The paper proves regularity for varifolds with bounded anisotropic mean curvature.
problem Regularity of varifolds with bounded anisotropic mean curvature.
method Local anisotropic regularity theorem and touching balls approach.
result Varifolds can be covered by countably many C2-regular submanifolds. The paper generalizes TQFTs to fermionic systems and classifies SPTs and SETs.
problem Classifying fermionic SPTs and SETs with finite group symmetries.
method Formulating fermionic TQFTs, gauging SPTs, using bordism groups, and constructing anomalous boundary states.
result Explicit classification of fermionic SPTs and SETs, including new anomalous boundary states.
In this paper we propose a novel application of Gaussian processes (GPs) to financial asset allocation. Our approach is deeply rooted in Stochastic Portfolio Theory (SPT), a stochastic analysis framework introduced by Robert Fernholz that aims at flexibly analysing the performance of certain investment strategies in st…
A new test controls type 1 error and has good power for online experiments.
problem Testing complex metrics and preventing type 1 error inflation in online randomized experiments.
method Nonparametric sequential test using bootstrap and mixture SPT.
result The test controls type 1 error and has good power in online experiments.
SPT predicts age and mass of red giants from spectra.
problem Challenges in age and mass estimation of red giants using traditional methods.
method SPT framework with Multi-head Hadamard Self-Attention and Mahalanobis distance-based loss function.
result Remarkable age and mass estimations with low errors and uncertainties.
We classify higher-SPTs and their anomalies via cobordism theory.
problem Understanding higher symmetries and anomalies in quantum field theories.
method Developed a generalized cobordism theory using advanced mathematical tools.
result Classified higher-SPTs and their boundary anomalies.
This paper extends Euclidean theorems to anisotropic settings for varifolds.
problem Anisotropic mean curvature of codimension-one varifolds.
method Proves perpendicularity and locality of mean curvature for bounded anisotropic mean curvature varifolds.
result Anisotropic mean curvature agrees with the approximate mean curvature on the rectifiable part of the varifold.
The study extends SPT to account for real-world transaction costs, improving portfolio performance.
problem Real-world transaction costs affect portfolio performance, especially during market stress.
method Developed a continuous-time model with stochastic transaction costs and derived lower bounds for cost-adjusted wealth.
result Functionally generated portfolios can still achieve relative arbitrage after accounting for transaction costs.
Constructs rank-based continuous semimartingales for financial markets.
problem Model financial markets using rank-based diffusions.
method Uses Dirichlet forms and Feller property to construct semimartingales.
result Establishes nonexistence of triple collisions and simplified rank process dynamics.
Develops SPT with price impact, deriving formulas for wealth and arbitrage conditions.
problem Tackles price impact in high-dimensional markets.
method Incorporates nonlinear price impact and impact decay models.
result Derives master formula for trading strategies and wealth dynamics.
Study optimizes decay estimates for minimizing currents in submanifolds.
problem Optimizing decay estimates for minimizing currents in submanifolds.
method Proves excess-decay estimate for codimension 1 currents mod 2Q.
result Optimal dependence of estimates upon second fundamental form of submanifold.
Develops a new model-free approach to portfolio theory using rough paths.
problem Handles more general portfolios without probabilistic assumptions.
method Rough path theory for stochastic portfolio theory (SPT).
result Asymptotic growth rates of various portfolios match.
Constructs a path integral for fermionic SPTs, solving anomalies in 2+1D topological orders.
problem Anomalies in (2+1)D fermionic topological phases and their computation.
method Combining (2+1)D fermionic topological order with symmetry fractionalization data to construct a (3+1)D path integral.
result Reproduces the Z16 anomaly indicator for time-reversal symmetric topological superconductors. Paper generalizes properties of oriented 3d TFTs to unoriented case.
problem Generalize properties of oriented 3d TFTs to unoriented case.
method Show how Turaev-Viro construction can be generalized to unoriented 3d TFTs and Pin^+ TFTs.
result Pin^+ TFTs can be constructed from unoriented TFTs with a mixed anomaly.
Study SKK groups of manifolds to classify non-unitary TQFTs.
problem Classify non-unitary invertible topological quantum field theories.
method Apply Galatius-Madsen-Tillman-Weiss and Genauer-Schommer-Pries results to compute SKK groups.
result Complete classification of non-unitary invertible TQFTs in dimensions 1-5.
This paper proposes SPT to generate diverse and transferable adversarial examples.
problem Limitations of recent adversarial examples in diversity and transferability.
method Structure-preserving transformation (SPT) to generate natural and diverse adversarial examples.
result Adversarial examples generated by SPT transfer well to other models with high success rate.
The Clifford torus minimizes Willmore energy closely for small perturbations.
problem Finding the closest shape to the Clifford torus under small perturbations of Willmore energy.
method Analyzing integral 2-varifolds with specific properties and showing quantitative closeness to the Clifford torus.
result The support of the varifold is quantitatively close to the Clifford torus after a conformal transformation.
Paper provides estimates for varifolds with critical mean curvature.
problem Estimating tilt-excess on varifolds with critical mean curvature.
method Generalizing Lipschitz approximation and Sobolev-Poincaré estimates to almost-integral rectifiable varifolds.
result VMO-type estimates for quadratic tilt-excess on varifolds with critical mean curvature.
Discovering topological quantum field theories in 2+1 and 3+1 dimensions.
problem Exploring topological orders in condensed matter lattice models.
method Calculating braiding statistics and link invariants of anyon excitations.
result Identifying new spin topological quantum field theories with specific knot/link invariants.
New insights into 4d YM and 5d topological field theories with higher symmetries.
problem Exploring new topological field theories with higher symmetries.
method Dynamic gauging of 1-form symmetry, higher anomalies, and lattice simplicial complex regularizations.
result Discovery of new higher-form gauge fields and exotic anyonic statistics.
The paper studies the behavior of Möbius-invariant Willmore flow in 3-sphere, proving convergence to Clifford torus.
problem Investigating the behavior of Möbius-invariant Willmore flow in 3-sphere.
method Analyzing flow lines of the Möbius-invariant Willmore flow in 3-sphere, constructing divergent and convergent flow lines, and identifying limit surfaces.
result The flow lines of the Möbius-invariant Willmore flow in 3-sphere converge to parametrizations of the Clifford torus, up to Möbius transformations.
Study optimizes growth rate for investors with long-only constraints.
problem Maximizing growth rate under drift uncertainty and long-only constraints.
method Developed a finite dimensional approximation for concave functionally generated portfolios.
result Proved uniqueness and existence for optimal portfolios under long-only constraints.
Novel PCA method for high-dimensional inverse problems.
problem Optimizing large-scale random fields with gradient information.
method Gradient-Sensitive Principal Component Analysis (Gradient-SPCA) that modifies PCA using objective function gradients.
result Improvements in encoding quality for objective function minimization and field distribution.
Paper proves minimal surfaces near quadratic cones have specific smooth structure.
problem Characterize minimal surfaces near quadratic cones.
method Analyzes n-varifolds in the unit ball close to a minimizing quadratic cone. result Singularities modeled on these cones determine the local structure of nearby minimal surfaces.
Unified approach to equity markets with open and hybrid Jacobi models.
problem Stochastic Portfolio Theory problems in equity markets.
method Combining open markets and hybrid Jacobi processes.
result Stability of capital distribution curve and growth optimal strategies.
Study calculates tail risk for various mixture distributions.
problem Estimating tail risk for complex distribution mixtures.
method Analyzes tail conditional expectation for location-scale mixtures of elliptical distributions.
result Developed methods for calculating tail risk in various distributions.
Enhances mixture models with classifier-defined weights.
problem Density evaluation and sampling in mixture models.
method Introduces Classifier Weighted Mixtures (CWM) with functional weights.
result Improves expressivity in variational estimation without increasing complexity.
Two approaches improve parameter learning in various mixture models.
problem Parameter learning in mixture models.
method Complex-analytic and algebraic-combinatorial methods.
result Improved sample sufficiency for parameter estimation in specific mixture models.
We consider unsupervised estimation of mixtures of discrete graphical models, where the class variable corresponding to the mixture components is hidden and each mixture component over the observed variables can have a potentially different Markov graph structure and parameters. We propose a novel approach for estimati…
The paper models market crashes as phase transitions, finding dynamic transitions offer better predictions.
problem Understanding and predicting extreme financial events like market crashes.
method Employing phase transition theory, focusing on endogenous crashes, and comparing DPT, CPT, and SPT.
result Dynamic phase transitions provide more accurate predictions of market crashes compared to critical and stochastic models.
Paper introduces Normalized Wasserstein measure for better handling of imbalanced mixture distributions.
problem Wasserstein distance fails for mixture distributions with imbalanced proportions.
method Introduce mixture proportions as optimization variables to normalize Wasserstein formulation.
result Normalized Wasserstein measure leads to significant performance gains for mixture distributions.
Improved VB algorithm for NIG mixtures outperforms Gaussian mixtures for non-Gaussian data.
problem Clustering non-Gaussian data, especially heavy-tailed and asymmetric.
method Proposed an improved VB algorithm for NIG mixture models and extended Dirichlet process mixture models.
result Outperforms Gaussian mixtures and existing NIG mixture models, especially for highly non-normative data.
When estimating finite mixture models, it is common to make assumptions on the mixture components, such as parametric assumptions. In this work, we make no distributional assumptions on the mixture components and instead assume that observations from the mixture model are grouped, such that observations in the same gro…
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…
Optimal mixtures of generative models outperform individual models on image datasets.
problem Selecting the best single model from a group of trained generative models.
method Formulated a quadratic optimization problem and proposed the Mixture-UCB algorithm for efficient selection.
result Mixture of generative models achieves better evaluation scores than individual models on benchmark datasets.
New bounds on sample size for identifying mixture models with grouped samples.
problem Identifying mixture models with minimal sample size.
method Generalized identifiability bounds for mixture models with grouped samples.
result Identifiability with (2m−1)/(k−1) samples per group, with no improvement possible. Bayesian approach learns nonparametric mixture components from heterogeneous data.
problem Realistic modeling of heterogeneous data populations with nonparametric mixture components.
method Bayesian nonparametric modeling using Dirichlet process mixture priors.
result Posterior contraction rates for component densities are nearly polynomial, improving over deconvolution methods.
DGMM uses deep layers of Gaussian mixtures for flexible data modeling.
problem Efficiently modeling complex data relationships.
method Deep Gaussian Mixture Models (DGMM) with nested mixtures of linear models and factor models.
result DGMM provides a flexible nonlinear model for data description.
Robust learning mixtures of linear regressions improve robustness.
problem Improving robustness in learning mixtures of linear regressions.
method Connecting mixtures of linear regressions and mixtures of Gaussians with thresholding for a quasi-polynomial time algorithm.
result The algorithm has significantly better robustness than previous results.
Spatially constrained Gaussian mixture models reduce covariance complexity.
problem High dimensionality in finite mixture models for spatial data.
method Spatial covariance constraint with only four free parameters.
result Improves clustering of multi-way spatial data and inference of spatial patterns.
This paper compares EM and GD in two-component mixture models, finding EM escapes bad local optima more reliably.
problem Understanding the convergence of EM and GD in mixture models, especially in regions where one component is missing.
method Analyzing regions called one-cluster regions in two-component mixture models of Gaussians and Bernoullis, comparing the propensity of EM and GD to converge to these regions.
result EM escapes one-cluster regions exponentially fast, while GD escapes them linearly fast, indicating EM is less likely to converge to bad local optima.
A new method detects outliers using ensembles of Dirichlet process mixtures.
problem Challenges in unsupervised outlier detection using Dirichlet process mixtures.
method Ensembles of Dirichlet process Gaussian mixtures with random subspace and subsampling.
result Empirically outperforms existing approaches in unsupervised outlier detection.
The parsimonious Gaussian mixture models, which exploit an eigenvalue decomposition of the group covariance matrices of the Gaussian mixture, have shown their success in particular in cluster analysis. Their estimation is in general performed by maximum likelihood estimation and has also been considered from a parametr…
Information-theoretic measures such as the entropy, cross-entropy and the Kullback-Leibler divergence between two mixture models is a core primitive in many signal processing tasks. Since the Kullback-Leibler divergence of mixtures provably does not admit a closed-form formula, it is in practice either estimated using …
Paper establishes universal lower bounds and optimal rates for clustering sub-exponential mixture models.
problem Achieving optimal error rates in clustering sub-exponential mixture models.
method Establishes universal lower bounds and demonstrates iterative algorithms' optimality in sub-exponential mixture models.
result Iterative algorithms achieve the universal lower bound in sub-exponential mixture models.
New method for summarizing Bayesian mixture models using sliced Wasserstein distances.
problem Estimating the mixing measure in nonparametric Bayesian mixture models.
method Decision-theoretic approach using sliced Wasserstein distances for Gaussian mixtures.
result Effective estimation of the mixing measure and mixture density.
The paper tackles learning mixtures of two multinomial logits, showing identifiability and presenting an algorithm.
problem Learning an arbitrary mixture of two multinomial logits.
method Reduction to solving a system of univariate quartic equations, followed by an algorithm using polynomial and linear samples.
result Identifiability of the mixture models may only fail on an algebraic variety of negligible measure.
Algorithm estimates nonparametric mixtures from grouped data.
problem Estimating identifiable nonparametric mixture models from grouped observations.
method Oracle inequality for weighted kernel density estimators and general consistency result.
result Consistent estimation of mixture components from grouped observations.