Binary random variable
A binary random variable is a random variable that takes exactly two possible values, often represented as zero and one.
Statistics Every Programmer Needs
A binary decision variable is a decision variable restricted to the values zero and one to represent a yes-or-no choice.
- How it is used
- Distinguishes a two-category logistic-regression outcome from yes-or-no feature-selection decisions in optimization.
- How deep it goes
- Works through class coding and Python bounds construction, but does not develop a probability distribution for the binary outcome.
- Examples
- Uses Kecimen-versus-Besni raisin labels and selected-versus-excluded project features.
- What you can do after
- Apply it via pandas class mapping or configure 0–1 bounds for feature-selection variables.
Read how Statistics Every Programmer Needs explains binary random variable →
Math and Architectures of Deep Learning
A variable restricted to two possible values, used here to encode yes/no logical states in machine inputs and outputs.
- How it is used
- Encodes yes/no states and supplies categorical inputs or outputs for logical functions and classifiers.
- How deep it goes
- Defines binary variables as two-category quantities and connects them to logical operators and classifier outputs, without developing probability.
- Examples
- Uses stock-selling advice, face detection, cat threat decisions, self-driving braking, and logical operator diagrams.
- What you can do after
- Evaluate/understand how machine-learning systems represent and combine yes/no decisions as categorical values.
Read how Math and Architectures of Deep Learning explains binary random variable →
Machine Learning Algorithms in Depth
A binary random variable is a random variable restricted to two possible values, here −1 and +1.
- How it is used
- Models coin-flip outcomes for posterior inference and hidden pixel states for image denoising.
- How deep it goes
- Derives Bernoulli moments and likelihood, then uses binary-state means within a mean-field approximation.
- Examples
- Uses coin flips and noisy binary images, including a mean-field image-denoising implementation.
- What you can do after
- Apply it via mean-field variational inference to estimate binary pixel states from noisy observations.
Read how Machine Learning Algorithms in Depth explains binary random variable →
Related concepts
- maximum likelihood estimationused by · Maximum likelihood estimation is a statistical method that selects parameter values maximizing the likelihood of observed data under a specified probabilistic model.
- linear regressionused by · Linear regression is a statistical modeling method that estimates a continuous response as a linear combination of predictor variables and fitted coefficients.
- decision variablekind of · A decision variable is a quantity whose value is chosen by an optimization model to represent an available decision.
- sigmoidused by · A sigmoid is a smooth, bounded, S-shaped function that maps real-valued inputs between two limiting values, commonly zero and one.
- polynomial functionused by · A polynomial function is a function expressible as a finite sum of constant multiples of nonnegative integer powers of one or more variables.
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.