Machine Learning for function parameter estimation

Hi everyone,

I'm currently trying to use machine learning, in particular ANN to give parameter estimation of a function. For my data, i have classified the input conditions, as well as its corresponding fitting parameters which I would like to extract as outputs. I have two cases that I would like to investigate: (1) all data assumes the same form of function, (2) depending on the data, the corresponding function and thus fitting parameter is different. To give more context, the data were modelled using a mixture of log-normal functions, depending on the shape of the distribution, a sum of 1-3 log-normals are used. Since I'm new to this field, how should I approach the problem? Moreover, since I have multiple outputs that I'd like to extract is it better to create multiple ANN?

Answer 1

[Ayush]

Hey Jonathan,

I understand that you're working with Artificial Neural Networks (ANNs) for figuring out function parameters, and you're looking into two main types of tasks. Here's a simpler way to approach them:

Case 1: All Data Assumes the Same Form of Function

In this scenario, you can design an ANN that takes the input conditions as inputs and predicts the parameters of the log-normal functions as outputs.

Data Preparation: Organize your data into a format where each input condition is a feature vector, and each output is a parameter of the log-normal functions

Model Design: Design an ANN with an input layer matching the number of input features, several hidden layers (the number and size of these can be determined experimentally), and an output layer with neurons equal to the number of parameters you wish to predict. For example, if each data point is modeled using two log-normals, each with parameters mean (μ) and standard deviation (σ), your output layer should have four neurons

At last, Train the ANN using your dataset, adjusting hyperparameters as necessary to improve performance.

Case 2: Data Corresponds to Different Functions

Train separate ANNs for each structure of the model (one for data modeled by one log-normal, another for data modeled by two log-normals, etc.). This requires you to classify or otherwise determine the structure before choosing which ANN to use for parameter estimation.

Even if you're looking to predict several parameters, you don't necessarily need more than one ANN. Modern ANNs can predict many things at once as long as you set up the final layer correctly and choose a good method for measuring how well it's doing.

I hope this makes things clearer! If you're curious to learn more, a good resource is the MathWorks page on

https://in.mathworks.com/help/deeplearning/deep-learning-fundamentals.html.

Regards