In a distributed system, the interactions between agents are usually restricted to follow certain constraints on the flow of information imposed by the network structure. Such information constraints cause the agents to only be able to use locally available information. This contrasts with centralized approaches where all information and computation resources are available at a single location [24, 68, 64, 62]. One traditional problem in decision-making is that of parameter estimation or statistical learning. Given a set of noisy observations coming from a joint distribution one would like to estimate a parameter or distribution that minimizes a certain loss function. For example, Maximum a Posteriori (MAP) or Minimum Least Squared Error (MLSE) estimators fit a parameter to some model of the observations. Both, MAP and MLSE estimators require some form of Bayesian posterior computation based on models that explain the observations for a given parameter. Computation of such a posteriori distributions depends on having exact models about the likelihood of the corresponding observations.

Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large but finite number of loss functions. In this paper, we propose a novel Riemannian extension of the Euclidean stochastic variance reduced gradient algorithm (R-SVRG) to a manifold search space. The key challenges of averaging, adding, and subtracting multiple gradients are addressed with retraction and vector transport. We present a global convergence analysis of the proposed algorithm with a decay step size and a local convergence rate analysis under a fixed step size under some natural assumptions. The proposed algorithm is applied to problems on the Grassmann manifold, such as principal component analysis, low-rank matrix completion, and computation of the Karcher mean of subspaces, and outperforms the standard Riemannian stochastic gradient descent algorithm in each case.

Many machine learning applications are based on data collected from people, such as their tastes and behaviour as well as biological traits and genetic data. Regardless of how important the application might be, one has to make sure individuals' identities or the privacy of the data are not compromised in the analysis. Differential privacy constitutes a powerful framework that prevents breaching of data subject privacy from the output of a computation. Differentially private versions of many important Bayesian inference methods have been proposed, but there is a lack of an efficient unified approach applicable to arbitrary models. In this contribution, we propose a differentially private variational inference method with a very wide applicability. It is built on top of doubly stochastic variational inference, a recent advance which provides a variational solution to a large class of models. We add differential privacy into doubly stochastic variational inference by clipping and perturbing the gradients. The algorithm is made more efficient through privacy amplification from subsampling. We demonstrate the method can reach an accuracy close to non-private level under reasonably strong privacy guarantees, clearly improving over previous sampling-based alternatives especially in the strong privacy regime.

Machine Learning (ML) algorithms, like Convolutional Neural Networks (CNN), Support Vector Machines (SVM), etc. have become widespread and can achieve high statistical performance. However their accuracy decreases significantly in energy-constrained mobile and embedded systems space, where all computations need to be completed under a tight energy budget. In this work, we present a field of groves (FoG) implementation of random forests (RF) that achieves an accuracy comparable to CNNs and SVMs under tight energy budgets. Evaluation of the FoG shows that at comparable accuracy it consumes ~1.48x, ~24x, ~2.5x, and ~34.7x lower energy per classification compared to conventional RF, SVM_RBF , MLP, and CNN, respectively. FoG is ~6.5x less energy efficient than SVM_LR, but achieves 18% higher accuracy on average across all considered datasets.

Matching datasets of multiple modalities has become an important task in data analysis. Existing methods often rely on the embedding and transformation of each single modality without utilizing any correspondence information, which often results in sub-optimal matching performance. In this paper, we propose a nonlinear manifold matching algorithm using shortest-path distance and joint neighborhood selection. Specifically, a joint nearest-neighbor graph is built for all modalities. Then the shortest-path distance within each modality is calculated from the joint neighborhood graph, followed by embedding into and matching in a common low-dimensional Euclidean space. Compared to existing algorithms, our approach exhibits superior performance for matching disparate datasets of multiple modalities.

Improving the precision of heart diseases detection has been investigated by many researchers in the literature. Such improvement induced by the overwhelming health care expenditures and erroneous diagnosis. As a result, various methodologies have been proposed to analyze the disease factors aiming to decrease the physicians practice variation and reduce medical costs and errors. In this paper, our main motivation is to develop an effective intelligent medical decision support system based on data mining techniques. In this context, five data mining classifying algorithms, with large datasets, have been utilized to assess and analyze the risk factors statistically related to heart diseases in order to compare the performance of the implemented classifiers (e.g., Na\"ive Bayes, Decision Tree, Discriminant, Random Forest, and Support Vector Machine). To underscore the practical viability of our approach, the selected classifiers have been implemented using MATLAB tool with two datasets. Results of the conducted experiments showed that all classification algorithms are predictive and can give relatively correct answer. However, the decision tree outperforms other classifiers with an accuracy rate of 99.0% followed by Random forest. That is the case because both of them have relatively same mechanism but the Random forest can build ensemble of decision tree. Although ensemble learning has been proved to produce superior results, but in our case the decision tree has outperformed its ensemble version.

First, let's set things up in R by loading the necessary package and importing the data into R. the class package will be used to run the k-nearest neighbors algorithm. We will also use a specific seed so that you can reproduce this in R yourself. Importing the data, let's take a look at the basic structure of the dataset. The first variable, id, is there simply as a unique identifier for each observation. We will take it out for the purposes of our analysis.

Graphical causal models are an important tool for knowledge discovery because they can represent both the causal relations between variables and the multivariate probability distributions over the data. Once learned, causal graphs can be used for classification, feature selection and hypothesis generation, while revealing the underlying causal network structure and thus allowing for arbitrary likelihood queries over the data. However, current algorithms for learning sparse directed graphs are generally designed to handle only one type of data (continuous-only or discrete-only), which limits their applicability to a large class of multi-modal biological datasets that include mixed type variables. To address this issue, we developed new methods that modify and combine existing methods for finding undirected graphs with methods for finding directed graphs. These hybrid methods are not only faster, but also perform better than the directed graph estimation methods alone for a variety of parameter settings and data set sizes. Here, we describe a new conditional independence test for learning directed graphs over mixed data types and we compare performances of different graph learning strategies on synthetic data.

The classification of multivariate functional data is an important task in scientific research. Unlike point-wise data, functional data are usually classified by their shapes rather than by their scales. We define an outlyingness matrix by extending directional outlyingness, an effective measure of the shape variation of curves that combines the direction of outlyingness with conventional depth. We propose two classifiers based on directional outlyingness and the outlyingness matrix, respectively. Our classifiers provide better performance compared with existing depth-based classifiers when applied on both univariate and multivariate functional data from simulation studies. We also test our methods on two data problems: speech recognition and gesture classification, and obtain results that are consistent with the findings from the simulated data.

Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite, number of loss functions. In this paper, we propose a novel Riemannian extension of the Euclidean stochastic variance reduced gradient algorithm (R-SVRG) to a compact manifold search space. To this end, we show the developments on the Grassmann manifold. The key challenges of averaging, addition, and subtraction of multiple gradients are addressed with notions like logarithm mapping and parallel translation of vectors on the Grassmann manifold. We present a global convergence analysis of the proposed algorithm with decay step-sizes and a local convergence rate analysis under fixed step-size with some natural assumptions. The proposed algorithm is applied on a number of problems on the Grassmann manifold like principal components analysis, low-rank matrix completion, and the Karcher mean computation. In all these cases, the proposed algorithm outperforms the standard Riemannian stochastic gradient descent algorithm.