Distributed Computation of Generalized One-Sided Concept Lattices on Sparse Data Tables

In this paper we present the study on the usage of distributed version of the algorithm for generalized one-sided concept lattices (GOSCL), which provides a special case for fuzzy version of data analysis approach called formal concept analysis (FCA). The methods of this type create the conceptual model of the input data based on the theory of concept lattices and were successfully applied in several domains. GOSCL is able to create one-sided concept lattices for data tables with different attribute types processed as fuzzy sets. One of the problems with the creation of FCA-based models is their computational complexity. In order to reduce the computation times, we have designed the distributed version of the algorithm for GOSCL. The algorithm is able to work well especially for data where the number of newly generated concepts is reduced, i.e., for sparse input data tables which are often used in domains like text-mining and information retrieval. Therefore, we present the experimental results on sparse data tables in order to show the applicability of the algorithm on the generated data and the selected text-mining datasets

Approximate inference in Gaussian graphical models

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 161-169).The focus of this thesis is approximate inference in Gaussian graphical models. A graphical model is a family of probability distributions in which the structure of interactions among the random variables is captured by a graph. Graphical models have become a powerful tool to describe complex high-dimensional systems specified through local interactions. While such models are extremely rich and can represent a diverse range of phenomena, inference in general graphical models is a hard problem. In this thesis we study Gaussian graphical models, in which the joint distribution of all the random variables is Gaussian, and the graphical structure is exposed in the inverse of the covariance matrix. Such models are commonly used in a variety of fields, including remote sensing, computer vision, biology and sensor networks. Inference in Gaussian models reduces to matrix inversion, but for very large-scale models and for models requiring distributed inference, matrix inversion is not feasible. We first study a representation of inference in Gaussian graphical models in terms of computing sums of weights of walks in the graph -- where means, variances and correlations can be represented as such walk-sums. This representation holds in a wide class of Gaussian models that we call walk-summable. We develop a walk-sum interpretation for a popular distributed approximate inference algorithm called loopy belief propagation (LBP), and establish conditions for its convergence. We also extend the walk-sum framework to analyze more powerful versions of LBP that trade off convergence and accuracy for computational complexity, and establish conditions for their convergence. Next we consider an efficient approach to find approximate variances in large scale Gaussian graphical models.(cont.) Our approach relies on constructing a low-rank aliasing matrix with respect to the Markov graph of the model which can be used to compute an approximation to the inverse of the information matrix for the model. By designing this matrix such that only the weakly correlated terms are aliased, we are able to give provably accurate variance approximations. We describe a construction of such a low-rank aliasing matrix for models with short-range correlations, and a wavelet based construction for models with smooth long-range correlations. We also establish accuracy guarantees for the resulting variance approximations.by Dmitry M. Malioutov.Ph.D

Privacy-preserving recommendation system using federated learning

Federated Learning is a form of distributed learning which leverages edge devices for training. It aims to preserve privacy by communicating users’ learning parameters and gradient updates to the global server during the training while keeping the actual data on the users’ devices. The training on global server is performed on these parameters instead of user data directly while fine tuning of the model can be done on client’s devices locally. However, federated learning is not without its shortcomings and in this thesis, we present an overview of the learning paradigm and propose a new federated recommender system framework that utilizes homomorphic encryption. This results in a slight decrease in accuracy metrics but leads to greatly increased user-privacy. We also show that performing computations on encrypted gradients barely affects the recommendation performance while ensuring a more secure means of communicating user gradients to and from the global server

Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..