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Related Concept Videos

Downsampling01:20

Downsampling

147
When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
147
Upsampling01:22

Upsampling

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Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
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Bandpass Sampling01:17

Bandpass Sampling

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In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2....
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Sampling Theorem01:15

Sampling Theorem

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In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
321
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

202
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
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Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

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Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
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Shuffling-type gradient method with bandwidth-based step sizes for finite-sum optimization.

Yuqing Liang1, Yang Yang1, Jinlan Liu2

  • 1Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China.

Neural Networks : the Official Journal of the International Neural Network Society
|July 18, 2024
PubMed
Summary
This summary is machine-generated.

This study enhances the shuffling-type gradient method for machine learning optimization. It provides unified convergence guarantees and improves convergence rates for finite-sum problems.

Keywords:
Bandwidth-based step sizeLast iteration convergenceNon-convex objectivesPL conditionShuffling-type gradient algorithm

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Area of Science:

  • Machine Learning
  • Optimization Algorithms

Background:

  • Shuffling-type gradient methods are popular for finite-sum optimization.
  • Existing methods have restrictive assumptions on objective functions and gradients.

Purpose of the Study:

  • To explore and unify the convergence properties of shuffling-type gradient methods.
  • To relax existing assumptions and improve convergence guarantees.

Main Methods:

  • Employing a bandwidth-based step size strategy for unified convergence.
  • Replacing objective function lower bound with loss function assumption.
  • Analyzing convergence for non-convex objectives and under the Polyak-Łojasiewicz (PL) condition.

Main Results:

  • Unified convergence guarantee for shuffling-type gradient method.
  • Elimination of practical restrictions on stochastic gradient variance and second-order moment.
  • Improved convergence rates for finite-sum optimization problems.
  • Validation of theoretical results through numerical experiments.

Conclusions:

  • The study offers a deeper understanding of shuffling-type gradient methods.
  • Provides practical insights for optimizing finite-sum problems in machine learning.
  • Demonstrates the efficiency of the proposed method and its theoretical underpinnings.