We consider the topic of multivariate regression on manifold-valued output, that is, for a multivariate observation, its output response lies on a manifold. Moreover, we propose a new regression model to deal with the presence of grossly corrupted manifold-valued responses, a bottleneck issue commonly encountered in pr…
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48 results for “Gross corruption”
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.
Paper shows how to use geometric median for robust SGD in high dimensions.
problem Robustifying SGD for high-dimensional optimization problems with gross corruption.
method Applying geometric median to only chosen blocks of coordinates at a time.
result Retains optimal breakdown point of 0.5 for smooth non-convex problems.
We inspect a possible clustering structure of the corruption perception among 134 countries. Using the average linkage clustering, we uncover a well-defined hierarchy in the relationships among countries. Four main clusters are identified and they suggest that countries worldwide can be quite well separated according t…
In order to investigate whether government regulations against corruption can affect the economic growth of a country, we analyze the dependence between Gross Domestic Product (GDP) per capita growth rates and changes in the Corruption Perceptions Index (CPI). For the period 1999-2004 on average for all countries in th…
Robust PCA method optimizes low-rank matrices with corrupted data.
problem Recover a low-rank matrix from grossly corrupted observations.
method Nonconvex optimization on the manifold of low-rank matrices, using manifold optimization algorithms.
result Proposed algorithms converge to the underlying low-rank matrix linearly with proper initialization.
Truncated CauchyNMF robustly learns subspaces from noisy data.
problem Outliers in non-negative matrix factorization (NMF) cause failure.
method Proposes Truncated CauchyNMF loss to handle outliers.
result Theoretical analysis and experimental validation show Truncated CauchyNMF's robustness.
PCA is a classical statistical technique whose simplicity and maturity has seen it find widespread use as an anomaly detection technique. However, it is limited in this regard by being sensitive to gross perturbations of the input, and by seeking a linear subspace that captures normal behaviour. The first issue has bee…
Develops a two-stage approach for robust tensor completion of visual data.
problem Estimating missing values in high-order data with outliers.
method Coarse-to-fine framework and M-estimator-based robust tensor ring recovery.
result Superior performance compared to state-of-the-art robust algorithms.
Paper develops a method to robustly cluster tensors with outliers.
problem Clustering tensors contaminated by outliers or sample-specific corruptions.
method Transformed Tensor Low-Rank Representation (OR-TLRR) method.
result Provably recovers row space of clean data and detects outliers.
Scalable and robust TR decomposition for large-scale data with missing entries and outliers.
problem Handling large-scale tensor data with missing entries and outliers.
method Auto-weighted steepest descent method for missing entries and outliers identification, FGMC and RStS strategies.
result Outperforms existing TR decomposition methods in the presence of outliers and runs faster than robust tensor completion algorithms.
GroSS enables efficient search for grouped convolutional architectures.
problem Training grouped convolutional architectures efficiently and effectively.
method GroSS: Group-Size Series Decomposition for Grouped Architecture Search.
result Simultaneous training of differing numbers of groups within a single layer and all possible combinations between layers.
Summarizes geometric connections between sigma models and Gross-Neveu models.
problem Understanding geometric connections between sigma models and Gross-Neveu models.
method Geometric facts and connections to nilpotent orbits, Springer resolutions, and quiver varieties.
result Sheds light on the general setup of the correspondence.
Sigma models linked to Gross-Neveu models via quiver varieties.
problem Understanding the relationship between sigma models and Gross-Neveu models.
method Exploring the mathematical correspondence between sigma models and Gross-Neveu models, including their geometric and trigonometric/elliptic deformations.
result Sigma models are mathematically equivalent to Gross-Neveu models under certain conditions.
Grassmannian sigma models extend Gross-Neveu model formulations.
problem Understanding sigma models on Grassmannian targets.
method Chiral Gross-Neveu model formulations for orthogonal and symplectic Grassmannians.
result One-loop -functions proportional to dual Coxeter numbers.
Reformulated sigma models for complex Grassmannians using Gross-Neveu formalism.
problem Classical aspects of supersymmetric sigma models with Hermitian symmetric target spaces.
method Reformulation using Gross-Neveu formalism, proposing two types of equivalent Lagrangians.
result Proposed two types of equivalent Lagrangians for maximal isotropic Grassmannians, making either supersymmetry or geometry manifest.
Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning, the current methods of choice are arguably K-SVD and its variants, which learn a …
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient ascent (a variant of the tensor power method), and hard thresholding of the resid…
Paper proves BGW tau-function can be represented as Q-polynomials.
problem Enumerative geometric interpretations of BGW tau-function.
method Proves BGW tau-functions are hypergeometric tau functions of BKP hierarchy.
result Original BGW tau-function can be represented as a linear combination of Schur Q-polynomials.
Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study the problem of robust low-rank tensor recovery in a convex optimization framework,…
Study finds multiple solutions for Gross-Pitaevskii equations on curved spaces.
problem Finding multiple solutions for Gross-Pitaevskii equations on Riemannian manifolds.
method Critical point theory and Γ-convergence for Ginzburg-Landau functionals, plus new isoperimetric results.
result Lower bounds on the multiplicity of solutions in terms of the topology of the velocity set.
I studied what role the US stock markets and money markets have possibly played in the Gross Private Domestic Investment (GPDI) of the United States from the year 1959 to the year 2001, Gross Private Domestic Investment refers to the total amount of investment spending by businesses and firms located within the borders…
This paper proposed a new regression model called -regularized outlier isolation and regression (LOIRE) and a fast algorithm based on block coordinate descent to solve this model. Besides, assuming outliers are gross errors following a Bernoulli process, this paper also presented a Bernoulli estimate model which, …
Tax systems ensure sustainable economic development by adjusting production technologies and gross output volumes.
problem Ensuring sustainable economic development through optimal tax systems.
method Explicit formulas and mathematical proofs for tax systems based on production technologies and gross output volumes.
result The vector of gross output must belong to the interior of the cone formed by the columns of the total cost matrix under perfect taxation systems.
Study of quantum aspects of generalized Gross-Neveu models, focusing on sigma models.
problem Quantum aspects and anomalies in generalized Gross-Neveu models.
method Admissible gauge , study of chiral anomalies, integration over moduli spaces of connections on a Riemann surface.
result Integration over moduli spaces of connections on a Riemann surface.
Paper improves robust PCA for noisy, outlier, and missing data.
problem Robust PCA with noise, outliers, and missing data.
method Bridging convex and nonconvex optimization.
result Near-optimal statistical accuracy for robust PCA.
RKCA combines sparse dictionary learning and robust component analysis for robust low-rank modeling.
problem Learning robust low-rank representations from noisy data.
method Kronecker-decomposable component analysis (RKCA) with efficient learning algorithm.
result RKCA achieves robustness to gross corruption and low-rank modeling.
This study considers a model of the income distribution of agents whose pairwise interaction is asymmetric and price-invariant. Asymmetric transactions are typical for chain-trading groups who arrange their business such that commodities move from senior to junior partners and money moves in the opposite direction. The…
Torus quantum vortex knots in the Gross-Pitaevskii model for Bose-Einstein condensatescond-mat.quant-gas
We examine on the static and dynamical properties of quantum knots in a Bose-Einstein condensate. In particular, we consider the Gross-Pitaevskii model and revise a technique to construct ab initio the condensate wave-function of a generic torus knot. After analysing its excitation energy, we study its dynamics relatin…
Average Oracle outperforms DCC+NLS in portfolio optimization.
problem Optimizing portfolio performance in volatile markets.
method Comparing the Average Oracle to various DCC+NLS variants.
result The Average Oracle consistently yields higher Sharpe ratios.
Quantum flag manifold σ-models are integrable and satisfy Ricci flow equations.
problem Integrating quantum flag manifold σ-models with fermions.
method Gauging bosonic Thirring/Gross-Neveu-type systems, adding fermions to cancel anomalies, and checking Ricci flow equations.
result Trigonometrically deformed geometries of flag manifold σ-models satisfy generalized Ricci flow equations.
Develops a comprehensive theory of corruption in supervised learning.
problem Widespread corruption in data collection affects supervised learning problems.
method Introduces a general theory of corruption using Markov kernels, distinguishing and comparing corruption types.
result Establishes a unified framework for corruption types and develops mitigation strategies.
Counterexamples to a conjecture on ribbon graph genus changes were found and proven.
problem A conjecture on genus changes in ribbon graphs was formulated and disproven.
method A family of counterexamples was found and proven.
result Essentially, the counterexamples found by Qi Yan and Xian'an Jin are the only ones.
Predicting movie box office success using historical data and modern computing.
problem Manual prediction of movie revenue is difficult due to many exogenous variables.
method Use modern computing power and historical data to model movie revenue.
result Predicted movie revenues can be used for planning production and distribution stages.
New algorithm robust to label corruptions in active learning.
problem Active learning under unknown adversarial label corruptions.
method Proposed a new active learning algorithm that is provably correct without assumptions on corruptions.
result Achieves minimax label complexity in non-corrupted setting and only requires additional labels to achieve desired accuracy in corrupted setting.
Study finds corruption negatively impacts firm performance.
problem The impact of corruption on firm performance is examined.
method Cross-sectional data analysis of a large international dataset.
result Corruption negatively affects corporate performance.
Study shows asymptotic behavior of metric near singular points of a Monge-Ampère equation.
problem Analyzing singularities of a metric defined by a Monge-Ampère equation.
method Using the tropical Monge-Ampère equation and asymptotic analysis.
result The solution is not across singular points and asymptotic to the Gross-Wilson metric.
Study improves image classifier robustness to random p-norm corruptions.
problem Improving robustness of image classifiers to real-world imperceptible corruptions.
method Training and testing with random p-norm corruptions, evaluating robustness against different p-norms.
result Training with a combination of p-norm corruptions significantly improves robustness.
New algorithm for linear optimization with adaptive corruption.
problem Stochastic linear optimization under adversarial corruption.
method Algorithm uses Löwner-John's ellipsoid for exploration and divides time into epochs.
result Regret increases linearly with corruption amount.
Unified framework for corruption-robust linear bandits with optimal gap-dependent misspecification bounds.
problem Effective learning in linear bandits with corrupted rewards across different corruption models.
method Unified framework for analyzing strong and weak corruption, connection to gap-dependent misspecification, and specialized algorithm.
result Optimal bounds for gap-dependent misspecification in linear bandits.
Detects spiky corruption in CRMDPs to learn optimal policies.
problem Learning optimal policies in environments with imperfect reward functions.
method Characterized spiky reward corruption, introduced algorithm to detect corrupt states.
result Algorithm can detect corrupt states and learn optimal policies.
We report quantitative relations between corruption level and economic factors, such as country wealth and foreign investment per capita, which are characterized by a power law spanning multiple scales of wealth and investments per capita. These relations hold for diverse countries, and also remain stable over differen…
Subtract the Corruption: Training-Data-Free Corrective Machine Unlearning using Task Arithmeticcs.LG
CUTS removes corruption from models without clean data, improving utility and security.
problem Removing corruption from models without access to clean training data.
method CUTS uses a proxy set to amplify corruption and subtract it from model weights.
result CUTS recovers a large fraction of lost utility and nearly eliminates attacks with minimal damage.
Study robust estimation under varying corruption probabilities in data.
problem Robust estimation in scenarios with heterogeneous corruption rates.
method Developed estimators for mean and regression under various corruption patterns.
result Optimal estimators can discard corrupted samples beyond a specific threshold.
Network science reveals corruption risk in EU procurement markets.
problem Identifying corruption risk in EU procurement markets.
method Analyzing a large dataset of public procurement contracts using network science.
result Corruption risk is clustered and varies by country, not just by market core or periphery.
Paper models corruption in contract negotiations between agents and producers.
problem Formalizing corruption in contract negotiations between agents and producers.
method Mathematical model and economic analysis for three producers, one agent, and one intermediary.
result Optimal non-corruption schemes of financial resources distribution are proposed.
Binary classification improves with a small fraction of corrupted labels.
problem Binary classification with corrupted labels.
method Established corruption as a form of regularization and computed upper bounds on estimation error.
result Corruption is beneficial only up to a small fraction of the total sample, scaling with the square root of the sample size.
We study the problem of corrupted sensing, a generalization of compressed sensing in which one aims to recover a signal from a collection of corrupted or unreliable measurements. While an arbitrary signal cannot be recovered in the face of arbitrary corruption, tractable recovery is possible when both signal and corrup…