![]() Why do we “minimize the negative log likelihood” instead of “maximizing the likelihood” when these are mathematically the same? It’s because we typically minimize loss functions, so we talk about the “negative log likelihood” because we can minimize it. Side Note on Maximum Likelihood Estimation (MLE) Reference for Setup, Likelihood, and Negative Log Likelihood: “Cross entropy and log likelihood” by Andrew Webb The negative log likelihood is then, literally, the negative of the log of the likelihood: One way of choosing good parameters to solve our task is to choose the parameters that maximize the likelihood of the observed data: We want to choose the member of the family that has a good set of parameters for solving our particular problem of –>. Our chosen architecture represents a family of possible models, where each member of the family has different weights (different parameters) and therefore represents a different relationship between the input image x and some output class predictions y. Let’s say we’ve chosen a particular neural network architecture to solve this multiclass classification problem – for example, VGG, ResNet, GoogLeNet, etc. Problem Setup: Multiclass Classification with a Neural Networkįirst we will use a multiclass classification problem to understand the relationship between log likelihood and cross entropy. In multilabel classification we want to assign multiple classes to an input, so we apply an element-wise sigmoid function to the raw output of our neural network. The short refresher is as follows: in multiclass classification we want to assign a single class to an input, so we apply a softmax function to the raw output of our neural network. If you are not familiar with this topic, please read the article Multi-label vs. ![]() Thorough understanding of the difference between multiclass and multilabel classification.If you would like more background in this area please read Introduction to Neural Networks. Basic understanding of neural networks.If you are not familiar with the connections between these topics, then this article is for you! sigmoid cross-entropy loss, maximum likelihood estimation, Kullback-Leibler (KL) divergence, logistic regression, and neural networks. This article will cover the relationships between the negative log likelihood, entropy, softmax vs. ![]()
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