Likelihood
A likelihood is the probability of observed data under a specified probabilistic model, regarded as a function of candidate hypotheses or parameter values.
Math and Architectures of Deep Learning
A function of model parameters measuring how probable observed data are under those parameters.
- How it is used
- Supports parameter estimation by scoring training data under candidate model parameters.
- How deep it goes
- Derives independent-data likelihoods, Gaussian forms, negative log-likelihood optimization, and Bayesian posterior roles.
- Examples
- Uses Gaussian mean and variance fitting, PyTorch gradient descent, and class selection in Gaussian mixture models.
- What you can do after
- Apply it via PyTorch to minimize Gaussian negative log-likelihood and estimate model parameters.
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Fabulous Adventures in Data Structures and Algorithms
A likelihood function expresses the plausibility of observed data as a function of a hypothesis or model parameter.
- How it is used
- Models observations conditional on a cause so a prior can produce joint and posterior distributions.
- How deep it goes
- Develops a C# conditional-distribution function, constructs integer-weight joint distributions, and derives posteriors by filtering and projection.
- Examples
- Uses cold-and-sneezing survey data, a rare-condition medical test, and two independent d20 rolls.
- What you can do after
- Build it from scratch with C# categorical distributions to combine priors and likelihoods and compute posteriors from observations.
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Bayesian Optimization in Action
A likelihood function quantifies how compatible observed data are with different values of a model's parameters or latent quantities.
- How it is used
- Updates beliefs about quantities or hypotheses by combining prior beliefs with the compatibility of observed data.
- How deep it goes
- Explains likelihood through competing psychic hypotheses and repeated Bayesian updates, while treating Bayes’ theorem at a high level.
- Examples
- Uses nearby-house prices and repeated carnival guesses to contrast informative evidence, irrelevant evidence, and prior sensitivity.
- What you can do after
- Evaluate/understand how observed evidence changes beliefs under competing hypotheses and different prior probabilities.
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Build a Robo-Advisor with Python (From Scratch)
A likelihood is the probability of observed data conditional on a specified parameter value or hypothesis.
- How it is used
- Frames observed evidence as conditional probability for Bayesian updating.
- How deep it goes
- Defines likelihood through conditional probability and extends it to uncertain distribution parameters, without deriving posterior distributions.
- Examples
- Uses professional basketball membership and height, then generalizes to exponential-rate and normal-mean parameters.
- What you can do after
- Evaluate how observed evidence changes beliefs about hypotheses or uncertain distribution parameters.
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Causal AI
Likelihood is the probability of observed data viewed as a function of a candidate model parameter value.
- How it is used
- Uses observed data to estimate parameters for statistical, machine-learning, and causal models.
- How deep it goes
- Explains likelihood, log-likelihood, negative log-likelihood, regularization, and optimization, without deriving general closed-form estimators.
- Examples
- Uses regression weights, linear regression, neural networks, and L2 regularization as estimation examples.
- What you can do after
- Apply it via likelihood-based objectives, numerical optimization, and regularized loss functions when fitting models.
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.
- probability distributioncontrasts with · A probability distribution is a mathematical specification assigning probabilities to the possible values or outcomes of a random variable, with total probability one.
- cross entropy lossequivalent to · Cross-entropy loss measures the expected negative log probability that a predicted distribution assigns to outcomes drawn from a target distribution.
- bayesian statisticsused by · Bayesian statistics is a framework for statistical inference that combines prior probability distributions with observed-data likelihoods to update probabilities over hypotheses or unknown quantities.
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