Representations and algorithms for finite-state bisimulations of linear discrete-time control systems

While a large amount of research over the past two decades has focused on discrete abstractions of infinite-state dynamical systems, many structural and algorithmic details of these abstractions remain unknown. To clarify the computational resources needed to perform discrete abstractions, this paper examines the algorithmic properties of an existing method for deriving finite-state systems that are bisimilar to linear discrete-time control systems. We explicitly find the structure of the finite-state system, show that it can be enormous compared to the original linear system, and give conditions to guarantee that the finite-state system is reasonably sized and efficiently computable. Though constructing the finite-state system is generally impractical, we see that special cases could be amenable to satisfiability based verification techniques. ©2009 IEEE.

N-best error simulation for training spoken dialogue systems

A recent trend in spoken dialogue research is the use of reinforcement learning to train dialogue systems in a simulated environment. Past researchers have shown that the types of errors that are simulated can have a significant effect on simulated dialogue performance. Since modern systems typically receive an N-best list of possible user utterances, it is important to be able to simulate a full N-best list of hypotheses. This paper presents a new method for simulating such errors based on logistic regression, as well as a new method for simulating the structure of N-best lists of semantics and their probabilities, based on the Dirichlet distribution. Off-line evaluations show that the new Dirichlet model results in a much closer match to the receiver operating characteristics (ROC) of the live data. Experiments also show that the logistic model gives confusions that are closer to the type of confusions observed in live situations. The hope is that these new error models will be able to improve the resulting performance of trained dialogue systems. © 2012 IEEE.

Distributed flow algorithms for scalable similarity visualization

We describe simple yet scalable and distributed algorithms for solving the maximum flow problem and its minimum cost flow variant, motivated by problems of interest in objects similarity visualization. We formulate the fundamental problem as a convex-concave saddle point problem. We then show that this problem can be efficiently solved by a first order method or by exploiting faster quasi-Newton steps. Our proposed approach costs at most O(|ε|) per iteration for a graph with |ε| edges. Further, the number of required iterations can be shown to be independent of number of edges for the first order approximation method. We present experimental results in two applications: mosaic generation and color similarity based image layouting. © 2010 IEEE.

Convex relaxation of mixture regression with efficient algorithms

We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data.

Distribution matching for transduction

Many transductive inference algorithms assume that distributions over training and test estimates should be related, e.g. by providing a large margin of separation on both sets. We use this idea to design a transduction algorithm which can be used without modification for classification, regression, and structured estimation. At its heart we exploit the fact that for a good learner the distributions over the outputs on training and test sets should match. This is a classical two-sample problem which can be solved efficiently in its most general form by using distance measures in Hilbert Space. It turns out that a number of existing heuristics can be viewed as special cases of our approach.