Weighted average
A weighted average is an average in which each value contributes according to an assigned numerical weight.
Experimentation for Engineers
A weighted average is an average in which each value contributes in proportion to an assigned weight.
- How it is used
- Uses weighted averages to estimate CPU time at unmeasured parameter values during experimental optimization.
- How deep it goes
- Defines normalization and proximity weighting, then connects them to squared-exponential kernels and a Gaussian-process implementation.
- Examples
- Works through CPU-time measurements at parameters 0.5 and 0.0, estimating values near 0.4 and 0.25.
- What you can do after
- Apply it via NumPy to construct proximity-weighted estimates from measured parameter–outcome pairs.
Read how Experimentation for Engineers explains weighted average →
Math for Web Design
A weighted average is an average in which each value contributes according to an assigned numerical weight.
- How it is used
- Uses weighted contributions to calculate grayscale colors, transparency results, and smooth animation paths.
- How deep it goes
- Explains coefficients and formulas through color and animation examples, without developing weighted-average theory beyond these applications.
- Examples
- Demonstrates RGB grayscale coefficients, a half-transparent blue square over red, and quadratic Bézier control-point weighting.
- What you can do after
- Apply weighted calculations to build grayscale colors, understand transparency results, and interpret Bézier animation paths.
Inside Deep Learning: Math, Algorithms, Models
An average in which each term is multiplied by a weight before summation.
- How it is used
- Uses weighted averages to combine item-level representations into one attention-based representation for bag classification.
- How deep it goes
- Explains the formula, tensor alignment, normalization, and Combiner implementation, but stops short of deriving the attention scores.
- Examples
- Demonstrates three digit images, learned attention scores, feature vectors, and a plotted weighted bag representation workflow.
- What you can do after
- Apply it via PyTorch by building a Combiner that aggregates normalized attention-weighted feature vectors.
Read how Inside Deep Learning: Math, Algorithms, Models explains weighted average →
Deep Learning with R, Third Edition
A weighted average is an average in which each value contributes according to an associated numerical weight.
- How it is used
- Combines classifier predictions at inference time to form a stronger ensemble result.
- How deep it goes
- Explains unequal prediction weights and validation-set optimization, but does not provide a mathematical derivation.
- Examples
- Uses four classifier prediction vectors combined with weights of 0.5, 0.25, 0.1, and 0.15.
- What you can do after
- Apply weighted averaging to classifier predictions and tune weights on validation data with random search or Nelder–Mead.
Read how Deep Learning with R, Third Edition explains weighted average →
Deep Learning with Python, Third Edition
An averaging operation that assigns different weights to different values before combining them into a single result.
- How it is used
- Combines classifier predictions at inference time to build an ensemble.
- How deep it goes
- Defines equal and learned weighting, demonstrates implementation, and stops short of deriving the optimization algorithms.
- Examples
- Uses four classifier prediction arrays with equal weights and with weights of 0.5, 0.25, 0.1, and 0.15.
- What you can do after
- Apply it via validation-data weight optimization to combine classifier predictions into a strong ensemble baseline.
Read how Deep Learning with Python, Third Edition explains weighted average →
Related concepts
- vector spaceused by · A vector space is a set equipped with vector addition and scalar multiplication over a field that satisfy the vector-space axioms.
- accuracyconfigured by · Accuracy is the degree to which an output, prediction, or measurement agrees with a correct or reference outcome under a specified criterion.
- inner productequivalent to · An inner product is a scalar-valued operation on two vectors that combines their corresponding components, summing their products and, for complex vectors, using conjugation.
- exponential moving averageused by · An exponential moving average is a recursively updated weighted average that gives greater influence to recent observations while exponentially decreasing the influence of older ones.
These guides are generated from the text of Manning books by Manning's knowledge graph and link to the sections they draw on. The full books are available on liveBook and at manning.com.