Inference and Evaluation of the Multinomial Mixture Model for Text Clustering

In this article, we investigate the use of a probabilistic model for unsupervised clustering in text collections. Unsupervised clustering has become a basic module for many intelligent text processing applications, such as information retrieval, text classification or information extraction. The model considered in this contribution consists of a mixture of multinomial distributions over the word counts, each component corresponding to a different theme. We present and contrast various estimation procedures, which apply both in supervised and unsupervised contexts. In supervised learning, this work suggests a criterion for evaluating the posterior odds of new documents which is more statistically sound than the "naive Bayes" approach. In an unsupervised context, we propose measures to set up a systematic evaluation framework and start with examining the Expectation-Maximization (EM) algorithm as the basic tool for inference. We discuss the importance of initialization and the influence of other features such as the smoothing strategy or the size of the vocabulary, thereby illustrating the difficulties incurred by the high dimensionality of the parameter space. We also propose a heuristic algorithm based on iterative EM with vocabulary reduction to solve this problem. Using the fact that the latent variables can be analytically integrated out, we finally show that Gibbs sampling algorithm is tractable and compares favorably to the basic expectation maximization approach

Arriving on time: estimating travel time distributions on large-scale road networks

Most optimal routing problems focus on minimizing travel time or distance traveled. Oftentimes, a more useful objective is to maximize the probability of on-time arrival, which requires statistical distributions of travel times, rather than just mean values. We propose a method to estimate travel time distributions on large-scale road networks, using probe vehicle data collected from GPS. We present a framework that works with large input of data, and scales linearly with the size of the network. Leveraging the planar topology of the graph, the method computes efficiently the time correlations between neighboring streets. First, raw probe vehicle traces are compressed into pairs of travel times and number of stops for each traversed road segment using a `stop-and-go' algorithm developed for this work. The compressed data is then used as input for training a path travel time model, which couples a Markov model along with a Gaussian Markov random field. Finally, scalable inference algorithms are developed for obtaining path travel time distributions from the composite MM-GMRF model. We illustrate the accuracy and scalability of our model on a 505,000 road link network spanning the San Francisco Bay Area