Scalable k-Means Clustering via Lightweight Coresets

Coresets are compact representations of data sets such that models trained on a coreset are provably competitive with models trained on the full data set. As such, they have been successfully used to scale up clustering models to massive data sets. While existing approaches generally only allow for multiplicative approximation errors, we propose a novel notion of lightweight coresets that allows for both multiplicative and additive errors. We provide a single algorithm to construct lightweight coresets for k-means clustering as well as soft and hard Bregman clustering. The algorithm is substantially faster than existing constructions, embarrassingly parallel, and the resulting coresets are smaller. We further show that the proposed approach naturally generalizes to statistical k-means clustering and that, compared to existing results, it can be used to compute smaller summaries for empirical risk minimization. In extensive experiments, we demonstrate that the proposed algorithm outperforms existing data summarization strategies in practice.Comment: To appear in the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (KDD

Training Gaussian Mixture Models at Scale via Coresets

How can we train a statistical mixture model on a massive data set? In this work we show how to construct coresets for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also provide a good fit for the original data set. We show that, perhaps surprisingly, Gaussian mixtures admit coresets of size polynomial in dimension and the number of mixture components, while being independent of the data set size. Hence, one can harness computationally intensive algorithms to compute a good approximation on a significantly smaller data set. More importantly, such coresets can be efficiently constructed both in distributed and streaming settings and do not impose restrictions on the data generating process. Our results rely on a novel reduction of statistical estimation to problems in computational geometry and new combinatorial complexity results for mixtures of Gaussians. Empirical evaluation on several real-world datasets suggests that our coreset-based approach enables significant reduction in training-time with negligible approximation error

Coresets-Methods and History: A Theoreticians Design Pattern for Approximation and Streaming Algorithms

We present a technical survey on the state of the art approaches in data reduction and the coreset framework. These include geometric decompositions, gradient methods, random sampling, sketching and random projections. We further outline their importance for the design of streaming algorithms and give a brief overview on lower bounding techniques

On the Intersection of Communication and Machine Learning

The intersection of communication and machine learning is attracting increasing interest from both communities. On the one hand, the development of modern communication system brings large amount of data and high performance requirement, which challenges the classic analytical-derivation based study philosophy and encourages the researchers to explore the data driven method, such as machine learning, to solve the problems with high complexity and large scale. On the other hand, the usage of distributed machine learning introduces the communication cost as one of the basic considerations for the design of machine learning algorithm and system.In this thesis, we first explore the application of machine learning on one of the classic problems in wireless network, resource allocation, for heterogeneous millimeter wave networks when the environment is with high dynamics. We address the practical concerns by providing the efficient online and distributed framework. In the second part, some sampling based communication-efficient distributed learning algorithm is proposed. We utilize the trade-off between the local computation and the total communication cost and propose the algorithm with good theoretical bound. In more detail, this thesis makes the following contributionsWe introduced an reinforcement learning framework to solve the resource allocation problems in heterogeneous millimeter wave network. The large state/action space is decomposed according to the topology of the network and solved by an efficient distribtued message passing algorithm. We further speed up the inference process by an online updating process.We proposed the distributed coreset based boosting framework. An efficient coreset construction algorithm is proposed based on the prior knowledge provided by clustering. Then the coreset is integrated with boosting with improved convergence rate. We extend the proposed boosting framework to the distributed setting, where the communication cost is reduced by the good approximation of coreset.We propose an selective sampling framework to construct a subset of sample that could effectively represent the model space. Based on the prior distribution of the model space or the large amount of samples from model space, we derive a computational efficient method to construct such subset by minimizing the error of classifying a classifier