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Maximum Likelihood Estimator Properties
- The true distribution must lie within the model family . Otherwise, no esitmator can recover .
- The true distribution must correspond exactly to one value of . Otherwise, the maximum likelihood can recover the correct but will not be able to determine which value of was used by the data generating process.
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Relationship between KL Divergence and MLE
Cross-entropy loss
Mean Squared Error
The property of consistency of maximum likelihood
Statistical Efficiency Principal of MLE
Maximum Likelihood Estimator Properties
Log-Likelihood Gradient
Maximum Likelihood Training Objective for a Dataset of Sequences
Kullback-Leibler Divergence
Model Selection via Likelihood
Training Objective as Loss Minimization over a Dataset
Mathematical Equivalence of General and Sequential MLE Objectives
A researcher is modeling a series of coin flips. They observe the following sequence of outcomes: Heads, Tails, Heads, Heads. The researcher wants to find the best parameter for their model, where the parameter represents the probability of the coin landing on Heads. According to the principle of maximum likelihood estimation, which of the following parameter values best explains the observed data?
Parameter Estimation via Conditional Log-Likelihood Maximization
Equivalence of Maximizing Likelihood and Minimizing Loss
Equivalence of Squared Loss and Maximum Likelihood Estimation
Negative Log-Likelihood Objective for Softmax Regression