Maximum likelihood estimation
Maximum likelihood estimation is a statistical method that selects parameter values maximizing the likelihood of observed data under a specified probabilistic model.
Math and Architectures of Deep Learning
A parameter-estimation method that chooses values maximizing the likelihood of the observed data under a probabilistic model.
- How it is used
- Fits probability-model parameters from observed training data, especially for unsupervised distributions and supervised optimization.
- How deep it goes
- Derives Gaussian closed-form estimates, presents negative-log-likelihood optimization, and distinguishes iterative Gaussian-mixture fitting.
- Examples
- Uses adult-height samples to fit a Gaussian and PyTorch code to calculate a height-range probability.
- What you can do after
- Apply it via PyTorch to estimate Gaussian parameters from samples and evaluate probabilities of value ranges.
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Statistics Slam Dunk
Maximum likelihood estimation is a parameter-estimation method that selects values maximizing the likelihood of the observed data under a model.
- How it is used
- Uses likelihood-based logistic regression to classify playoff qualification without producing impossible probabilities.
- How deep it goes
- Defines the logit equation and demonstrates glm() fitting, then defers broader model-result evaluation.
- Examples
- Demonstrates playoff prediction from z_o_pts and compares it with a model using z_pts.
- What you can do after
- Apply it via base R glm() to fit binary models and evaluate thresholded playoff predictions.
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Causal AI
Maximum likelihood estimation selects parameter values that maximize the probability or likelihood of the observed data.
- How it is used
- Estimates probability-distribution parameters from observed data, including conditional probability tables in a causal graphical model.
- How deep it goes
- Defines the objective, explains log-likelihood and optimization, and works through categorical count proportions without deriving a general optimizer.
- Examples
- Uses a conditional probability estimated from categorical counts and the default estimator in pgmpy’s BayesianNetwork.fit.
- What you can do after
- Apply it via pgmpy’s BayesianNetwork.fit to estimate categorical conditional probability tables, or recognize when numerical optimization is needed.
Grokking Statistics
A parameter-estimation technique that selects parameter values maximizing the likelihood of the observed data.
- How it is used
- Fits logistic-regression coefficients by maximizing the likelihood of observed binary outcomes.
- How deep it goes
- Defines likelihood fitting and contrasts it with least squares, but defers the mathematical derivation to libraries.
- Examples
- Uses hours without a nap, toddler meltdown outcomes, a fitted curve, and a predicted probability at 4.78 hours.
- What you can do after
- Apply it via scikit-learn to fit logistic-regression parameters and predict probabilities from observed data.
Read how Grokking Statistics explains maximum likelihood estimation →
Related concepts
- logistic regressionused by · Logistic regression is a statistical classification model that estimates categorical outcome probabilities by applying a logistic or softmax function to a linear combination of input features.
- likelihooduses · A likelihood is the probability of observed data under a specified probabilistic model, regarded as a function of candidate hypotheses or parameter values.
- optimizationuses · Optimization is the systematic selection or adjustment of values, actions, or system designs to improve a specified objective, often subject to constraints.
- ordinary least squaresequivalent to · Ordinary least squares is a regression parameter-estimation method that minimizes the sum of squared residuals between observed and predicted responses.
- categorical distributionequivalent to · A categorical distribution is a discrete probability distribution over a finite set of mutually exclusive categories or outcomes.
- bayesian statisticscontrasts with · 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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