How to compute the jacobian in derivatives in theano?

This recipe helps you to compute the jacobian in derivatives in theano.

Recipe Objective - How to compute the jacobian in derivatives in theano?

The term Jacobian refers to the tensor that contains the first partial derivatives of a function's output with regard to its inputs, as defined by Theano. Theano provides the theano.gradient.jacobian() macro, which does all of the calculations required to compute the Jacobian. We need to utilise scan to manually compute the Jacobian of a function y with respect to a parameter x. We compute the gradient of y[i] with respect to x by looping through the entries in y.

For more related projects -

/projects/data-science-projects/keras-deep-learning-projects
/projects/data-science-projects/neural-network-projects

Example -

# Import libraries
import theano
from theano import tensor

# Creating a vector
x = tensor.dvector('x')

# Creating 'y' expression
y = (2 * x ** 3)

# Computing derivative
Output, updates = theano.scan(lambda i, y, x : tensor.grad(y[i], x), sequences=tensor.arange(y.shape[0]), non_sequences=[y, x])

# Creating function
fun = theano.function([x], Output, updates=updates)

# Calling function
fun([3,3])

Output -
array([[54.,  0.],
       [ 0., 54.]])

In this way, we can compute the jacobian in derivatives in theano.

What Users are saying..

profile image

Ameeruddin Mohammed

ETL (Abintio) developer at IBM
linkedin profile url

I come from a background in Marketing and Analytics and when I developed an interest in Machine Learning algorithms, I did multiple in-class courses from reputed institutions though I got good... Read More

Relevant Projects

Build CNN for Image Colorization using Deep Transfer Learning
Image Processing Project -Train a model for colorization to make grayscale images colorful using convolutional autoencoders.

NLP Project for Multi Class Text Classification using BERT Model
In this NLP Project, you will learn how to build a multi-class text classification model using using the pre-trained BERT model.

Learn to Build an End-to-End Machine Learning Pipeline - Part 2
In this Machine Learning Project, you will learn how to build an end-to-end machine learning pipeline for predicting truck delays, incorporating Hopsworks' feature store and Weights and Biases for model experimentation.

PyTorch Project to Build a LSTM Text Classification Model
In this PyTorch Project you will learn how to build an LSTM Text Classification model for Classifying the Reviews of an App .

Credit Card Fraud Detection as a Classification Problem
In this data science project, we will predict the credit card fraud in the transactional dataset using some of the predictive models.

Build a Text Generator Model using Amazon SageMaker
In this Deep Learning Project, you will train a Text Generator Model on Amazon Reviews Dataset using LSTM Algorithm in PyTorch and deploy it on Amazon SageMaker.

Census Income Data Set Project-Predict Adult Census Income
Use the Adult Income dataset to predict whether income exceeds 50K yr based oncensus data.

Build a Multi-Class Classification Model in Python on Saturn Cloud
In this machine learning classification project, you will build a multi-class classification model in Python on Saturn Cloud to predict the license status of a business.

Credit Card Default Prediction using Machine learning techniques
In this data science project, you will predict borrowers chance of defaulting on credit loans by building a credit score prediction model.

Deep Learning Project- Real-Time Fruit Detection using YOLOv4
In this deep learning project, you will learn to build an accurate, fast, and reliable real-time fruit detection system using the YOLOv4 object detection model for robotic harvesting platforms.