Markov Models
Modelling Uncertainty in the Game of Go
Stern, David H., Graepel, Thore, MacKay, David
Go is an ancient oriental game whose complexity has defeated attempts to automate it. We suggest using probability in a Bayesian sense to model the uncertainty arising from the vast complexity of the game tree. We present a simple conditional Markov random field model for predicting the pointwise territory outcome of a game. The topology of the model reflects the spatial structure of the Go board. We describe a version of the Swendsen-Wang process for sampling from the model during learning and apply loopy belief propagation for rapid inference and prediction. The model is trained on several hundred records of professional games. Our experimental results indicate that the model successfully learns to predict territory despite its simplicity.
Planning for Markov Decision Processes with Sparse Stochasticity
Likhachev, Maxim, Thrun, Sebastian, Gordon, Geoffrey J.
Planning algorithms designed for deterministic worlds, such as A* search, usually run much faster than algorithms designed for worlds with uncertain action outcomes, such as value iteration. Real-world planning problems often exhibit uncertainty, which forces us to use the slower algorithms to solve them. Many real-world planning problems exhibit sparse uncertainty: there are long sequences of deterministic actions which accomplish tasks like moving sensor platforms into place, interspersed with a small number of sensing actions which have uncertain outcomes. In this paper we describe a new planning algorithm, called MCP (short for MDP Compression Planning), which combines A* search with value iteration for solving Stochastic Shortest Path problem in MDPs with sparse stochasticity. We present experiments which show that MCP can run substantially faster than competing planners in domains with sparse uncertainty; these experiments are based on a simulation of a ground robot cooperating with a helicopter to fill in a partial map and move to a goal location.
Incremental Learning for Visual Tracking
Lim, Jongwoo, Ross, David A., Lin, Ruei-sung, Yang, Ming-Hsuan
Most existing tracking algorithms construct a representation of a target object prior to the tracking task starts, and utilize invariant features to handle appearance variation of the target caused by lighting, pose, and view angle change. In this paper, we present an efficient and effective online algorithm that incrementally learns and adapts a low dimensional eigenspace representation to reflect appearance changes of the target, thereby facilitating the tracking task. Furthermore, our incremental method correctly updates the sample mean and the eigenbasis, whereas existing incremental subspace update methods ignore the fact the sample mean varies over time. The tracking problem is formulated as a state inference problem within a Markov Chain Monte Carlo framework and a particle filter is incorporated for propagating sample distributions over time. Numerous experiments demonstrate the effectiveness of the proposed tracking algorithm in indoor and outdoor environments where the target objects undergo large pose and lighting changes.
Conditional Models of Identity Uncertainty with Application to Noun Coreference
McCallum, Andrew, Wellner, Ben
Coreference analysis, also known as record linkage or identity uncertainty, is a difficult and important problem in natural language processing, databases, citation matching and many other tasks. This paper introduces several discriminative, conditional-probability models for coreference analysis, all examples of undirected graphical models. Unlike many historical approaches to coreference, the models presented here are relational--they do not assume that pairwise coreference decisions should be made independently from each other. Unlike other relational models of coreference that are generative, the conditional model here can incorporate a great variety of features of the input without having to be concerned about their dependencies--paralleling the advantages of conditional random fields over hidden Markov models.
VDCBPI: an Approximate Scalable Algorithm for Large POMDPs
Poupart, Pascal, Boutilier, Craig
Existing algorithms for discrete partially observable Markov decision processes can at best solve problems of a few thousand states due to two important sources of intractability: the curse of dimensionality and the policy space complexity. This paper describes a new algorithm (VDCBPI) that mitigates both sources of intractability by combining the Value Directed Compression (VDC) technique [13] with Bounded Policy Iteration (BPI) [14]. The scalability of VDCBPI is demonstrated on synthetic network management problems with up to 33 million states.
A Hidden Markov Model for de Novo Peptide Sequencing
Fischer, Bernd, Roth, Volker, Grossmann, Jonas, Baginsky, Sacha, Gruissem, Wilhelm, Roos, Franz, Widmayer, Peter, Buhmann, Joachim M.
De novo Sequencing of peptides is a challenging task in proteome research. While there exist reliable DNAsequencing methods, the highthroughput de novo sequencing of proteins by mass spectrometry is still an open problem. Current approaches suffer from a lack in precision to detect mass peaks in the spectrograms. In this paper we present a novel method for de novo peptide sequencing based on a hidden Markov model. Experiments effectively demonstrate that this new method significantly outperforms standard approaches in matching quality.
Learning first-order Markov models for control
First-order Markov models have been successfully applied to many problems, for example in modeling sequential data using Markov chains, and modeling control problems using the Markov decision processes (MDP) formalism. If a first-order Markov model's parameters are estimated from data, the standard maximum likelihood estimator considers only the first-order (single-step) transitions. But for many problems, the firstorder conditional independence assumptions are not satisfied, and as a result the higher order transition probabilities may be poorly approximated. Motivated by the problem of learning an MDP's parameters for control, we propose an algorithm for learning a first-order Markov model that explicitly takes into account higher order interactions during training. Our algorithm uses an optimization criterion different from maximum likelihood, and allows us to learn models that capture longer range effects, but without giving up the benefits of using first-order Markov models. Our experimental results also show the new algorithm outperforming conventional maximum likelihood estimation in a number of control problems where the MDP's parameters are estimated from data.
Coarticulation in Markov Decision Processes
Rohanimanesh, Khashayar, Platt, Robert, Mahadevan, Sridhar, Grupen, Roderic
We investigate an approach for simultaneously committing to multiple activities, each modeled as a temporally extended action in a semi-Markov decision process (SMDP). For each activity we define a set of admissible solutions consisting of the redundant set of optimal policies, and those policies that ascend the optimal statevalue function associated with them. A plan is then generated by merging them in such a way that the solutions to the subordinate activities are realized in the set of admissible solutions satisfying the superior activities. We present our theoretical results and empirically evaluate our approach in a simulated domain.
Modeling Conversational Dynamics as a Mixed-Memory Markov Process
Choudhury, Tanzeem, Basu, Sumit
There is a long history of work in the social sciences aimed at understanding the interactions between individuals and the influences they have on each others' behavior. However, existing studies of social network interactions have either been restricted to online communities, where unambiguous measurements about how people interact can be obtained, or have been forced to rely on questionnaires or diaries to get data on face-to-face interactions. Survey-based methods are error prone and impractical to scale up. Studies show that self-reports correspond poorly to communication behavior as recorded by independent observers [3]. In contrast, we have used wearable sensors and recent advances in speech processing techniques to automatically gather information about conversations: when they occurred, who was involved, and who was speaking when.