We study the community detection problem on a Gaussian mixture model, in which vertices are divided into $k\geq 2$ distinct communities. The major difference in our model is that the intensities for Gaussian perturbations are different for different entries in the observation matrix, and we do not assume that every community has the same number of vertices. We explicitly find the threshold for the exact recovery of the maximum likelihood estimation. Applications include the community detection on hypergraphs.

Recently, the surge in popularity of Internet of Things (IoT), mobile devices, social media, etc. has opened up a large source for graph data. Graph embedding has been proved extremely useful to learn low-dimensional feature representations from graph structured data. These feature representations can be used for a variety of prediction tasks from node classification to link prediction. However, existing graph embedding methods do not consider users' privacy to prevent inference attacks. That is, adversaries can infer users' sensitive information by analyzing node representations learned from graph embedding algorithms. In this paper, we propose Adversarial Privacy Graph Embedding (APGE), a graph adversarial training framework that integrates the disentangling and purging mechanisms to remove users' private information from learned node representations. The proposed method preserves the structural information and utility attributes of a graph while concealing users' private attributes from inference attacks. Extensive experiments on real-world graph datasets demonstrate the superior performance of APGE compared to the state-of-the-arts. Our source code can be found at https://github.com/uJ62JHD/Privacy-Preserving-Social-Network-Embedding.

Federated learning platforms are gaining popularity. One of the major benefits is to mitigate the privacy risks as the learning of algorithms can be achieved without collecting or sharing data. While federated learning (i.e., many based on stochastic gradient algorithms) has shown great promise, there are still many challenging problems in protecting privacy, especially during the process of gradients update and exchange. This paper presents the first gradient-free federated learning framework called GRAFFL for learning a Bayesian generative model based on approximate Bayesian computation. Unlike conventional federated learning algorithms based on gradients, our framework does not require to disassemble a model (i.e., to linear components) or to perturb data (or encryption of data for aggregation) to preserve privacy. Instead, this framework uses implicit information derived from each participating institution to learn posterior distributions of parameters. The implicit information is summary statistics derived from SuffiAE that is a neural network developed in this study to create compressed and linearly separable representations thereby protecting sensitive information from leakage. As a sufficient dimensionality reduction technique, this is proved to provide sufficient summary statistics. We propose the GRAFFL-based Bayesian Gaussian mixture model to serve as a proof-of-concept of the framework. Using several datasets, we demonstrated the feasibility and usefulness of our model in terms of privacy protection and prediction performance (i.e., close to an ideal setting). The trained model as a quasi-global model can generate informative samples involving information from other institutions and enhances data analysis of each institution.

For a learning task, Gaussian process (GP) is interested in learning the statistical relationship between inputs and outputs, since it offers not only the prediction mean but also the associated variability. The vanilla GP however struggles to learn complicated distribution with the property of, e.g., heteroscedastic noise, multi-modality and non-stationarity, from massive data due to the Gaussian marginal and the cubic complexity. To this end, this article studies new scalable GP paradigms including the non-stationary heteroscedastic GP, the mixture of GPs and the latent GP, which introduce additional latent variables to modulate the outputs or inputs in order to learn richer, non-Gaussian statistical representation. We further resort to different variational inference strategies to arrive at analytical or tighter evidence lower bounds (ELBOs) of the marginal likelihood for efficient and effective model training. Extensive numerical experiments against state-of-the-art GP and neural network (NN) counterparts on various tasks verify the superiority of these scalable modulated GPs, especially the scalable latent GP, for learning diverse data distributions.

Relevance Feedback in Content-Based Image Retrieval is a method where the feedback of the performance is being used to improve itself. Prior works use feature re-weighting and classification techniques as the Relevance Feedback methods. This paper shows a novel addition to the prior methods to further improve the retrieval accuracy. In addition to all of these, the paper also shows a novel idea to even improve the 0-th iteration retrieval accuracy from the information of Relevance Feedback.

This is one of the most fascinating ideas in Linear Algebra. By multiplying a matrix to a vector, we linearly transform that vector. If you feel like your grip on basic linear algebra is a little loose, I strongly recommend that you watch 3b1b's series on Linear Algebra. A non-trivial vector whose span doesn't change upon being multiplied by a matrix is an eigenvector of that matrix. Now, let me clarify two things here- firstly, the span loosely means the direction of that vector and secondly, although the direction doesn't change, the magnitude can. How stretched or squished the eigenvector becomes i.e. the factor by which the magnitude changes upon multiplication is called the eigenvalue of that eigenvector.

The main purpose of this post is to explore the different ways in which Logistic Regression can be applied to the dataset and hence understanding how the model actually works. The idea is not to solve the problem itself. This post doesn't focus on getting best score using different models however it assumes that there's only one model available for use. This is part of the series of posts to learn and share the details of Logistic Regression. If you're new to this kindly refer my earlier posts on the same topic: The data set has different features like Demographics, Behavioural which includes current smoker, cigarettes per day and Medical history and our task is to predict if the person has 10 year risk of coronary heart disease.

Online display advertising is growing rapidly in recent years thanks to the automation of the ad buying process. Real-time bidding (RTB) allows the automated trading of ad impressions between advertisers and publishers through real-time auctions. In order to increase the effectiveness of their campaigns, advertisers should deliver ads to the users who are highly likely to be converted (i.e., purchase, registration, website visit, etc.) in the near future. In this study, we introduce and examine different models for estimating the probability of a user converting, given their history of visited URLs. Inspired by natural language processing, we introduce three URL embedding models to compute semantically meaningful URL representations. To demonstrate the effectiveness of the different proposed representation and conversion prediction models, we have conducted experiments on real logged events collected from an advertising platform.

Low level classification extracts features from the elements, i.e. physical to use them to train a model for a later classification. High level classification uses high level features, the existent patterns, relationship between the data and combines low and high level features for classification. High Level features can be got from Complex Network created over the data. Local and global features are used to describe the structure of a Complex Network, i.e. Average Neighbor Degree, Average Clustering.The present work proposed a novel feature to describe the architecture of the Network following a Ant Colony System approach. The experiments shows the advantage of using this feature because the sensibility with data of different classes.

The p-tensor Ising model is a one-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic is a multi-linear form of degree p 2. This is a natural generalization of the matrix Ising model, that provides a convenient mathematical framework for capturing, not just pairwise, but higher-order dependencies in complex relational data. In this paper, we consider the problem of estimating the natural parameter of the p-tensor Ising model given a single sample from the distribution on N nodes. Our estimate is based on the maximum pseudo-likelihood (MPL) method, which provides a computationally efficient algorithm for estimating the parameter that avoids computing the intractable partition function. We derive general conditions under which the MPL estimate is N-consistent, that is, it converges to the true parameter at rate 1/ N. Our conditions are robust enough to handle a variety of commonly used tensor Ising models, including spin glass models with random interactions and models where the rate of estimation undergoes a phase transition. In particular, this includes results on N-consistency of the MPL estimate in the well-known p-spin Sherrington-Kirkpatrick (SK) model, spin systems on general p-uniform hypergraphs, and Ising models on the hypergraph stochastic block model (HSBM). In fact, for the HSBM we pin down the exact location of the phase transition threshold, which is determined by the positivity of a certain mean-field variational problem, such that above this threshold the MPL estimate is N-consistent, while below the threshold no estimator is consistent. Finally, we derive the precise fluctuations of the MPL estimate in the special case of the p-tensor Curie-Weiss model, which is the Ising model on the complete p-uniform hypergraph. An interesting consequence of our results is that the MPL estimate in the Curie-Weiss model saturates the Cramer-Rao lower bound at all points above the estimation threshold, that is, the MPL estimate incurs no loss in asymptotic statistical efficiency in the estimability regime, even though it is obtained by minimizing only an approximation of the true likelihood function for computational tractability.