Probabilistic Models of Melodic Interval

2014 ◽  
Vol 32 (1) ◽  
pp. 85-99 ◽  
Author(s):  
David Temperley
Keyword(s):  
Markov Model ◽  
Probabilistic Models ◽  
Music Cognition ◽  
Gaussian Model ◽  
Cross Entropy ◽  
Mathematical Function ◽  
Interval Probability ◽  
Previous Note ◽  
Melodic Expectation

Two probabilistic models of melodic interval are compared. In the Markov model, the “interval probability” of a note is defined by the corpus frequency of its melodic interval (the interval to the previous note), conditioned on the previous one or two intervals; in the Gaussian model, the interval probability is a simple mathematical function of the size of the note’s melodic interval and its position in relation to the range of the melody. In both models, this interval probability is then multiplied by the probability of the note’s scale degree to yield its actual probability. The two models were tested on four corpora of tonal melodies using cross-entropy. The Markov model yielded a somewhat lower (better) cross-entropy than the Gaussian model, but is also much more complex, requiring far more parameters. The models were also tested on melodic expectation data, and on their ability to predict the distribution of intervals in a corpus. Possible ways of improving the models are discussed, as well as their broader implications for music cognition.

Modeling Common-Practice Rhythm

2010 ◽  
Vol 27 (5) ◽  
pp. 355-376 ◽  
Author(s):  
David Temperley
Keyword(s):  
Folk Music ◽  
Probabilistic Models ◽  
Classical Music ◽  
String Quartets ◽  
Folk Songs ◽  
Cross Entropy ◽  
Duration Model ◽  
Previous Note ◽  
Hierarchical Position ◽  
The One

THIS STUDY EXPLORES WAYS OF MODELING the compositional processes involved in common-practice rhythm (as represented by European classical music and folk music). Six probabilistic models of rhythm were evaluated using the method of cross-entropy: according to this method, the best model is the one that assigns the highest probability to the data. Two corpora were used: a corpus of European folk songs (the Essen Folksong Collection) and a corpus of Mozart and Haydn string quartets. The model achieving lowest cross-entropy was the First-Order Metrical Duration Model, which chooses a metrical position for each note conditional on the position of the previous note. Second best was the Hierarchical Position Model, which decides at each beat whether or not to generate a note there, conditional on the note status of neighboring strong beats (i.e., whether or not they contain notes).When complexity (number of parameters) is also considered, it is argued that the Hierarchical Position Model is preferable overall.

scholarly journals Automatic Recognition of Human Interaction via Hybrid Descriptors and Maximum Entropy Markov Model Using Depth Sensors

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 817 ◽  
Author(s):  
Ahmad Jalal ◽  
Nida Khalid ◽  
Kibum Kim
Keyword(s):  
Markov Model ◽  
Maximum Entropy ◽  
Social Activity ◽  
Gaussian Mixture ◽  
Features Extraction ◽  
Human Interaction ◽  
Cross Entropy ◽  
Automatic Identification ◽  
Depth Sensors ◽  
Entropy Optimization

Automatic identification of human interaction is a challenging task especially in dynamic environments with cluttered backgrounds from video sequences. Advancements in computer vision sensor technologies provide powerful effects in human interaction recognition (HIR) during routine daily life. In this paper, we propose a novel features extraction method which incorporates robust entropy optimization and an efficient Maximum Entropy Markov Model (MEMM) for HIR via multiple vision sensors. The main objectives of proposed methodology are: (1) to propose a hybrid of four novel features—i.e., spatio-temporal features, energy-based features, shape based angular and geometric features—and a motion-orthogonal histogram of oriented gradient (MO-HOG); (2) to encode hybrid feature descriptors using a codebook, a Gaussian mixture model (GMM) and fisher encoding; (3) to optimize the encoded feature using a cross entropy optimization function; (4) to apply a MEMM classification algorithm to examine empirical expectations and highest entropy, which measure pattern variances to achieve outperformed HIR accuracy results. Our system is tested over three well-known datasets: SBU Kinect interaction; UoL 3D social activity; UT-interaction datasets. Through wide experimentations, the proposed features extraction algorithm, along with cross entropy optimization, has achieved the average accuracy rate of 91.25% with SBU, 90.4% with UoL and 87.4% with UT-Interaction datasets. The proposed HIR system will be applicable to a wide variety of man–machine interfaces, such as public-place surveillance, future medical applications, virtual reality, fitness exercises and 3D interactive gaming.

Probabilistic Models for Wind Turbine and Wind Farm Performance

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Sanjay R. Arwade ◽  
Matthew A. Lackner ◽  
Mircea D. Grigoriu
Keyword(s):  
Markov Model ◽  
Wind Turbine ◽  
Large Scale ◽  
Wind Farm ◽  
Probabilistic Models ◽  
Performance Metrics ◽  
Wind Farms ◽  
Component Reliability ◽  
Mc Simulation ◽  
Farm Performance

A Markov model for the performance of wind turbines is developed that accounts for component reliability and the effect of wind speed and turbine capacity on component reliability. The model is calibrated to the observed performance of offshore turbines in the north of Europe, and uses wind records obtained from the coast of the state of Maine in the northeast United States in simulation. Simulation results indicate availability of 0.91, with mean residence time in the operating state that is nearly exponential and has a mean of 42 days. Using a power curve typical for a 2.5 MW turbine, the capacity factor is found to be beta distributed and highly non-Gaussian. Noticeable seasonal variation in turbine and farm performance metrics are observed and result from seasonal fluctuations in the characteristics of the wind record. The input parameters to the Markov model, as defined in this paper, are limited to those for which field data are available for calibration. Nevertheless, the framework of the model is readily adaptable to include, for example: site specific conditions; turbine details; wake induced loading effects; component redundancies; and dependencies. An on-off model is introduced as an approximation to the stochastic process describing the operating state of a wind turbine, and from this on-off process an Ornstein–Uhlenbeck (O–U) process is developed as a model for the availability of a wind farm. The O–U model agrees well with Monte Carlo (MC) simulation of the Markov model and is accepted as a valid approximation. Using the O–U model in design and management of large wind farms will be advantageous because it can provide statistics of wind farm performance without resort to intensive large scale MC simulation.

scholarly journals Activation Detection on fMRI Time Series Using Hidden Markov Model

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Rong Duan ◽  
Hong Man
Keyword(s):  
Time Series ◽  
Brain Tumor ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Viterbi Algorithm ◽  
Hidden Markov ◽  
Gaussian Model ◽  
Model Parameters ◽  
Ratio Test ◽  
Activation Detection

This paper introduces two unsupervised learning methods for analyzing functional magnetic resonance imaging (fMRI) data based on hidden Markov model (HMM). HMM approach is focused on capturing the first-order statistical evolution among the samples of a voxel time series, and it can provide a complimentary perspective of the BOLD signals. Two-state HMM is created for each voxel, and the model parameters are estimated from the voxel time series and the stimulus paradigm. Two different activation detection methods are presented in this paper. The first method is based on the likelihood and likelihood-ratio test, in which an additional Gaussian model is used to enhance the contrast of the HMM likelihood map. The second method is based on certain distance measures between the two state distributions, in which the most likely HMM state sequence is estimated through the Viterbi algorithm. The distance between the on-state and off-state distributions is measured either through a t-test, or using the Kullback-Leibler distance (KLD). Experimental results on both normal subject and brain tumor subject are presented. HMM approach appears to be more robust in detecting the supplemental active voxels comparing with SPM, especially for brain tumor subject.

A generalized interval probability-based optimization method for training generalized hidden Markov model

2014 ◽  
Vol 94 ◽  
pp. 319-329 ◽  
Author(s):  
Fengyun Xie ◽  
Bo Wu ◽  
Youmin Hu ◽  
Yan Wang ◽  
Guangfei Jia ◽  
...  
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Hidden Markov ◽  
Optimization Method ◽  
Interval Probability

Multiscale Uncertainty Quantification Based on a Generalized Hidden Markov Model

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Yan Wang
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
System Analysis ◽  
Hidden Markov ◽  
Uncertainty Propagation ◽  
Information Loss ◽  
Bayes Rule ◽  
Scale Dependency ◽  
Interval Probability ◽  
Information Assimilation

Variability is the inherent randomness in systems, whereas incertitude is due to lack of knowledge. In this paper, a generalized hidden Markov model (GHMM) is proposed to quantify aleatory and epistemic uncertainties simultaneously in multiscale system analysis. The GHMM is based on a new imprecise probability theory that has the form of generalized interval. The new interval probability resembles the precise probability and has a similar calculus structure. The proposed GHMM allows us to quantify cross-scale dependency and information loss between scales. Based on a generalized interval Bayes’ rule, three cross-scale information assimilation approaches that incorporate uncertainty propagation are also developed.

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