly related to the distance to the true value function, even with all state-action pairs.
This work introduces significativity indices for agreement values between classifiers.
problem Evaluating the quality of agreement measures between classifiers.
method Proposes general approach and two specific indices for evaluation.
result Introduces two new significativity indices for evaluating agreement values.
OTCP extends conformal prediction to multivariate data using optimal transport.
problem Uncertainty quantification in multivariate machine learning models.
method OTCP leverages optimal transport to rank multivariate conformity scores.
result Preserves distribution-free coverage guarantees in multidimensional settings.
Regularization improves causal models even in infinite data scenarios.
problem Improving causal models in infinite data scenarios.
method Regularization in regression methods, especially Ridge and Lasso, to reduce confounding effects.
result Proven causal generalization bound for non-linear regression models.
The paper develops Kalman filters for unknown systems with sample complexity bounds.
problem Designing Kalman filters for systems with unknown parameters and noise.
method Combines system identification with Kalman filter design, ensuring robustness and sub-optimality guarantees.
result Proves sub-optimality guarantees for both Certainty Equivalent and robust Kalman filters with sample complexity bounds.
New algorithm interpolates data with neural nets, independent of sample size.
problem Understanding neural networks' ability to memorize training data.
method Randomized algorithm for constructing interpolating neural networks.
result Guarantees that are independent of the number of samples, moving beyond worst-case memorization capacity bounds.
We study the problem of distinguishing between two distributions on a metric space; i.e., given metric measure spaces (X,d,μ1) and (X,d,μ2), we are interested in the problem of determining from finite data whether or not μ1 is μ2. The key is to use pairwise distances between observat…
We propose a novel method for clustering data which is grounded in information-theoretic principles and requires no parametric assumptions. Previous attempts to use information theory to define clusters in an assumption-free way are based on maximizing mutual information between data and cluster labels. We demonstrate …
A typical problem in causal modeling is the instability of model structure learning, i.e., small changes in finite data can result in completely different optimal models. The present work introduces a novel causal modeling algorithm for longitudinal data, that is robust for finite samples based on recent advances in st…
Many modern data analysis problems involve inferences from streaming data. However, streaming data is not easily amenable to the standard probabilistic modeling approaches, which assume that we condition on finite data. We develop population variational Bayes, a new approach for using Bayesian modeling to analyze strea…
The development of a metric for structural data is a long-term problem in pattern recognition and machine learning. In this paper, we develop a general metric for comparing nonlinear dynamical systems that is defined with Perron-Frobenius operators in reproducing kernel Hilbert spaces. Our metric includes the existing …
Optimal ridge regularization computed iteratively from generative parameters.
problem Finding the optimal ridge regularization strength for linear regression.
method Iterative procedure to compute optimal regularization strength numerically.
result The proposed procedure attains near-optimal generalization across various conditions.
Develops PAC-Bayesian framework for physics-informed machine learning.
problem Lack of statistical generalisation understanding for PIML models.
method PAC-Bayesian framework with multi-task perspective, incorporating physical structure.
result High-probability generalisation guarantees with unbounded losses.
We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as much as possible from limited data. When many parameters are poorly constrained by …
The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way using methods from statistical field theory. Here I describe new results that allo…
Paper achieves logarithmic regret for online Kalman filter learning.
problem Predicting observations from an unknown, partially observed linear system with stochastic noise.
method Online least-squares algorithm exploiting the approximate linearity of Kalman filter predictions.
result Achieves regret of order poly(log(N)) with high probability.
New method uses Gaussian processes for solving linear PDEs with boundary conditions.
problem Solving linear PDEs with boundary conditions.
method Boundary Ehrenpreis--Palamodov Gaussian Processes (B-EPGPs).
result Significant accuracy and resource improvements over existing methods.
This paper analyzes the posterior variance of Gaussian processes and derives a new bound.
problem Lack of suitable analysis of posterior variance for finite and infinite training data.
method Derives a novel bound for posterior variance requiring only local information.
result Proves sufficient conditions for the convergence of posterior variance to zero and demonstrates improved average learning bound.
VR methods improve SGD for faster machine learning.
problem Efficiency in stochastic optimization for machine learning.
method Variance reduction techniques for stochastic optimization.
result VR methods achieve faster convergence than SGD.
Our goal in this paper is to develop an effective estimator of fractal dimension. We survey existing ideas in dimension estimation, with a focus on the currently popular method of Grassberger and Procaccia for the estimation of correlation dimension. There are two major difficulties in estimation based on this method. …
Study reveals how high-dimensional models are vulnerable to consistent adversarial attacks.
problem Understanding the vulnerability of high-dimensional linear classifiers to adversarial attacks.
method Introducing a new error metric to quantify model vulnerability, and rigorously characterizing these metrics in asymptotic settings.
result As models become more overparameterized, their vulnerability to label-preserving perturbations increases.
Gradient descent converges geometrically to optimal self-attention parameters.
problem Training softmax self-attention layers for linear regression.
method Structure-aware gradient descent with preconditioner and regularizer.
result Gradient descent converges geometrically to global minima.
The paper analyzes system identification with finite data.
problem Recovering system parameters and Kalman filter gain from noisy output measurements.
method Subspace identification algorithm, finite number of output samples, random matrix theory, self-normalized martingales, SVD robustness.
result Estimation errors decrease with a rate of 1/\sqrt{N}, valid even for marginally stable systems.
Paper analyzes mistake and generalization of MNIC classifiers.
problem Understanding the performance of interpolating classifiers.
method Elementary analyses of MNIC's regret and generalization.
result MNIC generalizes with a rate proportional to the norm of the interpolating solution and inversely proportional to the number of data points.
Paper provides unbiased spectral moment estimates from finite data.
problem Challenges in estimating spectral moments from limited data.
method Dynamic programming approach to estimate spectral moments of kernel integral operator.
result Demonstrates consistency with theoretical spectra and practical utility in neural networks.
New insights into RL efficiency from managing time discretization.
problem The impact of time discretization on RL methods in continuous-time systems.
method Analysis of Monte-Carlo policy evaluation for LQR systems.
result An optimal choice of temporal resolution for a given data budget improves policy evaluation efficiency.
Analyzes large-margin classifiers under high-dimensional data.
problem Selecting the best classifier among various margin-based methods.
method Investigates asymptotic performance of large-margin classifiers under two component mixture models.
result Analytical results closely match with Monte Carlo simulations.
We learn linear models from nonlinear systems using multiple trajectories and regularization.
problem Identifying linear models from data when the underlying dynamics are nonlinear.
method Multiple trajectories data acquisition followed by regularized least squares.
result Learn linearized dynamics with arbitrarily small error given enough samples.
We study 'meta-dependence' in conditional independence tests across different empirical distributions.
problem Understanding the breakdown of conditional independence properties in finite data.
method Geometric intuition and information projections to measure meta-dependence between conditional independences.
result We provide a measure of meta-dependence that consolidates findings across synthetic and real-world data.
New theory explains how strong models can learn from weak ones.
problem Learning from weak, incomplete, or incorrect labels.
method New bounds based on data distribution and student hypothesis class.
result Existing weak supervision theory fails to account for pseudolabel correction and coverage expansion.