Log-Likelihood Gradient
The gradient of the log-likelihood which is used in Maximum Likelihood Estimation can be decomposed into the following: Where is the unnormalized probabilioty density and is the partition function. This is well-known as the decomposition into the positive phase and negative phase of learning. Due to the reliance of the partition function on the parameters, learning models by maximum likelihood is particularly difficult.
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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
Pseudolikelihood
Log-Likelihood Gradient
Log-Likelihood Gradient
Normalizing Model Outputs
A model produces unnormalized scores for three possible outcomes: {Outcome A: 8, Outcome B: 10, Outcome C: 2}. To convert these scores into a valid probability distribution, a normalization constant must be calculated by summing all the unnormalized scores. What is the final, normalized probability for Outcome B?
Computational Cost of Normalization