Unified Growth Theory debunked: economic growth is insecure and unsustainable.
problem The mystery of the great divergence in income per capita.
method Analysis of economic data to show that growth trajectories are increasing vertically over time.
result Unified Growth Theory is incorrect and promotes misleading concepts.
We derive an exponential inequality for Rényi divergence estimation.
problem Consistent estimation of divergences in machine learning.
method Generalized exponential concentration inequality for Rényi divergence estimation.
result Finite sample exponential inequality convergence bound for Rényi-α divergence estimator. The paper analyzes the statistical properties of GANs using f-divergence.
problem Understanding the statistical behavior of GANs and comparing different f-divergences. method Asymptotic analysis of f-divergence GANs, including Kullback-Leibler divergence. result Asymptotically equivalent GANs with the same discriminator classes for correctly specified models.
Study compares machine learning algorithms for predicting SST in the Great Barrier Reef.
problem Predicting sea surface temperature in the Great Barrier Reef region.
method Ridge regression, LASSO, Random Forest, and Extreme Gradient Boosting (XGBoost) algorithms were evaluated.
result XGBoost significantly outperforms other algorithms in terms of predictive accuracy and Kullback-Leibler Divergence.
The paper improves model robustness by regularizing posterior differences.
problem Improving model robustness in noisy input scenarios.
method Posterior differential regularization with f-divergence. result Regularizing with f-divergence improves model robustness. Replicated Softmax model, a well-known undirected topic model, is powerful in extracting semantic representations of documents. Traditional learning strategies such as Contrastive Divergence are very inefficient. This paper provides a novel estimator to speed up the learning based on Noise Contrastive Estimate, extende…
We study generalized Killing spinors on the standard sphere S3, which turn out to be related to Lagrangian embeddings in the nearly Kähler manifold S3×S3 and to great circle flows on S3. Using our methods we generalize a well known result of Gluck and Gu concerning divergence-free geod…
Paper introduces a new method to improve GANs by leveraging the discriminator's energy.
problem Improving the quality of generated samples in GANs.
method Discriminator Contrastive Divergence (DCD) method.
result Significant improvement in generation quality on synthetic and real-world data.
MsIGN tackles high-dimensional Bayesian inference using multiscale structure.
problem High-dimensional Bayesian inference challenges due to the curse of dimensionality.
method MsIGN generates samples from coarse to fine scale, minimizing Jeffreys divergence.
result MsIGN outperforms previous approaches in posterior approximation and mode capture.
This paper analyzes discrete diffusion models, deriving convergence bounds for their generated samples.
problem Theoretical guarantees for discrete-state diffusion models remain under-explored.
method Continuous Time Markov Chain (CTMC) framework and discrete-time sampling algorithm.
result Convergence bounds for KL divergence and TV distance are derived, showing linear dependence on dimension.
A new method detects anomalies in images without needing model adjustments.
problem Automatic detection of medical image anomalies for radiologists.
method Complementing VAEs with KL-divergence for anomaly localization.
result The method outperforms existing techniques in various settings.
Introduces new metrics to measure performance of deep Bayesian neural networks.
problem Lack of specific criteria to measure performance of deep Bayesian neural networks.
method Proposes several metrics including model calibration, data rejection ability, and uncertainty divergence.
result Introduces more specific criteria for measuring deep Bayesian neural network performance.
The paper simplifies Bayesian posterior using clustering to make inference more manageable.
problem Handling large-scale, redundant datasets in Bayesian learning.
method Construct an approximate posterior by replacing data points in the same cluster with the centroid.
result The approximate posterior is close to the exact posterior and easier to sample from.
Study shows diffusion models adapt to manifold hypothesis without dimensionality issues.
problem Empirical success of diffusion models in high-dimensional data.
method Developed a new framework connecting diffusion models to Gaussian Processes theory.
result Achieves rates independent of ambient dimension in terms of score learning and sampling complexity.
In the last decades the estimation of the intrinsic dimensionality of a dataset has gained considerable importance. Despite the great deal of research work devoted to this task, most of the proposed solutions prove to be unreliable when the intrinsic dimensionality of the input dataset is high and the manifold where th…
This work proposes a model averaging method for SVM that avoids redundant covariates and achieves asymptotic optimality.
problem Redundant covariates impair SVM performance in high-dimensional settings.
method Frequentist model averaging procedure for SVM using cross-validation to select optimal weights.
result The proposed method achieves asymptotic optimality in SVM model averaging.
A new method improves adversarial robustness by optimizing importance weights.
problem Adversarial training's non-uniform robustness across different data points.
method Doubly-robust instance reweighted adversarial training using distributionally robust optimization.
result Improves robustness against attacks on the weakest data points.
Study shows flash crashes in finance are self-organized criticality events.
problem Understanding and predicting anomalous price events in high-frequency finance.
method Investigated volume distributions during flash crashes and linked them to self-organized criticality.
result Volume distributions during flash crashes indicate a diverging second moment, suggesting self-organized criticality.
Great circle fibrations on 3-sphere yield tight contact structures.
problem Understanding contact structures on the 3-sphere from great circle fibrations.
method Proving contact structures via differential inequalities on transverse disks.
result Great circle fibrations on 3-sphere result in tight contact structures.
Harmonic and minimal great circle fibrations have special Gauss maps.
problem Characterizing Gauss maps of harmonic and minimal great circle fibrations.
method Analyzing the relationship between the Gauss map and the generating unit vector field.
result The Gauss map of a great circle fibration is harmonic (minimal) if and only if the generating unit vector field is harmonic (minimal).
New findings on great circle fibrations and contact structures on odd spheres.
problem Understanding contact structures on odd-dimensional spheres.
method Analysis of great circle fibrations and their associated hyperplane distributions.
result For odd-dimensional spheres, starting from the 5-sphere, not all fibrations result in contact structures.
New divergences extend Bregman and skew Jensen, including f-divergences.
problem Developing new divergences to include f-divergences.
method Introducing g-Bregman and skew g-Jensen divergences, showing they include f-divergences.
result g-divergences generalize existing divergences and inequalities.
We investigate great circle links in the three-sphere, the class of links where each component is a great circle. Using the geometry of their complements, we classify such links up to five components. For any two-bridge knot complement, there is a finite cover that is the complement of a link of great circles in S3.…
Paper shows how to break down a specific type of divergence into simpler parts.
problem Understanding and simplifying divergence functions.
method Decomposes the symmetric Bregman divergence into two types of Jensen divergences and a Bregman divergence, and extends this to include f-divergences.
result Sum decomposition of divergence into simpler parts is possible.
A two-network architecture learns intractable exponential family models.
problem Learning a model itself, not just optimizing parameters of a single distribution.
method Two-network architecture and optimization procedure for exponential family models.
result Accurately learns exponential family models, enabling generic operations.
Classifies surfaces with great and small circles through each point.
problem Identifying surfaces with specific circle properties.
method Topological classification of surfaces in 3D unit sphere.
result Surfaces are homeomorphic to five normal forms.
Study explores relationship between Hölder and FDPD divergences.
problem Understanding the relationship between Hölder and FDPD divergences.
method Intersection and generalization of divergence families, proving nonnegativity, deriving inequalities.
result Established ξ-Hölder divergence and derived inequalities. Unified representation of density-power-based divergences simplifies estimation to M-estimation.
problem Outliers in density estimation.
method Define a norm-based Bregman density power divergence (NB-DPD) that reduces to M-estimation.
result NB-DPD connects and generalizes existing divergences, highlighting robustness properties.
Financial planners helped preserve and increase household net financial assets during the Great Recession.
problem Impact of financial planners on household net financial assets during the Great Recession.
method Utilized 2007-2009 Survey of Consumer Finances (SCF) panel dataset, analyzed 3,862 respondents.
result Starting to use a financial planner during the Great Recession had a positive impact on preserving and increasing household net financial assets.
Gaussian kernel tests are optimal against smooth alternatives.
problem Understanding the statistical properties of nonparametric tests using Gaussian kernels.
method Analysis of Gaussian kernel-based goodness-of-fit, homogeneity, and independence tests.
result Gaussian kernel tests are minimax optimal against smooth alternatives in all three settings.
Paper explores how analysts balance rule-based and situational aspects of data analytics.
problem Balancing mechanistic and situational aspects of data analytics.
method CSCW and social science research, ethnographic fieldwork.
result Effective data vision requires straddling formal abstraction and empirical contingency.
This paper improves active learning by using robust divergences for committee disagreement.
problem Active learning with high measurement costs.
method Query by committee with Bregman divergence (including Kullback-Leibler divergence as a special case).
result The proposed method is more robust and performs as well as or better than conventional methods.
The aim of this paper is a characterization of great antipodal sets of complex Grassmannian manifolds as certain designs with the smallest cardinalities.
Heinz Hopf's famous fibrations of the 2n+1-sphere by great circles, the 4n+3-sphere by great 3-spheres, and the 15-sphere by great 7-spheres have a number of interesting properties. Besides providing the first examples of homotopically nontrivial maps from one sphere to another sphere of lower dimension, they all share…
New divergence measures improve KL approximation.
problem Improving KL divergence approximation without AC condition.
method Introduced α-geodesical skew divergence. result Properties of α-geodesical skew divergence studied. New method to study group invariants using divergence spectra.
problem Understanding group invariants through divergence.
method Introducing divergence spectrum to compare classical notions and study relatively hyperbolic groups.
result Existence of groups with exponential divergence but different divergence spectra.
Logarithmic divergences linked to curvature in statistical manifolds.
problem Understanding the geometric interpretation of curvature in statistical manifolds.
method Analyzing logarithmic L(α)-divergence and its equivalence to conformal transformations and Kurose's geometric divergence. result Logarithmic divergence is a canonical divergence of a statistical manifold with constant sectional curvature −α. The paper improves semi-supervised learning using f-divergences and α-Rényi divergences.
problem Improving semi-supervised learning with noisy pseudo-labels.
method Inspired by f-divergences and α-Rényi divergences, the paper develops new empirical risk functions and regularization techniques. result The new methods show better performance than traditional self-training methods, especially in noisy pseudo-label scenarios.
Develops a new method for solving equivalence problems in pseudo-groups.
problem Solving equivalence problems in pseudo-groups.
method Combining Cartan's equivalence method and equivariant moving frame for pseudo-groups.
result A hybrid equivalence method that extends and illuminates its two progenitors.
We construct an explicit diffeomorphism taking any fibration of a sphere by great circles into the Hopf fibration, using elementary geometry--indeed the diffeomorphism is a local (differential) invariant, algebraic in derivatives.
This work generalizes Log-Determinant divergences to infinite-dimensional settings.
problem Generalizing Log-Determinant divergences to infinite-dimensional spaces.
method Introducing a parametrized family of divergences, Alpha-Beta Log-Determinant divergences, for positive definite unitized trace class operators.
result The Alpha-Beta Log-Det divergences encompass various divergences and metrics, including the affine-invariant Riemannian distance and symmetric Stein divergence.
New divergences introduced in dually flat spaces with properties.
problem Measuring discrepancy between probability distributions in dually flat spaces.
method Introducing two types of divergences based on affine coordinates and potentials, and deriving relational equations.
result Generalization of the law of cosines and new inequalities between divergences.
f-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance e…
The paper extends Gluck and Warner's result on fibrations of spheres by great subspheres.
problem Understanding when two Hopf fibrations of S2n−1 agree on a fiber. method Characterizing the conditions for two Hopf fibrations of S2n−1 to agree on a fiber. result A complete characterization of the conditions for two Hopf fibrations of S2n−1 to agree on a fiber. Discusses a new divergence function in information geometry.
problem Symmetry properties of divergence functions in information geometry.
method Analyzes a recently introduced canonical divergence function.
result Outlines open problems regarding symmetry properties.
The study defines divergence for multivector fields on infinite-dimensional manifolds.
problem Defining divergence for multivector fields on infinite-dimensional manifolds.
method Definition of divergence consistent with finite-dimensional geometry, properties transferred from finite to infinite dimensions.
result Natural properties of divergence are preserved in infinite dimensions.
Technical report on f-divergences and f-GAN training properties.
problem Understanding and optimizing f-divergences for GAN training.
method Elementary derivation and detailed expressions of f-divergences and their variational lower bounds.
result Informative properties of f-divergences and f-GAN training, including gradient matching and stability improvements.
The paper evaluates biased methods for alpha-divergence minimization.
problem The impact of bias on solutions found for alpha-divergence minimization.
method Empirical evaluation of biased methods for alpha-divergence minimization, focusing on bias effects and dimensionality.
result Solutions are biased towards KL-divergence minimizers and require impractical computation in high dimensions to minimize alpha-divergence.