Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman-Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models. However, for some applications, this assumption is inappropriate. For example, when performing entity resolution, the size of each cluster should be unrelated to the size of the data set, and each cluster should contain a negligible fraction of the total number of data points. These applications require models that yield clusters whose sizes grow sublinearly with the size of the data set. We address this requirement by defining the microclustering property and introducing a new class of models that can exhibit this property. We compare models within this class to two commonly used clustering models using four entity-resolution data sets.
Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has gained popularity due to its modular parametrization of joint distributions. Among other properties, copulas provide a recipe for combining flexible models for univariate marginal distributions with parametric families suitable for potentially high dimensional dependence structures. More radically, the extended rank likelihood approach of Hoff (2007) bypasses learning marginal models completely when such information is ancillary to the learning task at hand as in, e.g., standard dimensionality reduction problems or copula parameter estimation. The main idea is to represent data by their observable rank statistics, ignoring any other information from the marginals. Inference is typically done in a Bayesian framework with Gaussian copulas, and it is complicated by the fact this implies sampling within a space where the number of constraints increase quadratically with the number of data points. The result is slow mixing when using off-the-shelf Gibbs sampling. We present an efficient algorithm based on recent advances on constrained Hamiltonian Markov chain Monte Carlo that is simple to implement and does not require paying for a quadratic cost in sample size.
This week at MWC, Husqvarna announced its first all-wheel drive (AWD) option with the 435X. In addition to some other unique features, this new "automower" works with Amazon's Alexa and Google Home to fit in with the rest of your smart home devices. And yes, the integration with virtual assistants means you can control the robotic landscaper with your voice. AWD adds the ability to handle slopes and rough terrain better. Husqvarna says the 435X can handle an incline of up to 70 percent, which is quite steep.
Apple has become the world's first publicly traded company to be valued at $1 trillion, the financial fruit of stylish technology that has redefined what we expect from our gadgets. Apple's new 175-acre "spaceship" campus dubbed Apple Park. It was designed by Lord Norman Foster and cost roughly $5 billion. It will house 12,000 employees in over 2.8 million square feet of office space and will have nearly 80 acres of parking to accommodate 11,000 cars. SAN FRANCISCO – In a few weeks, Apple will unveil its newest iPhone.
In addition to being accurate, it is important that diagnostic systems for use in automobiles also have low development and hardware costs. Model-based methods have shown promise at reducing hardware costs since they use analytical redundancy to reduce physical redundancy. In addition to requiring no extra sensors, the diagnostic system presented in this paper also allows for high accuracy and low development costs by using information from multiple simple models. This is made possible by the use of a Bayesian network to process model residuals. A hybrid, dynamic Bayesian network is used to model the temporal behavior of the faults and determine fault probabilities. A prototype of the system has been implemented and tested on a Mercedes-Benz E320 sedan. This paper describes the prototype system and presents results demonstrating the system's advantages over traditional residual threshold techniques.