How deeply does Math and Architectures of Deep Learning cover law of large numbers?

Defines convergence informally, explains finite-sample uncertainty, and relates required sample size to variance without specifying a threshold.

Law of large numbers

As explained in Math and Architectures of Deep Learning

A probabilistic principle stating that sample averages converge toward the expected value as the number of samples grows.

The law of large numbers says that averaging many samples from a probability distribution produces a value close to the distribution’s expected value. With infinitely many samples, the average matches the mean; with finite samples, closeness is probable rather than guaranteed. section 5.8

This principle explains why the sample mean can estimate an unknown distribution’s true mean. No universal sample count defines “enough”: distributions with larger variance require more samples for a similarly reliable approximation. section 5.8

Casino outcomes

A casino can lose individual bets while still making money overall when its win probability is slightly higher. Across a very large number of bets, the average outcome approaches the expected casino advantage. section 5.8

How Math and Architectures of Deep Learning covers it

Cover of Math and Architectures of Deep Learning

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Related concepts

independencecontrasts with · Two events or random quantities are independent when knowing the outcome or value of one does not change the probability or distribution of the other.
meanmeasures · A mean is a measure of central tendency, calculated as the arithmetic average of values or, for a random variable, as the probability-weighted average of its possible values.
varianceused by · Variance is the expected squared deviation of a random variable from its mean, measuring the spread of its distribution.

This explainer was generated by Manning's knowledge graph from the text of Math and Architectures of Deep Learning. The section links point to the parts of the book it draws on.