85 research outputs found
Measuring the Discrepancy between Conditional Distributions: Methods, Properties and Applications
We propose a simple yet powerful test statistic to quantify the discrepancy
between two conditional distributions. The new statistic avoids the explicit
estimation of the underlying distributions in highdimensional space and it
operates on the cone of symmetric positive semidefinite (SPS) matrix using the
Bregman matrix divergence. Moreover, it inherits the merits of the correntropy
function to explicitly incorporate high-order statistics in the data. We
present the properties of our new statistic and illustrate its connections to
prior art. We finally show the applications of our new statistic on three
different machine learning problems, namely the multi-task learning over
graphs, the concept drift detection, and the information-theoretic feature
selection, to demonstrate its utility and advantage. Code of our statistic is
available at https://bit.ly/BregmanCorrentropy.Comment: manuscript accepted at IJCAI 20; added additional notes on
computational complexity and auto-differentiable property; code is available
at https://github.com/SJYuCNEL/Bregman-Correntropy-Conditional-Divergenc
Robust Adaptive Generalized Correntropy-based Smoothed Graph Signal Recovery with a Kernel Width Learning
This paper proposes a robust adaptive algorithm for smooth graph signal
recovery which is based on generalized correntropy. A proper cost function is
defined for this purpose. The proposed algorithm is derived and a kernel width
learning-based version of the algorithm is suggested which the simulation
results show the superiority of it to the fixed correntropy kernel version of
the algorithm. Moreover, some theoretical analysis of the proposed algorithm
are provided. In this regard, firstly, the convexity analysis of the cost
function is discussed. Secondly, the uniform stability of the algorithm is
investigated. Thirdly, the mean convergence analysis is also added. Finally,
the complexity analysis of the algorithm is incorporated. In addition, some
synthetic and real-world experiments show the advantage of the proposed
algorithm in comparison to some other adaptive algorithms in the literature of
adaptive graph signal recovery
Proportionate Recursive Maximum Correntropy Criterion Adaptive Filtering Algorithms and their Performance Analysis
The maximum correntropy criterion (MCC) has been employed to design
outlier-robust adaptive filtering algorithms, among which the recursive MCC
(RMCC) algorithm is a typical one. Motivated by the success of our recently
proposed proportionate recursive least squares (PRLS) algorithm for sparse
system identification, we propose to introduce the proportionate updating (PU)
mechanism into the RMCC, leading to two sparsity-aware RMCC algorithms: the
proportionate recursive MCC (PRMCC) algorithm and the combinational PRMCC
(CPRMCC) algorithm. The CPRMCC is implemented as an adaptive convex combination
of two PRMCC filters. For PRMCC, its stability condition and mean-square
performance were analyzed. Based on the analysis, optimal parameter selection
in nonstationary environments was obtained. Performance study of CPRMCC was
also provided and showed that the CPRMCC performs at least as well as the
better component PRMCC filter in steady state. Numerical simulations of sparse
system identification corroborate the advantage of proposed algorithms as well
as the validity of theoretical analysis
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