Study compares synthetic and distributional Ricci curvature bounds.
problem Comparing synthetic and distributional approaches to lower Ricci curvature bounds.
method Analyzes synthetic via weak displacement convexity and distributional via non-negativity of Ricci-tensor.
result Distributional bounds imply entropy bounds for C1 metrics and vice versa for C1,1 under convergence condition. Synthetic theory defines orbifolds as microlinear types with finite identifications.
problem Defining orbifolds in traditional set-level foundations with internal symmetries.
method Synthetic differential cohesive homotopy type theory, microlinearity, finite identifications.
result Proper étale groupoids are orbifolds in synthetic theory.
New k-means method clusters radar image sequences using SPD matrices.
problem Clustering radar image sequences efficiently.
method Developed k-means on SPD matrices for non-Euclidean data. result Effective clustering of radar image sequences via SPD matrices.
New relation between curvature bounds and spacetime inextendibility.
problem Inextendibility of spacetimes under low regularity conditions.
method Synthetic curvature and causal character analysis.
result Low-regularity spacetimes with unbounded curvature.
Paper creates fair synthetic data ensuring equal predictions across sensitive attributes.
problem Ensuring fair predictions across sensitive attributes in synthetic data.
method Equalizing target probability distributions across sensitive attributes in synthetic data generation.
result Synthetic data provides strong fair predictions, equal across all thresholds.
New relation between curvature bounds and spacetime inextendibility.
problem Inextendibility of spacetimes under low regularity conditions.
method Synthetic curvature and causal character maximizers.
result Low-regularity inextendibility linked to unbounded curvature.
The paper develops methods to create private synthetic spatial point patterns.
problem Generating private synthetic spatial point patterns.
method Developed differentially private Poisson and Cox point synthesizers.
result The synthesizers effectively maintain privacy and utility of synthetic data.
Improved method for computing Fréchet means on SPD matrices.
problem Computing Fréchet means on the manifold of SPD matrices.
method Random matrix theory-based approach for estimating Fréchet means.
result Significantly outperforms state-of-the-art methods in experiments.
New method classifies manifold-valued data using Riemannian geometry.
problem Classifying data on curved Riemannian manifolds.
method Probabilistic Learning Vector Quantization on Symmetric Positive Definite Matrices.
result The method outperforms traditional Euclidean methods on manifold-valued data.
DECAF generates fair synthetic data by embedding causal relationships.
problem Generating fair synthetic data from biased training data.
method DECAF uses a GAN with a structural causal model to embed causal relationships and debias synthetic data.
result DECAF successfully removes bias and generates high-quality synthetic data.
This work tackles regression on non-Euclidean spaces, specifically positive-definite matrices with the Bures-Wasserstein metric.
problem Regression on non-Euclidean spaces, specifically positive-definite matrices with the Bures-Wasserstein metric.
method Developed a sufficient condition for the existence of a minimizer of the conditional barycenter problem, characterized the optimization landscape, and developed a projection-free algorithm for approximate computation of first-order stationary points.
result The objective is free of local maxima under the sufficient condition, and the algorithm enables the use of stochastic Riemannian optimization methods for large-scale setups.
Like most learning algorithms, the multilayer perceptrons (MLP) is designed to learn a vector of parameters from data. However, in certain scenarios we are interested in learning structured parameters (predictions) in the form of symmetric positive definite matrices. Here, we introduce a variant of the MLP, referred to…
Study on cones over metric spaces with curvature bounds.
problem Establishing curvature bounds for cones over metric spaces.
method Developed a localization technique to prove synthetic curvature bounds.
result Riemannian and Lorentzian cones over CD-spaces satisfy MCP and vice versa.
Predicting not only the target but also an accurate measure of uncertainty is important for many machine learning applications and in particular safety-critical ones. In this work we study the calibration of uncertainty prediction for regression tasks which often arise in real-world systems. We show that the existing d…
Kernel K-means clusters probability distributions.
problem Clustering a sample of probability distributions.
method Mapping distributions to kernel mean embeddings in RKHS, then applying K-means.
result Effective unsupervised classification of probability distributions.
We propose a novel framework of the model specification test in regression using unlabeled test data. In many cases, we have conducted statistical inferences based on the assumption that we can correctly specify a model. However, it is difficult to confirm whether a model is correctly specified. To overcome this proble…
A new imputation method estimates missing values by matching observed marginals from masked data.
problem Missing values in data undermine statistical and machine learning analysis.
method Estimates a distribution from masked observations using positive semi-definite kernel density estimation.
result The method yields both single and multiple imputations from the same fitted density, with statistical consistency and fast adaptive excess risk.
Synthetic learning improves neonatal brain MRI segmentation robustness.
problem Challenges in neonatal brain MRI segmentation due to image contrast and anatomical variations.
method Synthetic learning model trained on few T2-weighted volumes, then enhanced with motion artifacts and over-segmentation.
result Synthetic learning robust to image contrast and improves segmentation of both T1- and T2-weighted images.
Birg{é} and Massart proposed in 2001 the slope heuristics as a way to choose optimally from data an unknown multiplicative constant in front of a penalty. It is built upon the notion of minimal penalty, and it has been generalized since to some "minimal-penalty algorithms". This paper reviews the theoretical results ob…
The paper explores conjugate points in Lorentzian spaces, comparing different definitions and proving related theorems.
problem Understanding conjugate points in Lorentzian geometry.
method Introducing and comparing different definitions of conjugate points in synthetic Lorentzian length spaces.
result All defined notions of conjugate points are compatible with the smooth spacetime setting.
The paper formalizes feature attribution to address inconsistent definitions and evaluate methods.
problem Inconsistent definitions of feature relevance in feature attribution.
method Formalization based on relaxed functional dependence, extended to instance-wise setting.
result State-of-the-art methods often fail to verify necessary properties for candidate selection.
Evaluating the log determinant of a positive definite matrix is ubiquitous in machine learning. Applications thereof range from Gaussian processes, minimum-volume ellipsoids, metric learning, kernel learning, Bayesian neural networks, Determinental Point Processes, Markov random fields to partition functions of discret…
New fairness approach removes direct effects of unprivileged groups through causal regularization.
problem Ensuring fairness in machine learning models for unprivileged groups.
method Proposes a new fairness definition based on causal effects and develops regularizations to remove the impact of unprivileged groups on model outcomes.
result Demonstrates effectiveness of the approach on various datasets, reducing unfairness with minimal performance loss.
New framework for fairness in machine learning models using SHAP values and adversarial learning.
problem Fairness of model predictions, especially for unprivileged groups.
method Develops a new fairness definition and a framework using SHAP values and adversarial learning to mitigate bias.
result Models produced are fairer and performant, demonstrating the approach on various datasets.
Proposes a new method to analyze the distributional effects of treatments.
problem Analyzing the full distributional impact of treatments beyond just the mean.
method Uses kernel conditional mean embeddings and U-statistic regression to investigate the CoDiTE.
result Demonstrates the effectiveness of the proposed method through experiments.
Investigates concavity of spacetimes, showing conditions for local concavity.
problem Understanding the concavity of spacetimes in Finsler geometry.
method Analyzes flag curvature and future capsules to characterize concavity.
result Berwald spacetimes are locally concave if and only if their flag curvature is nonnegative in timelike directions.
Study shows pooling scores for conformal prediction distorts group coverage.
problem Pooling scores for conformal prediction distorts group coverage.
method Derived conservation law and lower bound, demonstrated tension between fairness definitions, quantified trade-off between policies.
result Pooling scores for conformal prediction distorts group coverage.
We introduce a wrapped Gaussian for SPD matrices, enhancing data analysis.
problem Handling circular and non-flat data distributions on SPD manifolds.
method Introduced a non-isotropic wrapped Gaussian using the exponential map, derived theoretical properties, and proposed a maximum likelihood framework.
result Demonstrated the robustness and flexibility of the wrapped Gaussian model on synthetic and real-world datasets.
This paper presents a framework for exact discovery of the top-k sequential patterns under Leverage. It combines (1) a novel definition of the expected support for a sequential pattern - a concept on which most interestingness measures directly rely - with (2) SkOPUS: a new branch-and-bound algorithm for the exact disc…
Method estimates sparse inverse covariance and partial correlation matrices efficiently.
problem Sparse high-dimensional inverse covariance and partial correlation matrix estimation.
method Two-stage estimation method using partial regression with positive semi-definiteness.
result Efficient estimation of inverse covariance and partial correlation matrices with derived non-asymptotic rates.
Efficiently clusters data on manifolds using Fréchet maps.
problem Clustering on high-dimensional, non-Euclidean manifolds is computationally challenging.
method Introduces p-Fréchet map to embed manifold data into Euclidean space for k-means clustering. result Significant performance gains in runtime and accuracy compared to existing methods.
A knot K is definite if ∣σ(K)∣=2g(K). We prove that the quotient of a definite periodic knot is definite by considering equivariant minimal genus Seifert surfaces.
In this paper, we present ℓ1,p multi-task structure learning for Gaussian graphical models. We analyze the sufficient number of samples for the correct recovery of the support union and edge signs. We also analyze the necessary number of samples for any conceivable method by providing information-theoretic lowe…
SNAP efficiently identifies causal effects without needing full graph learning.
problem Efficiently estimating causal effects on a subset of variables.
method Sequential Non-Ancestor Pruning (SNAP) framework.
result SNAP reduces independence tests and computation time without sacrificing causal effect estimations.
A new geometric definition of integration for differential forms.
problem Standard integration definitions are coordinate-dependent and not suitable for certain contexts.
method Uses triangulations and cochains on the pair groupoid to define integration.
result Natural definition in Lie algebroids, stochastic integration, and quantum field theory.
This study proves new financial market theorems breaking standard risk definitions.
problem Breaking standard risk definitions in financial markets.
method Presenting proofs for new financial market theorems.
result New definitions are richer and broader than standard ones considering shape.
When quantitative models are used to support decision-making on complex and important topics, understanding a model's ``reasoning'' can increase trust in its predictions, expose hidden biases, or reduce vulnerability to adversarial attacks. However, the concept of interpretability remains loosely defined and applicatio…
Proposes a normalization technique for manifold valued data.
problem Instability in optimization for manifold valued data.
method Develops a general normalization technique for manifold valued data.
result Demonstrates performance gain in synthetic and real datasets.
The paper defines cross-section continuity for angular momentum definitions and finds the CWY definition valid.
problem Defining angular momentum at null infinity and ensuring its continuity across different cross-sections.
method Introducing cross-section continuity as a criterion and proving it for specific angular momentum definitions.
result The Chen-Wang-Yau definition of angular momentum satisfies cross-section continuity, while the Compere-Nichols modification does not.
We propose an L-BFGS optimization algorithm on Riemannian manifolds using minibatched stochastic variance reduction techniques for fast convergence with constant step sizes, without resorting to linesearch methods designed to satisfy Wolfe conditions. We provide a new convergence proof for strongly convex functions wit…
We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nyström approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the training set. When building low-rank kernel approximations in KCCA, previous work mostl…
Detecting anomalous activity in human mobility data has a number of applications including road hazard sensing, telematic based insurance, and fraud detection in taxi services and ride sharing. In this paper we address two challenges that arise in the study of anomalous human trajectories: 1) a lack of ground truth dat…
Local positive definite Z2^n-superfunctions can be extended.
problem Bounding and extending local positive definite Z2^n-superfunctions.
method Defining boundedness for Z2^n-superfunctions and extending them.
result Local positive definite Z2^n-superfunctions have positive definite extensions.
This paper proposes a new differential privacy definition using Rao distance.
problem Improving differential privacy definitions for better sequential composition.
method Using Rao distance instead of divergences of densities to define privacy.
result Proposed definition shares interpretation with previous definitions but improves sequential composition.
New definition resolves ambiguity in non-stationary bandit classification.
problem Ambiguity in classifying non-stationary bandits using existing definitions.
method Introducing a formal definition that resolves ambiguity and provides a unified approach.
result Unified approach applicable to both Bayesian and frequentist formulations, resolves classification issues.
A recent trend of fair machine learning is to define fairness as causality-based notions which concern the causal connection between protected attributes and decisions. However, one common challenge of all causality-based fairness notions is identifiability, i.e., whether they can be uniquely measured from observationa…
Study negative definite spin fillings of knot covers.
problem Existence of negative definite spin fillings in branched double covers.
method Derive obstructions and characterize special knots.
result Characterization of special alternating knots.
We provide a rigorous definition of the visual cause of a behavior that is broadly applicable to the visually driven behavior in humans, animals, neurons, robots and other perceiving systems. Our framework generalizes standard accounts of causal learning to settings in which the causal variables need to be constructed …