In this paper we present a novel scheme for unstructured audio scene classification that possesses three highly desirable and powerful features: autonomy, scalability, and robustness. Our scheme is based on our recently introduced machine learning algorithm called Simultaneous Temporal And Contextual Splitting (STACS) that discovers the appropriate number of states and efficiently learns accurate Hidden Markov Model (HMM) parameters for the given data. STACS-based algorithms train HMMs up to five times faster than Baum-Welch, avoid the overfitting problem commonly encountered in learning large state-space HMMs using Expectation Maximization (EM) methods such as Baum-Welch, and achieve superior classification results on a very diverse dataset with minimal pre-processing. Furthermore, our scheme has proven to be highly effective for building real-world applications and has been integrated into a commercial surveillance system as an event detection component.

Stability is a desirable characteristic for linear dynamical systems, but it is often ignored by algorithms that learn these systems from data. We propose a novel method for learning stable linear dynamical systems: we formulate an approxima- tion of the problem as a convex program, start with a solution to a relaxed version of the program, and incrementally add constraints to improve stability. Rather than continuing to generate constraints until we reach a feasible solution, we test stability at each step; because the convex program is only an approximation of the desired problem, this early stopping rule can yield a higher-quality solution. We apply our algorithm to the task of learning dynamic textures from image sequences as well as to modeling biosurveillance drug-sales data. The constraint generation approach leads to noticeable improvement in the quality of simulated sequences. We compare our method to those of Lacy and Bernstein [1, 2], with positive results in terms of accuracy, quality of simulated sequences, and efficiency.

For Hidden Markov Models (HMMs) with fully connected transition models, the three fundamental problems of evaluating the likelihood of an observation sequence, estimating an optimal state sequence for the observations, and learning the model parameters, all have quadratic time complexity in the number of states. We introduce a novel class of non-sparse Markov transition matrices called Dense-Mostly-Constant (DMC) transition matrices that allow us to derive new algorithms for solving the basic HMM problems in sub-quadratic time. We describe the DMC HMM model and algorithms and attempt to convey some intuition for their usage. Empirical results for these algorithms show dramatic speedups for all three problems. In terms of accuracy, the DMC model yields strong results and outperforms the baseline algorithms even in domains known to violate the DMC assumption.