The protection of private data is a hot research issue in the era of big data. Differential privacy is a strong privacy guarantees in data analysis. In this paper, we propose DP-MSNM, a parametric density estimation algorithm using multivariate skew-normal mixtures (MSNM) model to differential privacy. MSNM can solve the asymmetric problem of data sets, and it is could approximate any distribution through expectation–maximization (EM) algorithm. In this model, we add two extra steps on the estimated parameters in the M step of each iteration. The first step is adding calibrated noise to the estimated parameters based on Laplacian mechanism. The second step is post-processes those noisy parameters to ensure their intrinsic characteristics based on the theory of vector normalize and positive semi definition matrix. Extensive experiments using both real data sets evaluate the performance of DP-MSNM, and demonstrate that the proposed method outperforms DPGMM.

Multi-center heterogeneous data are a hot topic in federated learning. The data of clients and centers do not follow a normal distribution, posing significant challenges to learning. Based on the assumption that the client data have a multivariate skewed normal distribution, we improve the DP-Fed-mv-PPCA model. We use a Bayesian framework to construct prior distributions of local parameters and use expectation maximization and pseudo-Newton algorithms to obtain robust parameter estimates. Then, the clipping algorithm and differential privacy algorithm are used to solve the problem in which the model parameters do not have a display solution and achieve privacy guarantee. Furthermore, we verified the effectiveness of our model using synthetic and actual data from the Internet of vehicles.

Image segmentation technology has been widely used in various business and social fields. In recent years, more and more scholars have studied the theories in this field. Many models and methods have good effects in image segmentation. However, as people's demand for image is getting higher and higher, people often face images with complex structure and multimode, which makes us need to study and analyze the theory of image segmentation more deeply. In this paper, we study the Rényi entropy and Shannon entropy of finite multivariate skew t mixture distribution (this distribution was proposed based on Sahu and Branco (2003; https://doi.org/10.2307/3316064), and it has better properties and wider application range than the traditional skew t distribution). In addition to the specific calculation results of the two kinds of entropy, we use Hölder inequality and polynomial theorem to obtain the upper bound and lower bound of the two kinds of entropy of finite multivariate skew t mixture distribution.

Multi-center heterogeneous data is a hot issue in federated learning nowadays. The data of clients and centers do not follow the normal distribution, which brings great challenges to learning. Based on the assumption that the client data with multivariate skewed normal distribution, we improve the DP-Fed-mv-PPCA model. We use a Bayesian framework to construct prior distributions of local parameters, and use Expectation Maximization (EM) algorithm and pseudo-Newton algorithm to obtain robust estimates of parameters. Then, the clipping algorithm and Differential Privacy (DP) algorithm are used to solve the problem that the model parameters do not have the display solution and achieve the privacy guarantee.