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Related Concept Videos

Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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Basic Continuous Time Signals01:22

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Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
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Continuous -time Fourier Transform01:11

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The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
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The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modeled using a combination of sine and cosine functions. Consider a simplified surface water wave that moves across the water's surface. Unlike complex ocean waves, in surface water waves, water moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. If a seagull is floating on the...
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Automatic Detection of Highly Organized Theta Oscillations in the Murine EEG
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Compressed computations using wavelets for hidden Markov models with continuous observations.

Luca Bello1, John Wiedenhöft2, Alexander Schliep1,3

  • 1Computer Science and Engineering, University of Gothenburg, Chalmers, Gothenburg, Sweden.

Plos One
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Summary
This summary is machine-generated.

Compression significantly speeds up Hidden Markov Model (HMM) algorithms for continuous data. This new method accelerates computations for big data machine learning without sacrificing accuracy.

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Area of Science:

  • Computational Biology
  • Machine Learning
  • Statistical Modeling

Background:

  • Compression is vital for accelerating big data machine learning.
  • Previous work demonstrated compression's benefits for discrete Hidden Markov Models (HMMs).
  • Compression also accelerates Bayesian HMMs with continuous data under specific assumptions.

Purpose of the Study:

  • To extend compressive computation to frequentist HMM algorithms for continuous-valued observations.
  • To provide the first compressive approach for classical frequentist HMM algorithms on continuous data.
  • To evaluate the performance of compressed HMM algorithms against classical methods.

Main Methods:

  • Applied compression techniques to classical frequentist HMM algorithms (Forward Filtering, Backward Smoothing, Viterbi).
  • Conducted large-scale simulations to compare compressed and classical HMM algorithms.
  • Utilized continuous-valued observations in the HMM framework.

Main Results:

  • Compressed HMM algorithms significantly outperform classical algorithms in many settings.
  • The compression method has no, or only an insignificant, effect on computed probabilities and inferred state paths.
  • Demonstrated empirical evidence of accelerated computations for big data HMMs.

Conclusions:

  • Compressive computation offers an efficient approach for big data analysis using HMMs.
  • The developed method accelerates frequentist HMM algorithms on continuous data without compromising accuracy.
  • An open-source implementation is available for broader adoption and research.