HMM based scenario generation for an investment optimisation problem

This is the post-print version of the article. The official published version can be accessed from the link below - Copyright @ 2012 Springer-Verlag.The Geometric Brownian motion (GBM) is a standard method for modelling financial time series. An important criticism of this method is that the parameters of the GBM are assumed to be constants; due to this fact, important features of the time series, like extreme behaviour or volatility clustering cannot be captured. We propose an approach by which the parameters of the GBM are able to switch between regimes, more precisely they are governed by a hidden Markov chain. Thus, we model the financial time series via a hidden Markov model (HMM) with a GBM in each state. Using this approach, we generate scenarios for a financial portfolio optimisation problem in which the portfolio CVaR is minimised. Numerical results are presented.This study was funded by NET ACE at OptiRisk Systems

Inducing Probabilistic Grammars by Bayesian Model Merging

We describe a framework for inducing probabilistic grammars from corpora of positive samples. First, samples are {\em incorporated} by adding ad-hoc rules to a working grammar; subsequently, elements of the model (such as states or nonterminals) are {\em merged} to achieve generalization and a more compact representation. The choice of what to merge and when to stop is governed by the Bayesian posterior probability of the grammar given the data, which formalizes a trade-off between a close fit to the data and a default preference for simpler models (`Occam's Razor'). The general scheme is illustrated using three types of probabilistic grammars: Hidden Markov models, class-based $n$-grams, and stochastic context-free grammars.Comment: To appear in Grammatical Inference and Applications, Second International Colloquium on Grammatical Inference; Springer Verlag, 1994. 13 page

Computational identification of adaptive mutants using the VERT system

<p/> <p>Background</p> <p>Evolutionary dynamics of microbial organisms can now be visualized using the Visualizing Evolution in Real Time (VERT) system, in which several isogenic strains expressing different fluorescent proteins compete during adaptive evolution and are tracked using fluorescent cell sorting to construct a population history over time. Mutations conferring enhanced growth rates can be detected by observing changes in the fluorescent population proportions.</p> <p>Results</p> <p>Using data obtained from several VERT experiments, we construct a hidden Markov-derived model to detect these adaptive events in VERT experiments without external intervention beyond initial training. Analysis of annotated data revealed that the model achieves consensus with human annotation for 85-93% of the data points when detecting adaptive events. A method to determine the optimal time point to isolate adaptive mutants is also introduced.</p> <p>Conclusions</p> <p>The developed model offers a new way to monitor adaptive evolution experiments without the need for external intervention, thereby simplifying adaptive evolution efforts relying on population tracking. Future efforts to construct a fully automated system to isolate adaptive mutants may find the algorithm a useful tool.</p

Second-Order Belief Hidden Markov Models

Hidden Markov Models (HMMs) are learning methods for pattern recognition. The probabilistic HMMs have been one of the most used techniques based on the Bayesian model. First-order probabilistic HMMs were adapted to the theory of belief functions such that Bayesian probabilities were replaced with mass functions. In this paper, we present a second-order Hidden Markov Model using belief functions. Previous works in belief HMMs have been focused on the first-order HMMs. We extend them to the second-order model

Reductions of Hidden Information Sources

In all but special circumstances, measurements of time-dependent processes reflect internal structures and correlations only indirectly. Building predictive models of such hidden information sources requires discovering, in some way, the internal states and mechanisms. Unfortunately, there are often many possible models that are observationally equivalent. Here we show that the situation is not as arbitrary as one would think. We show that generators of hidden stochastic processes can be reduced to a minimal form and compare this reduced representation to that provided by computational mechanics--the epsilon-machine. On the way to developing deeper, measure-theoretic foundations for the latter, we introduce a new two-step reduction process. The first step (internal-event reduction) produces the smallest observationally equivalent sigma-algebra and the second (internal-state reduction) removes sigma-algebra components that are redundant for optimal prediction. For several classes of stochastic dynamical systems these reductions produce representations that are equivalent to epsilon-machines.Comment: 12 pages, 4 figures; 30 citations; Updates at http://www.santafe.edu/~cm

Implementing EM and Viterbi algorithms for Hidden Markov Model in linear memory

<p>Abstract</p> <p>Background</p> <p>The Baum-Welch learning procedure for Hidden Markov Models (HMMs) provides a powerful tool for tailoring HMM topologies to data for use in knowledge discovery and clustering. A linear memory procedure recently proposed by <it>Miklós, I. and Meyer, I.M. </it>describes a memory sparse version of the Baum-Welch algorithm with modifications to the original probabilistic table topologies to make memory use independent of sequence length (and linearly dependent on state number). The original description of the technique has some errors that we amend. We then compare the corrected implementation on a variety of data sets with conventional and checkpointing implementations.</p> <p>Results</p> <p>We provide a correct recurrence relation for the emission parameter estimate and extend it to parameter estimates of the Normal distribution. To accelerate estimation of the prior state probabilities, and decrease memory use, we reverse the originally proposed forward sweep. We describe different scaling strategies necessary in all real implementations of the algorithm to prevent underflow. In this paper we also describe our approach to a linear memory implementation of the Viterbi decoding algorithm (with linearity in the sequence length, while memory use is approximately independent of state number). We demonstrate the use of the linear memory implementation on an extended Duration Hidden Markov Model (DHMM) and on an HMM with a spike detection topology. Comparing the various implementations of the Baum-Welch procedure we find that the checkpointing algorithm produces the best overall tradeoff between memory use and speed. In cases where sequence length is very large (for Baum-Welch), or state number is very large (for Viterbi), the linear memory methods outlined may offer some utility.</p> <p>Conclusion</p> <p>Our performance-optimized Java implementations of Baum-Welch algorithm are available at <url>http://logos.cs.uno.edu/~achurban</url>. The described method and implementations will aid sequence alignment, gene structure prediction, HMM profile training, nanopore ionic flow blockades analysis and many other domains that require efficient HMM training with EM.</p

Gaussian Process Pseudo-Likelihood Models for Sequence Labeling

Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian processes (GPs) provide a Bayesian approach to learning in a kernel based framework. The pseudo-likelihood model enables one to capture long range dependencies among the output components of the sequence without becoming computationally intractable. We use an efficient variational Gaussian approximation method to perform inference in the proposed model. We also provide an iterative algorithm which can effectively make use of the information from the neighboring labels to perform prediction. The ability to capture long range dependencies makes the proposed approach useful for a wide range of sequence labeling problems. Numerical experiments on some sequence labeling data sets demonstrate the usefulness of the proposed approach.Comment: 18 pages, 5 figure

A compact statistical model of the song syntax in Bengalese finch

Songs of many songbird species consist of variable sequences of a finite number of syllables. A common approach for characterizing the syntax of these complex syllable sequences is to use transition probabilities between the syllables. This is equivalent to the Markov model, in which each syllable is associated with one state, and the transition probabilities between the states do not depend on the state transition history. Here we analyze the song syntax in a Bengalese finch. We show that the Markov model fails to capture the statistical properties of the syllable sequences. Instead, a state transition model that accurately describes the statistics of the syllable sequences includes adaptation of the self-transition probabilities when states are repeatedly revisited, and allows associations of more than one state to the same syllable. Such a model does not increase the model complexity significantly. Mathematically, the model is a partially observable Markov model with adaptation (POMMA). The success of the POMMA supports the branching chain network hypothesis of how syntax is controlled within the premotor song nucleus HVC, and suggests that adaptation and many-to-one mapping from neural substrates to syllables are important features of the neural control of complex song syntax

Characterization of 3 PET Tracers for Quantification of Mitochondrial and Synaptic Function in Healthy Human Brain: {18}^F-BCPP-EF, {11}^C-SA-4503, and {11}^C-UCB-J

Mitochondrial complex 1 is involved in maintaining brain bioenergetics; σ-1 receptor responds to neuronal stress; and synaptic vesicle protein 2A reflects synaptic integrity. Expression of each of these proteins is altered in neurodegenerative diseases. Here, we characterize the kinetic behavior of 3 PET radioligands—{18}^F-BCPP-EF, {11}^C-SA-4503, and {11}^C-UCB-J for the measurement of mitochondrial complex 1, σ-1 receptor, and synaptic vesicle protein 2A, respectively, and determine appropriate analysis workflows for their application in future studies of the in vivo molecular pathology of these diseases. METHODS: Twelve human subjects underwent dynamic PET scans with each radioligand, including associated arterial blood sampling. A range of kinetic models was investigated to identify an optimal kinetic analysis method for each radioligand and a suitable acquisition duration. RESULTS: All 3 radioligands readily entered the brain and yielded heterogeneous uptake consistent with the known distribution of the targets. The optimal models determined for the regional estimates of volume of distribution were multilinear analysis 1 (MA1) and the 2-tissue-compartment model for {18}^F-BCPP-EF, MA1 for 11}^C-SA-4503, and both MA1 and the 1-tissue-compartment model for {11}^C-UCB-J, respectively, provided good estimates of regional volume of distribution values. An effect of age was observed on {18}^F-BCPP-EF and {11}^C-UCB-J signal in the caudate. CONCLUSION: These ligands can be assessed for their potential to stratify patients or monitor the progression of molecular neuropathology in neurodegenerative diseases