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

The BRICS in the Global Order: A New Political Agenda?

Regarding the BRICS (Brazil, Russia, India, China and South Africa) it’s important to analyze comparatively the new power cycle in order to understand not only the impact of the world crisis as well as the relationship between the official political discourses and the economic instability. Actually, the trade liberalization and economic interdependence accompanied with an uncertain international system are putting pressure to the BRICS with their own agendas for global order in seeking for a balance and also to regain a new political and economical dynamic for the promotion of new strategies

Positive Art: Artistic Expression and Appreciation as an Exemplary Vehicle for Flourishing.

The relevance of the arts to wellbeing has been recognised within clinical fields, as reflected in therapeutic forms based on various art modalities, from music to drama therapy. However, there has hitherto been little appreciation in fields such as positive psychology of the broader potential of the arts as a vehicle for flourishing and fulfilment. As such, this paper proposes the creation of ‘positive art’ as a field encompassing theory and research concerning the wellbeing value of art. To show the scope and possibilities of this proposed field, the paper provides an indicative summary of literature pertaining to four major art forms: visual art, music, literature and drama. Moreover, the paper identifies five main positive outcomes that are consistently found in the literature across all these forms: sense-making, enriching experience, aesthetic appreciation, entertainment, and bonding. The paper aims to encourage a greater focus on the arts in fields like positive psychology, enabling science to more fully understand and appreciate the positive power of the arts