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Abstract-Constrained adaptive filtering algorithms including 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 the mean square error (MSE) criterion, which is an ideal optimality criterion under Gaussian noises. This assumption however fails to model the behavior of non-Gaussian noises found in practice. Motivated by the robustness and simplicity of maximum correntropy criterion (MCC) for non-Gaussian impulsive noises, this paper proposes a new adaptive filtering algorithm called constrained maximum correntropy criterion (CMCC). Specifically, CMCC incorporates a linear constraint into a MCC filter to solve a constrained optimization problem explicitly. The proposed adaptive filtering algorithm is easy to implement and has low computational complexity, and in terms of convergence accuracy (say lower mean square deviation) and stability, it can significantly outperform those MSE based constrained adaptive algorithms in presence of heavy-tailed impulsive noises. Additionally, the mean square convergence behaviors are studied under energy conservation relation, and a sufficient condition to ensure the mean square convergence and the steady-state mean square deviation (MSD) of the proposed algorithm are obtained. Simulation results confirm the theoretical predictions under both Gaussian and non-Gaussian noises, and demonstrate the excellent performance of the novel algorithm by comparing it with other conventional methods.

Using housing market data of Beijing and Hangzhou, China, we conduct a case study to detect how the difference of urban structure can affect the relationship between the subway system and housing prices. To quantify the characteristics of urban structure, we propose a constrained clustering method, which can not only reveal the spatial heterogeneity of the housing market, but also provides a link between heterogeneity and the underlying urban structure. Applying constrained clustering to Beijing and Hangzhou, we find that the relationship between accessibility to metro stations and housing prices is weak and vulnerable, while the improvement of commuting efficiency, measured by a key variable, the metro index, does have a robust connection to metro premium on housing units. In particular, only a large metro index can be associated with a positive metro premium. Structural features, such as the size of urban core and the existence of multiple sub-centers, influence the metro premium by affecting the value and spatial distribution of the metro index. The evidence from Beijing and Hangzhou supports that in a mono-centric city, the size of the urban core is positively associated with the metro index and the metro premium, while in a poly-centric city with a small urban core, the metro index tends to be lower in the core region and higher in the satellite regions, which enforces the metro premium to be negative in the core while positive outside of the core.

Learning causal effects from observational data greatly benefits a variety of domains such as health care, education, and sociology. For instance, one could estimate the impact of a new drug on specific individuals to assist clinical planning and improve the survival rate. In this paper, we focus on studying the problem of estimating the Conditional Average Treatment Effect (CATE) from observational data. The challenges for this problem are two-fold: on the one hand, we have to derive a causal estimator to estimate the causal quantity from observational data, in the presence of confounding bias; on the other hand, we have to deal with the identification of the CATE when the distributions of covariates over the treatment group units and the control units are imbalanced. To overcome these challenges, we propose a neural network framework called Adversarial Balancing-based representation learning for Causal Effect Inference (ABCEI), based on recent advances in representation learning. To ensure the identification of the CATE, ABCEI uses adversarial learning to balance the distributions of covariates in the treatment and the control group in the latent representation space, without any assumptions on the form of the treatment selection/assignment function. In addition, during the representation learning and balancing process, highly predictive information from the original covariate space might be lost. ABCEI can tackle this information loss problem by preserving useful information for predicting causal effects under the regularization of a mutual information estimator. The experimental results show that ABCEI is robust against treatment selection bias, and matches/outperforms the state-of-the-art approaches. Our experiments show promising results on several datasets, encompassing several health care (and other) domains.

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In this paper, we first investigate into six popular entropies extracted from a set of intrinsic mode functions (IMFs) as a feature pattern for radar-based mini-size unmanned aerial vehicles (mini-UAV) classification. The six entropies include Shannon entropy, spectral entropy, log energy entropy, approximate entropy, fuzzy entropy and permutation entropy. Via an empirical comparison among the six entropies on real measurement radar data, the first three are selected as the representative due to their high efficiency and accuracy. To enhance the classification accuracy, the three selected entropies are then extracted from eight different sets of IMFs obtained by signal downsampling, and then fused at feature level. The nonlinear support vector machine classifier is adopted to predict the class label of unseen test radar signals. Our empirical results on a set of real-world continuous wave radar data show that the proposed method outperforms the state-of-the-art method in terms of the mini-UAV classification accuracy.

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