As a novel similarity measure that is defined as the expectation of a kernel function between two random variables, correntropy has been successfully applied in robust machine learning and signal processing to combat large outliers. The kernel function in correntropy is usually a zero-mean Gaussian kernel. In a recent …
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48 results for “maximum correntropy”
Correntropy is a local similarity measure defined in kernel space and the maximum correntropy criterion (MCC) has been successfully applied in many areas of signal processing and machine learning in recent years. The kernel function in correntropy is usually restricted to the Gaussian function with center located at ze…
As a robust nonlinear similarity measure in kernel space, correntropy has received increasing attention in domains of machine learning and signal processing. In particular, the maximum correntropy criterion (MCC) has recently been successfully applied in robust regression and filtering. The default kernel function in c…
This paper proposed a bias-compensated normalized maximum correntropy criterion (BCNMCC) algorithm charactered by its low steady-state misalignment for system identification with noisy input in an impulsive output noise environment. The normalized maximum correntropy criterion (NMCC) is derived from a correntropy based…
Robust PCA reduces to power iterations for outlier-resilient feature extraction.
problem Sensitivity of PCA to non-Gaussian samples and outliers.
method Robust formulation of PCA based on maximum correntropy criterion.
result MCPI reduces to power iterations, making PCA more robust to outliers.
Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises, the performance of KF will deteriorate serious…
Enhances robustness of BLS using MCC criterion.
problem Outliers sensitivity in standard BLS.
method Adopting maximum correntropy criterion (MCC) for training output weights.
result C-BLS achieves excellent robustness to outliers.
The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilizing a derivative-free higher-order approximation by approximating a Gaussian distribution rather than approximating a non-linear function. Applying the UT to a Kalman filter type estimat…
The maximum correntropy criterion (MCC) has recently been successfully applied in robust regression, classification and adaptive filtering, where the correntropy is maximized instead of minimizing the well-known mean square error (MSE) to improve the robustness with respect to outliers (or impulsive noises). Considerab…
Constrained adaptive filtering algorithms inculding constrained least mean square (CLMS), constrained affine projection (CAP) and constrained recursive least squares (CRLS) have been extensively studied in many applications. Most existing constrained adaptive filtering algorithms are developed under mean square error (…
Paper studies MCCR models with scale parameters tending to zero, revealing optimal learning rate and comparing robustness.
problem Analyzing MCCR models with scale parameters approaching zero.
method Investigates MCCR models with scale parameters tending to zero, revealing optimal learning rate and comparing robustness.
result Optimal learning rate of MCCR models is in the asymptotic sense.
Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adaptation to combination MCC and combination to adaptation MCC, are developed to deal with the distributed estimation over network in impulsive (long-tailed) noise environments. The cost functions used in distri…
New tensor completion method reduces impact of outliers.
problem Recover tensors from incomplete data with outliers.
method Proposes a new correntropy-based objective function and half-quadratic minimization.
result Demonstrates robust performance with real and synthetic data.
Study improves PM concentration forecasting using MCCR loss.
problem Forecasting particulate matter concentration in South Korea.
method Used MCCR loss for regression analysis of air pollution and weather data.
result MCCR loss is more effective for extreme value forecasting.
A new asymmetric correntropy method improves robust adaptive filtering for asymmetric error distributions.
problem Inadequate handling of asymmetric error distributions in adaptive filtering.
method Proposes asymmetric correntropy using an asymmetric Gaussian kernel and develops a robust adaptive filtering algorithm.
result The proposed algorithm shows better steady-state convergence performance for asymmetric error distributions.
Adaptive sparseness for correntropy-based robust regression via automatic relevance determinationcs.LG
Adaptive sparseness enhances robust regression using MCC and ARD.
problem Developing a robust regression method with adaptive sparseness.
method Integrating MCC with ARD in a Bayesian framework using variational Bayesian inference.
result MCC-ARD regression outperforms existing methods in prediction and feature selection.
In this letter, we propose a method for period estimation in light curves from periodic variable stars using correntropy. Light curves are astronomical time series of stellar brightness over time, and are characterized as being noisy and unevenly sampled. We propose to use slotted time lags in order to estimate corrent…
In recent years, correntropy and its applications in machine learning have been drawing continuous attention owing to its merits in dealing with non-Gaussian noise and outliers. However, theoretical understanding of correntropy, especially in the statistical learning context, is still limited. In this study, within the…
New insights into correntropy-based regression reveal robustness and unified approaches.
problem Learning robust regression functions under additive noise.
method Minimum distance estimation and conditional mean, mode, median functions.
result Unified approach to conditional mean, mode, and median functions.
In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral unmixing approach for hyperspectral images. The robustness is achieved by writi…
Kernel Risk-Sensitive Loss: Definition, Properties and Application to Robust Adaptive Filteringstat.ML
Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher-order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non-Gaussian signal processing and machine learning. In this work, we propose a new similarity me…
Measuring the Discrepancy between Conditional Distributions: Methods, Properties and Applicationscs.LG
A new test statistic measures discrepancy between conditional distributions.
problem Measuring the discrepancy between two conditional distributions.
method Proposes a Bregman matrix divergence-based statistic that avoids explicit distribution estimation.
result The new statistic inherits high-order statistics and demonstrates utility in multi-task learning, concept drift detection, and feature selection.
This paper studies the nonparametric modal regression problem systematically from a statistical learning view. Originally motivated by pursuing a theoretical understanding of the maximum correntropy criterion based regression (MCCR), our study reveals that MCCR with a tending-to-zero scale parameter is essentially moda…
Correntropy is a second order statistical measure in kernel space, which has been successfully applied in robust learning and signal processing. In this paper, we define a nonsecond order statistical measure in kernel space, called the kernel mean-p power error (KMPE), including the correntropic loss (CLoss) as a speci…
Since exchange economy considerably varies in the market assets, asset prices have become an attractive research area for investigating and modeling ambiguous and uncertain information in today markets. This paper proposes a new generative uncertainty mechanism based on the Bayesian Inference and Correntropy (BIC) tech…
Paper proposes robust tensor regression method for tensor data analysis.
problem Outliers in tensor data analysis can make existing methods sensitive.
method Nonconvex relaxation of tensor tubal rank in optimization framework.
result Global convergence of proposed estimation algorithm under mild assumptions.
Paper proposes ConvSCN for robust subspace clustering and classification.
problem Insufficient handling of nonlinear manifolds, data corruptions, and out-of-sample data.
method Self-supervised convolutional subspace clustering network (ConvSCN) with FC layer, CIM for robustness, and BD regularization.
result Robust ConvSCN outperforms baseline on unseen data.
The maximum number of maximum cliques in a graph is determined for graphs with at least 15 vertices.
problem Determining the maximum number of maximum cliques in a graph with n vertices.
method Defining prime and composite graphs, analyzing edge bounds, and using combinatorial arguments.
result For graphs with at least 15 vertices, the graph with the maximum number of maximum cliques is composite.
The paper establishes maximum principles and stochastic completeness for pseudo-Hermitian manifolds.
problem Maximum principles and stochastic completeness for pseudo-Hermitian manifolds.
method Established generalized maximum principles and proved stochastic completeness equivalence.
result Stochastic completeness for the heat semigroup is equivalent to generalized maximum principles.
One of the earliest conjectures in computational learning theory-the Sample Compression conjecture-asserts that concept classes (equivalently set systems) admit compression schemes of size linear in their VC dimension. To-date this statement is known to be true for maximum classes---those that possess maximum cardinali…
The study classifies graphs with specific curvature and maximum degree.
problem Graphs with nonnegative Ricci curvature and maximum degree constraints.
method Classification of graphs with Lin-Lu-Yau-Ollivier Ricci curvature, maximum degree ≤ 3, and diameter ≥ 6.
result Classification of graphs meeting the specified criteria.
A new algorithm learns diverse policies in reinforcement learning.
problem Learning diverse behaviors in reinforcement learning.
method Proposes Maximum Entropy Diverse Exploration (MEDE) algorithm.
result The set of policies learned by MEDE capture the same modalities as the optimal maximum entropy policy.
We find the maximum mutual information for neural networks and its key determinants.
problem Understanding the maximum mutual information in neural architectures.
method Derived closed-form expression for maximum mutual information across neural network families.
result Maximum mutual information stems from a generalized formula and is influenced by network width and statistical invariances.
Establishes a boundary maximum principle for varifolds with fixed contact angle.
problem Boundary behavior of varifolds with contact angle constraints.
method Maximum principle for stationary pairs of varifolds with fixed contact angle condition.
result Boundary maximum principle proven for stationary varifolds.
In this paper we present a proof of a Neumann type maximum principle for the Laplace operator on compact Riemannian manifolds. A key p oint is the simple geometric nature of the constant in the a priori estimate of this maximum principle. In particular, this maximum principle can be applied to manifolds with Ricci curv…
Maximum likelihood estimation fails to be well-posed in Gaussian process regression.
problem Establishing well-posedness of maximum likelihood estimation in Gaussian process regression.
method Analyzing the conditions under which maximum likelihood estimation is not Lipschitz in the data with respect to the Hellinger distance.
result Maximum likelihood estimation is not well-posed in the noiseless data setting for any Gaussian process with a stationary covariance function whose lengthscale parameter is estimated using maximum likelihood.
Note establishes a local maximum principle for Ricci flow under curvature conditions.
problem Preserving nonnegativity of curvature along Ricci flow with unbounded curvature.
method Combining scaling invariant curvature condition with Dirichlet heat kernel estimates.
result Unified and more direct proof of localized maximum principle.
Modeling Maximum drawdown Records with Piecewise Deterministic Markov Processe in Capital Marketsq-fin.RM
Modeling maximum drawdown records in capital markets using PDMP.
problem Capturing the statistical properties of maximum drawdown records in financial markets.
method Piecewise Deterministic Markov Process (PDMP) for modeling, statistical analysis of mean and variance, simulation study, parameter estimation techniques.
result Derivation of statistical results including mean and variance of maximum drawdown records.
We present a new statistical learning paradigm for Boltzmann machines based on a new inference principle we have proposed: the latent maximum entropy principle (LME). LME is different both from Jaynes maximum entropy principle and from standard maximum likelihood estimation.We demonstrate the LME principle BY deriving …
The paper calculates genus bounds for multibranched surfaces.
problem Finding genus bounds for multibranched surfaces.
method Using the first Betti number and boundary genus, the paper provides lower bounds for maximum and minimum genus.
result The maximum and minimum genus of equals twice that of .
Improved text summarization using belief propagation on weighted bipartite graphs.
problem Text summarization from a graph theory perspective.
method Generalized belief propagation algorithm for weighted bipartite graphs.
result Our algorithm outperforms greedy methods in text summarization tasks.
Study proves Maximum Principles for unbounded Riemannian domains.
problem Proving Maximum Principles for unbounded Riemannian domains.
method Examines both ambient manifold and differential operator assumptions.
result Valid Maximum Principles established for unbounded domains.
New maximum score estimators using ReLU functions and deep neural networks.
problem Estimating parameters in models with sign restrictions.
method ReLU-based maximum score criterion and DNN architecture.
result RMS estimator achieves convergence rate and asymptotic normality.
In this paper we characterize the degenerate elliptic equations F(D^2u)=0 whose viscosity subsolutions, (F(D^2u) \geq 0), satisfy the strong maximum principle. We introduce an easily computed function f(t) for t > 0, determined by F, and we show that the strong maximum principle holds depending on whether the integral …
In this work we consider viscosity solutions to second order partial differential equations on Riemannian manifolds. We prove maximum principles for solutions to Dirichlet problem on a compact Riemannian manifold with boundary. Using a different method, we generalize maximum principles of Omori and Yau to a viscosity v…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth and invertible transformation that maps a simple distribution to the desired ma…
This article studies a discrete geometric structure on triangulated manifolds and an associated curvature flow (combinatorial Yamabe flow). The associated evolution of curvature appears to be like a heat equation on graphs, but it can be shown to not satisfy the maximum principle. The notion of a parabolic-like operato…
New graphs with maximum degree 4 found to be Ricci-flat.
problem Characterizing Ricci-flat graphs with maximum degree 4.
method Defined Ricci curvature on graphs and used previous results to find all such graphs.
result All Ricci-flat graphs with maximum degree at most 4 were determined.