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Related Concept Videos

Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

311
Sampling materials are classified into three main types: solid, liquid, and gas.
Solid samples include a variety of substances, such as sediments from water bodies, soil, metals, and biological tissues. Two standard methods for extracting sediments from water bodies are grab sampling and piston coring. Grab sampling involves using a device to collect a discrete sediment sample from the bottom of a water body with minimal disturbance. Grab samples do not always represent the entire area due to...
311
Sampling Methods: Overview01:06

Sampling Methods: Overview

393
A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of...
393
Sampling Distribution01:12

Sampling Distribution

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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
13.3K
Sampling Plans01:23

Sampling Plans

228
Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
228
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

302
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.
In the...
302
Sampling Theorem01:15

Sampling Theorem

422
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.
422

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Differentiable samplers for deep latent variable models.

Arnaud Doucet1, Eric Moulines2, Achille Thin2

  • 1Department of Statistics, Oxford University, Oxford, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|March 27, 2023
PubMed
Summary
This summary is machine-generated.

Deep latent variable models offer powerful machine learning applications but face challenges with intractable likelihoods. Recent Monte Carlo methods improve inference by providing unbiased estimates for these complex statistical models.

Keywords:
Bayesian inferenceMonte Carlo methodsimportance samplingvariational inference

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Area of Science:

  • Statistics
  • Machine Learning
  • Artificial Intelligence

Background:

  • Deep latent variable models (DLVMs) combine neural networks and latent variable models for enhanced expressivity.
  • A key challenge in DLVMs is the intractability of their likelihood function, necessitating approximation methods for inference.

Purpose of the Study:

  • To review recent advancements in Monte Carlo strategies for improving inference in deep latent variable models.
  • To address the limitations of the standard evidence lower bound (ELBO) when the variational family is insufficiently rich.

Main Methods:

  • Review of recent importance sampling, Markov chain Monte Carlo (MCMC), and sequential Monte Carlo (SMC) strategies.
  • Focus on techniques that provide unbiased, low-variance Monte Carlo estimates of the evidence to tighten variational bounds.

Main Results:

  • These advanced Monte Carlo methods offer a generic strategy to tighten evidence lower bounds (ELBOs) in DLVMs.
  • The reviewed techniques enhance the accuracy of posterior distribution approximations in complex models.

Conclusions:

  • Recent Monte Carlo sampling techniques are crucial for overcoming the intractability of likelihoods in deep latent variable models.
  • These methods provide a pathway to more robust and accurate Bayesian inference in machine learning applications.