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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 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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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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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.

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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.