Paper addresses the disparity between sampled and mean representations in disentangled learning.
problem Disparity between sampled and mean representations in disentangled learning.
method Proposes a method to eliminate the disparity by proving and utilizing the relationship between total correlation of sampled and mean representations for multivariate normal distributions.
result Demonstrates that a factorized mean representation can have lower total correlation than the sampled representation.
Paper proposes a method to reliably find correlations in categorical data.
problem Discovering reliable correlations in categorical data without distribution assumptions.
method Proposes a corrected-for-chance, consistent, and efficient estimator for normalized total correlation.
result Empirical evaluation shows low-regret optimization outcomes and effective algorithms for both small and large data.
New measures quantify dependence between variables without distribution estimation.
problem Measuring dependence between variables in arbitrary dimensions.
method Proposed matrix-based normalized total correlation and dual total correlation measures.
result Measures are differentiable and statistically more powerful than existing methods.
The study classifies term structure shapes in the two-factor Vasicek model using total positivity.
problem Classifying all possible term structure shapes in the two-factor Vasicek model of interest rates.
method Total positivity theory pioneered by Samuel Karlin.
result Four additional shapes can be produced in certain parameter regimes.
Paper introduces Wasserstein total correlation for disentangled representation learning.
problem Learning disentangled representations from data.
method Adversarial training of a critic to estimate Wasserstein total correlation in variational and Wasserstein autoencoders.
result Proposed method achieves comparable disentanglement performance with less reconstruction loss.
We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a CR-submanifold of a complex space form. We complete the local classification of normal holonomies for complex submanifolds. We show that the normal holonomy group of a coisotropic submanifold acts as the holonomy representation o…
We investigate the two components of the total daily return (close-to-close), the overnight return (close-to-open) and the daytime return (open-to-close), as well as the corresponding volatilities of the 2215 NYSE stocks from 1988 to 2007. The tail distribution of the volatility, the long-term memory in the sequence, a…
The following results are proved: Theorem 1. A totally real semiparallel submanifold of constant curvature with parallel f-structure in the normal bundle of a Kähler manifold N is flat or a totally geodesic submanifold of N. Theorem 2. A totally real minimal semiparallel submanifold M with parallel f-structure in the n…
Totally geodesic submanifolds in spheres have restricted curvature properties.
problem Characterizing submanifolds in spheres based on curvature conditions.
method Analyzing normal curvature, scalar curvature, and second fundamental form conditions.
result Compact pseudo-umbilical submanifolds in spheres are totally geodesic under specific curvature conditions.
In this paper, by studying the position of umbilical normal vectors in the normal bundle, we prove that pseudo-umbilical totally real submanifolds with flat normal connection in non-flat complex space forms must be minimal.
We decompose the evidence lower bound to show the existence of a term measuring the total correlation between latent variables. We use this to motivate our β-TCVAE (Total Correlation Variational Autoencoder), a refinement of the state-of-the-art β-VAE objective for learning disentangled representations, requiring n…
We deal with a notion of weak binormal and weak principal normal for non-smooth curves of the Euclidean space with finite total curvature and total absolute torsion. By means of piecewise linear methods, we first introduce the analogous notation for polygonal curves, where the polarity property is exploited, and then m…
Proposes TCWAE to learn disentangled representations using the Wasserstein Autoencoder.
problem Balancing reconstruction fidelity and disentanglement in learning representations.
method TCWAE (Total Correlation Wasserstein Autoencoder) using different KL estimators.
result Competitive results on data sets with known generative factors, and improved reconstructions on unknown factors.
Researchers create normal forms for CR manifolds in complex space.
problem Classifying and understanding 5D CR manifolds in C^4.
method Equivariant moving frames method to construct convergent normal forms.
result Complete normal forms for 5D CR submanifolds of C^4.
Planes are the only calibrated submanifolds with flat normal bundles.
problem Characterizing submanifolds with specific geometric properties.
method Using constant-coefficient differential forms and parallel calibrations.
result Calibrated submanifolds with flat normal bundles are planes.
If the probability of default parameters (PDs) fed as input into a credit portfolio model are estimated as through-the-cycle (TTC) PDs stressed market conditions have little impact on the results of the capital calculations conducted with the model. At first glance, this is totally different if the PDs are estimated as…
New method for mesh denoising using TGV of normal vector field.
problem Improving mesh quality by removing noise.
method Proposes a novel TGV formulation for normal vector fields on triangular meshes.
result New method outperforms existing techniques in mesh denoising experiments.
The study examines correlations of logarithms of integers at different scalings.
problem Analyzing pair correlations of logarithms of integers at various scalings.
method Examined correlations of logarithms of positive integers at different scalings, proving the existence of pair correlation functions.
result Level repulsion at linear scaling, total loss of mass at superlinear scalings, and Poissonian behavior at sublinear scalings.
Study shows Merton model limits to Poisson process with log-normal intensity, improving default portfolio prediction.
problem Improving prediction of default portfolios using complex models.
method Applying Merton model with log-normal intensity function to Poisson process, discussing temporal correlation effects.
result Power decay model provides better generalization for long-term default portfolio data.
New estimator for joint entropy outperforms existing methods in various distributions.
problem Estimating joint entropy in high-dimensional spaces.
method Partitioned sample spacing (PSS) for nonparametric estimation.
result PSS consistently outperforms k-NN and normalizing flow methods.
Enhances multimodal generation with Normalizing Flows and correlation analysis.
problem Generating coherent cross-modal data from multiple sources.
method Uses Deep Canonical Correlation Analysis for shared information, Normalizing Flows for diversity, and Product of Experts for scalability.
result Improves likelihood, diversity, and coherence in conditional generation.
The Normal Means problem plays a fundamental role in many areas of modern high-dimensional statistics, both in theory and practice. And the Empirical Bayes (EB) approach to solving this problem has been shown to be highly effective, again both in theory and practice. However, almost all EB treatments of the Normal Mean…
Characterizes metrics with finite total Q-curvature and introduces new volume entropy.
problem Understanding metrics with finite total Q-curvature and their geometric properties.
method Characterization of metrics through total Q-curvature and introduction of new volume entropy.
result Controlled volume growth for complete metrics with finite total Q-curvature and bounded scalar curvature.
A new method captures higher-order interactions in data clusters.
problem Accurately characterizing complex higher-order variable interactions.
method Local Correlation Explanation (CorEx) method: clustering and total correlation.
result Captures higher-order interactions at a local scale.
Study totally umbilic submanifolds using planar pseudo-geodesics.
problem Characterize totally umbilic isometric immersions with parallel normalized mean curvature vector.
method Introduce planar pseudo-geodesics and analyze their properties; prove the equivalence of totally umbilic immersions and planar geodesic extrinsic shapes.
result An isometric immersion is totally umbilic if and only if every geodesic of the manifold has planar extrinsic shape.
The study examines the limitations of bi-Lipschitz Normalizing Flows in approximating certain distributions.
problem The expressivity of bi-Lipschitz Normalizing Flows in approximating specific target distributions.
method Characterization of expressivity through lower bounds on Total Variation distance and discussion of potential remedies.
result Several target distributions are difficult to approximate using bi-Lipschitz Normalizing Flows, and lower bounds on their approximation are provided.
New Monte Carlo method outperforms existing strategy for estimating Sobol' indices.
problem Estimating first-and total-orders Sobol' indices accurately.
method Comparing two Monte Carlo estimators for Sobol' indices.
result New method outperforms current approach in accuracy.
This work improves texture segmentation by automatically tuning hyperparameters for Total-Variation.
problem The challenge is to automatically select hyperparameters for Total-Variation texture segmentation.
method The approach involves extending Stein's unbiased gradient estimator to handle correlated Gaussian noise, leading to an automatic tuning method.
result The method provides an automatic way to select hyperparameters for Total-Variation texture segmentation.
Paper relaxes differential privacy for correlated features, improving privacy-utility trade-off.
problem Standard differential privacy ignores feature correlation, leading to suboptimal privacy-utility balance.
method Introduces CorrDP framework that accounts for feature correlation, using total variation distance for quantification.
result CorrDP algorithms outperform standard DP in synthetic and real-world datasets with insensitive features.
The instability of historical risk factor correlations renders their use in estimating portfolio risk extremely questionable. In periods of market stress correlations of risk factors have a tendency to quickly go well beyond estimated values. For instance, in times of severe market stress, one would expect with certain…
We consider a unit normal vector field of (local) hyperfoliation on a given Riemannian manifold as a submanifold in the unit tangent bundle with Sasaki metric. We give an explicit expression of the second fundamental form for this submanifold and a rather simple condition its totally geodesic property in the case of a …
We prove that a maximal totally complex submanifold N2n of the quaternionic projective space HPn (n≥2) is a parallel submanifold, provided one of the following conditions is satisfied: (1) N is the orbit of a compact Lie group of isometries, (2) the restricted normal holonomy is a prop…
Learning by children and animals occurs effortlessly and largely without obvious supervision. Successes in automating supervised learning have not translated to the more ambiguous realm of unsupervised learning where goals and labels are not provided. Barlow (1961) suggested that the signal that brains leverage for uns…
Revisits conformal metrics with finite Q-curvature, providing necessary and sufficient conditions.
problem Understanding conformal metrics with finite total Q-curvature.
method Introduces conformal mass and provides necessary and sufficient conditions for normality.
result Derives volume comparison theorems and proves a positive mass type theorem related to Q-curvature.
The purpose of this paper is to classify totally umbilical slant submanifolds of a Kenmotsu manifold. We prove that a totally umbilical slant submanifold M of a Kenmotsu manifold Mˉ is either invariant or anti-invariant or dimM=1 or the mean curvature vector H of M lies in the invariant normal subbundle.…
New model improves portfolio selection by analyzing tensor data.
problem Improving portfolio selection through better analysis of style returns.
method Introducing a tensor dynamic conditional correlation (TDCC) model with trace-normalization and dimension-normalization.
result The TDCC model enhances portfolio selection across multiple markets.
We study properties of the cross-sectional distribution of returns. A significant anti-correlation between dispersion and cross-sectional kurtosis is found such that dispersion is high but kurtosis is low in panic times, and the opposite in normal times. The co-movement of stock returns also increases in panic times. W…
Study on how task sequence properties affect continual learning algorithms.
problem Understanding how task sequence properties influence continual learning algorithms.
method Proposes a new procedure using task space modeling and correlation analysis.
result Error rates are correlated to a task sequence's total complexity but not to sequential heterogeneity.
Total torsion of 3D lines of curvature is an integer multiple of 2π.
problem Understanding the total torsion of 3D lines of curvature in Riemannian manifolds.
method Analyzing the properties of well-positioned lines of curvature and using the total torsion theorem for spherical curves.
result The total torsion of a well-positioned line of curvature is an integer multiple of 2π.
For orthonormal normal sections of two-dimensional immersions in R^4 we define torsion coefficients and a functional for the total torsion. We discuss normal sections which are critical for this functional. In particular, a global estimate for the torsion coefficients of a critical normal section in terms of the curvat…
The study examines the normal growth exponent of submanifolds in negatively curved manifolds.
problem Understanding the normal growth exponent of submanifolds in negatively curved manifolds.
method Analyzing the geodesic flow and operator norms on submanifolds bi-Lipschitz to hyperbolic spaces.
result If a submanifold's normal growth exponent is at most 1, the ambient manifold is bi-Lipschitz to hyperbolic space.
Contradicts claims about Poincaré complexes and homology manifolds.
problem Claims about Poincaré complexes and homology manifolds are contradicted.
method Constructs a Poincaré complex with specific properties to contradict the claims.
result A Poincaré complex with vanishing periodic total surgery obstruction is not necessarily homotopy equivalent to a homology manifold.
Algorithm improves online canonical correlation analysis.
problem Online canonical correlation analysis.
method Stochastic Scaled-Gradient Descent (SSGD) for minimizing expectation over Riemannian manifolds.
result Achieved optimal one-time-scale algorithm with explicit rate of local asymptotic convergence.
We consider random vectors drawn from a multivariate normal distribution and compute the sample statistics in the presence of non-stationary correlations. For this purpose, we construct an ensemble of random correlation matrices and average the normal distribution over this ensemble. The resulting distribution contains…
Advances in unsupervised learning enable reconstruction and generation of samples from complex distributions, but this success is marred by the inscrutability of the representations learned. We propose an information-theoretic approach to characterizing disentanglement and dependence in representation learning using mu…
D2PCCA integrates deep learning and probabilistic modeling for nonlinear dynamical systems.
problem Analyzing nonlinear dynamical systems with probabilistic understanding.
method Combines deep learning and probabilistic modeling, using KL annealing and normalizing flows.
result Captures latent dynamics in sequential datasets with improved convergence and flexibility.
For time series comparisons, it has often been observed that z-score normalized Euclidean distances far outperform the unnormalized variant. In this paper we show that a z-score normalized, squared Euclidean Distance is, in fact, equal to a distance based on Pearson Correlation. This has profound impact on many distanc…
This paper benchmarks Bayesian models' ability to estimate predictive correlations, especially for active learning.
problem Benchmarking how accurately Bayesian models estimate predictive correlations, especially in active learning.
method Considered transductive active learning as a benchmark, introduced meta-correlations and cross-normalized likelihoods.
result Meta-correlations and cross-normalized likelihoods can efficiently evaluate predictive correlations and are consistent with TAL performance.