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  • 1.
    Mattila, Robert
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Krishnamurthy, V.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Computing monotone policies for Markov decision processes: a nearly-isotonic penalty approach2017In: IFAC-PapersOnLine, ISSN 2405-8963, Vol. 50, no 1, p. 8429-8434Article in journal (Refereed)
    Abstract [en]

    This paper discusses algorithms for solving Markov decision processes (MDPs) that have monotone optimal policies. We propose a two-stage alternating convex optimization scheme that can accelerate the search for an optimal policy by exploiting the monotone property The first stage is a linear program formulated in terms of the joint state-action probabilities. The second stage is a regularized problem formulated in terms of the conditional probabilities of actions given states. The regularization uses techniques from nearly-isotonic regression. While a variety of iterative method can be used in the first formulation of the problem, we show in numerical simulations that, in particular, the alternating method of multipliers (ADMM) can be significantly accelerated using the regularization step.

  • 2.
    Mattila, Robert
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Krishnamurthy, Vikram
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Asymptotically Efficient Identification of Known-Sensor Hidden Markov Models2017In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 24, no 12, p. 1813-1817Article in journal (Refereed)
    Abstract [en]

    We consider estimating the transition probability matrix of a finite-state finite-observation alphabet hidden Markov model with known observation probabilities. We propose a two-step algorithm: a method of moments estimator (formulated as a convex optimization problem) followed by a single iteration of a Newton-Raphson maximum-likelihood estimator. The two-fold contribution of this letter is, first, to theoretically show that the proposed estimator is consistent and asymptotically efficient, and second, to numerically show that the method is computationally less demanding than conventional methods-in particular for large datasets.

  • 3.
    Mattila, Robert
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Krishnamurthy, Vikram
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Identification of Hidden Markov Models Using Spectral Learning with Likelihood Maximization2017In: 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 5859-5864Conference paper (Refereed)
    Abstract [en]

    In this paper, we consider identifying a hidden Markov model (HMM) with the purpose of computing estimates of joint and conditional (posterior) probabilities over observation sequences. The classical maximum likelihood estimation algorithm (via the Baum-Welch/expectation-maximization algorithm), has recently been challenged by methods of moments. Such methods employ low-order moments to provide parameter estimates and have several benefits, including consistency and low computational cost. This paper aims to reduce the gap in statistical efficiency that results from restricting to only low-order moments in the training data. In particular, we propose a two-step procedure that combines spectral learning with a single Newton-like iteration for maximum likelihood estimation. We demonstrate an improved statistical performance using the proposed algorithm in numerical simulations.

  • 4.
    Mattila, Robert
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristián R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Krishnamurthy, V.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Inverse filtering for hidden Markov models2017In: Advances in Neural Information Processing Systems, Neural information processing systems foundation , 2017, Vol. 2017, p. 4205-4214Conference paper (Refereed)
    Abstract [en]

    This paper considers a number of related inverse filtering problems for hidden Markov models (HMMs). In particular, given a sequence of state posteriors and the system dynamics; i) estimate the corresponding sequence of observations, ii) estimate the observation likelihoods, and iii) jointly estimate the observation likelihoods and the observation sequence. We show how to avoid a computationally expensive mixed integer linear program (MILP) by exploiting the algebraic structure of the HMM filter using simple linear algebra operations, and provide conditions for when the quantities can be uniquely reconstructed. We also propose a solution to the more general case where the posteriors are noisily observed. Finally, the proposed inverse filtering algorithms are evaluated on real-world polysomnographic data used for automatic sleep segmentation.

  • 5.
    Mattila, Robert
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Siika, Antti
    Roy, Joy
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    A Markov Decision Process Model to Guide Treatment of Abdominal Aortic Aneurysms2016In: 2016 IEEE CONFERENCE ON CONTROL APPLICATIONS (CCA), IEEE, 2016Conference paper (Refereed)
    Abstract [en]

    An abdominal aortic aneurysm (AAA) is an enlargement of the abdominal aorta which, if left untreated, can progressively widen and may rupture with fatal consequences. In this paper, we determine an optimal treatment policy using Markov decision process modeling. The policy is optimal with respect to the number of quality adjusted life-years (QALYs) that are expected to be accumulated during the remaining life of a patient. The new policy takes into account factors that are ignored by the current clinical policy (e.g. the life-expectancy and the age-dependent surgical mortality). The resulting optimal policy is structurally different from the current policy. In particular, the policy suggests that young patients with small aneurysms should undergo surgery. The robustness of the policy structure is demonstrated using simulations. A gain in the number of expected QALYs is shown, which indicates a possibility of improved care for patients with AAAs.

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