Who Spoke What? A Latent Variable Framework for the Joint Decoding of Multiple Speakers and their Keywords

In this paper, we present a latent variable (LV) framework to identify all the speakers and their keywords given a multi-speaker mixture signal. We introduce two separate LVs to denote active speakers and the keywords uttered. The dependency of a spoken keyword on the speaker is modeled through a conditional probability mass function. The distribution of the mixture signal is expressed in terms of the LV mass functions and speaker-specific-keyword models. The proposed framework admits stochastic models, representing the probability density function of the observation vectors given that a particular speaker uttered a specific keyword, as speaker-specific-keyword models. The LV mass functions are estimated in a Maximum Likelihood framework using the Expectation Maximization (EM) algorithm. The active speakers and their keywords are detected as modes of the joint distribution of the two LVs. In mixture signals, containing two speakers uttering the keywords simultaneously, the proposed framework achieves an accuracy of 82% for detecting both the speakers and their respective keywords, using Student's-t mixture models as speaker-specific-keyword models.Comment: 6 pages, 2 figures Submitted to : IEEE Signal Processing Letter

Budget Constrained Auctions with Heterogeneous Items

In this paper, we present the first approximation algorithms for the problem of designing revenue optimal Bayesian incentive compatible auctions when there are multiple (heterogeneous) items and when bidders can have arbitrary demand and budget constraints. Our mechanisms are surprisingly simple: We show that a sequential all-pay mechanism is a 4 approximation to the revenue of the optimal ex-interim truthful mechanism with discrete correlated type space for each bidder. We also show that a sequential posted price mechanism is a O(1) approximation to the revenue of the optimal ex-post truthful mechanism when the type space of each bidder is a product distribution that satisfies the standard hazard rate condition. We further show a logarithmic approximation when the hazard rate condition is removed, and complete the picture by showing that achieving a sub-logarithmic approximation, even for regular distributions and one bidder, requires pricing bundles of items. Our results are based on formulating novel LP relaxations for these problems, and developing generic rounding schemes from first principles. We believe this approach will be useful in other Bayesian mechanism design contexts.Comment: Final version accepted to STOC '10. Incorporates significant reviewer comment