Model fitting, the perceptron and backpropagation (lectures 4-5-6)

12 Questions

What type of model tends to favor simpler models?

Bayesian Informations criteria

Which method is based on Bayes' theorem and combines evidence with expectations?

Optimizer

What is the main function of an optimizer or minimizer?

Find the point where the minimum is

What does a perceptron model represent in artificial intelligence?

A model of how neurons work

In neural networks, what aspect does the activation function control?

Output generation

Which feature was part of neuroscience but does not belong in the domain of artificial intelligence modeling?

Spatial complexity

What does the phrase 'All models are wrong, but some models are useful' mean?

Models are always inaccurate, but they can still be helpful in understanding specific problems.

What is the key difference between descriptive models and process models?

Descriptive models focus on fitting the data, while process models focus on the underlying cognitive or neural processes.

According to Occam's razor, which model should be preferred if two models accurately describe the data?

The model with fewer parameters, as it is less likely to fit the noise in the training data.

What is the main issue with overfitting, and how can it be avoided?

Overfitting occurs when the model starts fitting the noise in the training data, which can lead to poor performance on new, unseen data. It can be avoided by using cross-validation and information criteria to penalize model complexity.

What is the purpose of cross-validation in model comparison?

Cross-validation is used to split the data into training and test sets, in order to evaluate how well the model generalizes to new, unseen data.

What is the role of information criteria in model comparison?

Information criteria are used to penalize the number of parameters in a model, in order to avoid overfitting.

Study Notes

Model Fitting

All models are approximations of the world and are never 100% accurate, but they can be useful for understanding specific problems.
Descriptive models aim to fit the data and provide insights about the data itself.
Process models provide information about the underlying process and can be generative, but are harder to formulate.

Occam's Razor

If two models accurately describe the data, the simpler one is preferred.
This is because simpler models are more likely to generalize and less likely to overfit the data.

Overfitting

Overfitting occurs when a model has too many parameters and fits the noise in the training data, rather than the underlying pattern.
This can be avoided by using cross-validation, information criteria, and Bayesian information criteria.

Model Evaluation

Cross-validation involves evaluating the model on multiple subsets of the data.
Information criteria involve penalizing models with more parameters.
Bayesian information criteria tend to favor simpler models.

Maximum Likelihood

Maximum likelihood is based on Bayes' theorem and combines evidence with prior expectations.
It involves finding the parameters that maximize the likelihood of the data.

Optimizers

An optimizer, also known as a minimizer, finds the best parameters for a model.
Simple optimizers perform grid search, which can be computationally expensive.
Gradient descent is a more efficient optimizer that quickly finds the minimum log likelihood.

Good Model Characteristics

Accuracy: how well the model fits the data.
Understanding: how well the model's components are understood and relate to the predicted outputs.

Perceptron and Neural Networks

A perceptron is a simple model of a neuron that takes an input, scales it by a weight, and applies an activation function.
The perceptron is a classification model that outputs a binary decision.
Neural networks are composed of multiple perceptrons and are organized in a hierarchical manner, with lower levels being more sensory and higher levels being more integrative.
Feedback connections are important in neural networks and are involved in predictive coding.

Artificial Neural Networks

Artificial neural networks are inspired by the brain, but are simplified to focus on input-output transformations.
They do not capture the temporal dynamics and spatial complexity of real neural networks.
They are used for classification and other tasks, and are trained using forward propagation, backpropagation, and repeat.