Enhances DES by removing noise and defining regions more accurately.
problem Incompetent classifier selection in noisy regions and true indecision regions.
method FIRE-DES++ uses equal number of samples from each class and removes noise to define regions more accurately.
result FIRE-DES++ outperforms FIRE-DES and state-of-the-art DES frameworks.
Minimizes indecisions in selective classification to control misclassification rates.
problem Controlling misclassification rates in high-risk scenarios.
method Using indecisions to control misclassification rates, even below Bayes optimal.
result Control of misclassification rates to any user-specified level, even below Bayes optimal.
The SPS method constructs confidence regions for true parameters with optimal sample complexity.
problem Constructing exact, non-asymptotic confidence regions for true system parameters.
method Sign-Perturbed Sums (SPS) method, generalized to various types of problems.
result High probability upper bounds for SPS confidence regions show optimal shrinkage rate.
The paper extends the isoperimetric inequality to disconnected regions.
problem Generalizing the isoperimetric inequality to regions that can split area.
method Analyzes the inequality in Euclidean, spherical, and hyperbolic geometries, providing conditions for multiple regions.
result Necessary and sufficient conditions for the inequality to hold for multiple regions in different geometries.
SDG uses optimal control to improve classifier guidance in low-density regions.
problem Inefficient guidance in low-density regions of posterior distributions.
method Integrates stochastic optimal control with Stein variational inference to compute the steepest descent direction.
result SDG improves guidance in low-density regions, outperforming standard methods.
Generative model improves image realism with word phrase attention.
problem Natural language often involves complex foreground objects and variable background.
method Introduced region-phrase attention between true-grid regions and word phrases.
result Generated more realistic images compared to state-of-the-art algorithms.
VSPS creates flexible prediction regions for multi-target regression with guaranteed coverage.
problem Uncertainty quantification in multi-target regression with complex distributions.
method Conditional normalizing flows with conformal calibration to identify dense regions.
result VSPS produces smaller, more informative prediction regions with robust coverage guarantees.
Learn true model from metastable samples of discrete distributions.
problem Learning true model from samples that get stuck in metastable states.
method Conditional likelihood estimator based on strong metastability condition.
result True model can be recovered from metastable samples of discrete distributions.
Understanding how funding and 4H context regulate crypto markets.
problem Analyzing the chaotic appearance of financial markets.
method Observing interactions between market context and capital conditions in the 4H timeframe.
result Ranges in crypto markets are strategic positioning by informed participants, not indecision.
The study estimates the expressiveness of GCNs with bounds on the number of linear regions.
problem Characterizing the expressiveness of graph convolutional networks (GCNs).
method Estimates the number of linear regions for one-layer and multi-layer GCNs.
result GCNs with multiple layers have exponentially more expressivity per parameter than one-layer GCNs.
This paper examines how regional trade agreements affect global trade relationships.
problem The relationship between regional trade agreements and global trade purity.
method Defined and decomposed synthesized trade resistance, separated natural and artificial factors, used expectation maximization algorithm to optimize parameters, and quantified trade purity indicator.
result Regional trade agreements contribute to the relative prosperity of EU and NAFTA countries, but weaken the role of trade unions and accelerate multilateral trade liberalization.
New approach for handling uncertain probabilities.
problem Handling imprecise or uncertain probabilities.
method Introducing interval probability measures and updating rules.
result Formal solution to the Keynes-Ramsey controversy.
We prove a comparison theorem for the isoperimetric profiles of simple closed curves evolving by the normalized curve shortening flow: If the isoperimetric profile of the region enclosed by the initial curve is greater than that of some `model' convex region with exactly four vertices and with reflection symmetry in bo…
A new method, Residual-Permuted Sums, improves confidence region construction for linear regression models.
problem Constructing reliable confidence regions for linear regression models with non-symmetric noise.
method Residual-Permuted Sums (RPS) method, which permutes residuals instead of perturbing their signs.
result RPS provides exact finite sample coverage probabilities and is uniformly strongly consistent.
Low-rank matrix regression refers to the instances of recovering a low-rank matrix based on specially designed measurements and the corresponding noisy outcomes. In the last decade, numerous statistical methodologies have been developed for efficiently recovering the unknown low-rank matrices. However, in some applicat…
New algorithm for adaptive experimental design in scientific settings.
problem Identifying true positives while controlling false discoveries in adaptive experimental design.
method Provably sample efficient adaptive algorithm for FDR control.
result First provably sample efficient adaptive algorithm for adaptive experimental design.
A theorem of Kuranishi tells us that the moduli space of complex structures on any smooth compact manifold is always locally a finite-dimensional space. Globally, however, this is simply not true; we display examples in which the moduli space contains a sequence of regions for which the local dimension tends to infinit…
MIRA scores assess conditional distribution accuracy using joint samples.
problem Assessing the accuracy of candidate conditional distributions.
method Analytic expression for Mira score based on equal probability mass regions.
result Mira enables Bayesian model comparison by quantifying alignment with true process.
Waldo method constructs valid confidence regions for simulator-based inference.
problem Constructing valid confidence regions for simulator-based inference with high-dimensional data.
method Reframes Wald test statistic and uses regression-based machinery for Neyman inversion.
result Waldo method produces conditionally valid and precise confidence regions.
New insights into the top-K sparse softmax gating function for deep learning.
problem Understanding the theoretical effects of the top-K sparse softmax gating function on density and parameter estimations.
method Using a Gaussian mixture of experts, novel loss functions, and theoretical analysis.
result The convergence rates of density and parameter estimations are parametric under certain conditions, but slow under over-specified models.
This paper analyzes the sample complexity of SPS method for scalar linear regression.
problem Analyzing the sample complexity of the Sign-Perturbed Sums (SPS) identification method.
method The paper provides high probability upper bounds for the sizes of SPS confidence intervals under different sets of assumptions.
result The sizes of SPS confidence intervals shrink at a geometric rate around the true parameter, if observation noises are subgaussian.
Combines global and local search for efficient global optimization with Gaussian processes.
problem Difficulties in building accurate GP models and getting stuck in suboptimal regions.
method Adopting AGLGP model combining global and local GP models, dividing space into regions, and switching between global and local searches.
result Efficiently locates the global optimum with benefits of both global and local search.
We propose a methodological framework to study the dynamics of inter-regional investment flow in Europe from a Complex Networks perspective, an approach with recent proven success in many fields including economics. In this work we study the network of investment stocks in Europe at two different levels: first, we comp…
TRM improves long-horizon LLM RL by masking divergent sequences.
problem Long-horizon reinforcement learning with LLMs suffers from off-policy mismatch and approximation errors.
method Derives and applies trust region bounds to control divergence, proposing Trust Region Masking.
result First non-vacuous monotonic improvement guarantees for long-horizon LLM-RL.
TRM improves long-horizon reinforcement learning for LLMs by masking divergent sequences.
problem Long-horizon reinforcement learning for LLMs suffers from off-policy mismatch and approximation errors.
method Derives and applies trust region bounds to control divergence, proposing Trust Region Masking.
result First non-vacuous monotonic improvement guarantees for long-horizon LLM-RL.
CP4SBI improves the calibration of credible sets in SBI models.
problem Inaccurate credible sets in SBI models lead to underestimation of true parameters.
method Develops a local conformal calibration framework for SBI models.
result Improves the quality of uncertainty quantification for neural posterior estimators.
We will show that the period T of a closed orbit of the planar circular restricted three-body problem (viewed on rotating coordinates) depends on the region it encloses. Roughly speaking, we show that, 2T=kπ+∫Ωg where k is an integer, Ω is the region enclosed by the periodic orbit and $g:\mathbb{R}^2\to \m…
New theorem links symmetries to first integrals in plasma physics.
problem Understanding the relationship between symmetries and first integrals in divergence-free fields.
method Developed a Noether-type Theorem reformulation for three-dimensional divergence-free vector fields.
result Converse of the Noether-type Theorem holds on the toroidal region, proving the existence of flux coordinates.
FreB protocol uses AI to infer hidden parameters with valid confidence regions.
problem Generating biased or overconfident conclusions from AI-generated posterior distributions.
method Frequentist-Bayes (FreB) protocol reshapes AI-generated posterior distributions into valid confidence regions.
result FreB provides valid confidence regions that consistently include true parameters with expected probability.
A new learning method uses data to learn from large model sets.
problem Learning with large sets of candidate models where uniform convergence is hard.
method Data-dependent learning that incorporates empirical data less reliant on prior assumptions.
result Demonstrates improved generalization in various learning assumptions.
RGI improves robustness of GAN-inversion for image restoration and anomaly detection.
problem Robustness of GAN-inversion to unknown gross corruptions.
method Proposes RGI and R-RGI methods with provable robustness guarantees.
result Restored images and corrupted region masks converge to ground truth under mild assumptions.
Bayesian GNNs with temperature improve prediction efficiency in CP.
problem Efficiency of prediction sets in CP for GNNs.
method Introducing a temperature parameter into Bayesian GNNs within the CP framework.
result More efficient prediction sets achieved with the temperature parameter.
The paper provides bounds for the empirical angular measure and applies them to improve statistical learning in extreme regions.
problem Estimating the angular measure in high-dimensional data with different distributions.
method Established bounds for the maximal deviations of the empirical angular measure from the true measure, using rank transformation and analyzing the most extreme observations.
result The bounds provide performance guarantees for statistical learning procedures in extreme regions, such as binary classification and anomaly detection.
By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and that in this region the growth rate of each firm is independent of the firm's size (Gibrat's law of proportionate effect). We also find t…
We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly because this approximation tends to underestimate the true variance and other features…
Success conditioning optimizes policies by imitating successful trajectories, solving a trust-region optimization problem.
problem Improving policies through random actions that lead to desired outcomes.
method Success conditioning, which involves collecting and updating policies based on successful trajectories.
result Success conditioning solves a trust-region optimization problem, maximizing policy improvement with a χ2 divergence constraint. Optimal spectral initializers impact phase retrieval phase transitions.
problem Understanding the limits of phase retrieval algorithms.
method Developed Random duality theory (RDT) to characterize optimal spectral initializers.
result Optimal spectral initializers can fall into flat regions of the phase retrieval manifold, making phase retrieval difficult.
Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised. We derive considerably weaker conditions that can be used in practice to ensure t…
CoLT assesses neural posterior estimates by detecting discrepancies across conditioning inputs.
problem Validating neural posterior estimates from limited data.
method Conditional Localization Test (CoLT) learns a localization function to detect strong deviations.
result CoLT provides rigorous guarantees and practical scalability for comparing true and neural posterior distributions.
Topic models are Bayesian models that are frequently used to capture the latent structure of certain corpora of documents or images. Each data element in such a corpus (for instance each item in a collection of scientific articles) is regarded as a convex combination of a small number of vectors corresponding to `topic…
The two most extended density-based approaches to clustering are surely mixture model clustering and modal clustering. In the mixture model approach, the density is represented as a mixture and clusters are associated to the different mixture components. In modal clustering, clusters are understood as regions of high d…
This paper improves risk bounds and calibration for smart predict-then-optimize method.
problem Improving risk bounds and calibration for smart predict-then-optimize method.
method Develops risk bounds and uniform calibration results for the SPO+ loss relative to the SPO loss.
result Empirical minimizer of the SPO+ loss achieves low excess true risk with high probability.
We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and covariates. We first establish a form of local statistical consistency for the penalize…
MA-COPP predicts multi-agent system outcomes using data from a different policy, with probabilistic guarantees.
problem Predicting outcomes in multi-agent systems using data from a different policy.
method Conformal prediction framework applied to multi-agent systems, avoiding exhaustive search.
result Achieves probabilistic guarantees for multi-agent system predictions.
Study on decision-making cascades with agents having varying beliefs and noise levels.
problem Optimizing decision-making in a cascade of agents with heterogeneous beliefs and noise.
method Recursive belief update and analysis of optimal decision rules, predecessor selection problem characterization.
result Optimal decisions can deviate from true prior beliefs in certain conditions, highlighting the importance of social learning.
Framework predicts household incomes using common indicators across regions.
problem Finding a single policy for multiple regions with diverse issues.
method Regression analysis and Minimum Description Length (MDL) principle.
result Framework identifies largest regions with common indicators for efficient income prediction.
Using methods of statistical physics, we analyse the error of learning couplings in large Ising models from independent data (the inverse Ising problem). We concentrate on learning based on local cost functions, such as the pseudo-likelihood method for which the couplings are inferred independently for each spin. Assum…
SANE improves exploration of noisy, multimodal functions by finding multiple optima.
problem Finding multiple optima in noisy, non-differentiable functions.
method Strategic Autonomous Non-Smooth Exploration (SANE) with a cost-driven acquisition function and human knowledge gate.
result SANE outperforms classical Bayesian optimization in discovering multiple optima.