Visualizing regularization and the L1 and L2 norms

If you’ve taken an introductory Machine Learning class, you’ve certainly come across the issue of overfitting and been introduced to the concept of regularization and norm. I often see this being discussed purely by looking at the formulas, so I figured I’d try to give a better insight into why exactly minimising the norm induces regularization — and how L1 and L2 differ from each other — using some visual examples.

Prerequisite knowledge

  • Linear regression
  • Gradient descent
  • Some understanding of overfitting and regularization

Topics covered

  • Why does minimizing the norm induce regularization?
  • What’s the difference between the L1 norm and the L2 norm?

Recap of regularization

Using the example of linear regression, our loss is given by the Mean Squared Error (MSE):

Image for post

and our goal is to minimize this loss:

Image for post

To prevent overfitting, we want to add abias towards less complex functions.That is, given two functions that can fit our data reasonably well, we prefer the simpler one. We do this by adding a regularization term, typically either the L1 norm or the squared L2 norm:

Image for post

#overfitting #data-science #regularization #machine-learning #norms

What is GEEK

Buddha Community

Visualizing regularization and the L1 and L2 norms

Visualizing regularization and the L1 and L2 norms

If you’ve taken an introductory Machine Learning class, you’ve certainly come across the issue of overfitting and been introduced to the concept of regularization and norm. I often see this being discussed purely by looking at the formulas, so I figured I’d try to give a better insight into why exactly minimising the norm induces regularization — and how L1 and L2 differ from each other — using some visual examples.

Prerequisite knowledge

  • Linear regression
  • Gradient descent
  • Some understanding of overfitting and regularization

Topics covered

  • Why does minimizing the norm induce regularization?
  • What’s the difference between the L1 norm and the L2 norm?

Recap of regularization

Using the example of linear regression, our loss is given by the Mean Squared Error (MSE):

Image for post

and our goal is to minimize this loss:

Image for post

To prevent overfitting, we want to add abias towards less complex functions.That is, given two functions that can fit our data reasonably well, we prefer the simpler one. We do this by adding a regularization term, typically either the L1 norm or the squared L2 norm:

Image for post

#overfitting #data-science #regularization #machine-learning #norms

Arvel  Parker

Arvel Parker

1591177440

Visual Analytics and Advanced Data Visualization

Visual Analytics is the scientific visualization to emerge an idea to present data in such a way so that it could be easily determined by anyone.

It gives an idea to the human mind to directly interact with interactive visuals which could help in making decisions easy and fast.

Visual Analytics basically breaks the complex data in a simple way.

The human brain is fast and is built to process things faster. So Data visualization provides its way to make things easy for students, researchers, mathematicians, scientists e

#blogs #data visualization #business analytics #data visualization techniques #visual analytics #visualizing ml models

Arvel  Parker

Arvel Parker

1591184760

Visual Analytics Services for Data-Driven Decision Making

Visual analytics is the process of collecting, examining complex and large data sets (structured or unstructured) to get useful information to draw conclusions about the datasets and visualize the data or information in the form of interactive visual interfaces and graphical manner.

Data analytics is usually accomplished by extracting or collecting data from different data sources in the form of numbers, statistics and overall activity of any organization, with different deep learning and analytics tools, which is then processed using data visualization software and presented in the form of graphical charts, figures, and bars.

In today technology world, data are reproduced in incredible rate and amount. Visual Analytics helps the world to make the vast and complex amount of data useful and readable. Visual Analytics is the process to collect and store the data at a faster rate than analyze the data and make it helpful.

As human brain process visual content better than it processes plain text. So using advanced visual interfaces, humans may directly interact with the data analysis capabilities of today’s computers and allow them to make well-informed decisions in complex situations.

It allows you to create beautiful, interactive dashboards or reports that are immediately available on the web or a mobile device. The tool has a Data Explorer that makes it easy for the novice analyst to create forecasts, decision trees, or other fancy statistical methods.

#blogs #data visualization #data visualization tools #visual analytics #visualizing ml models

Visual Perception

Why do we visualize data?

It helps us to comprehend _huge _amounts of data by compressing it into a simple, easy to understand visualization. It helps us to find hidden patterns or see underlying problems in the data itself which might not have been obvious without a good chart.

Our brain is specialized to perceive the physical world around us as efficiently as possible. Evidence also suggests that we all develop the same visual systems, regardless of our environment or culture. This suggests that the development of the visual system isn’t solely based on our environment but is the result of millions of years of evolution. Which would contradict the tabula rasa theory (Ware 2021 ). Sorry John Locke. Our visual system splits tasks and thus has specialized regions that are responsible for segmentation (early rapid-processing), edge orientation detection, or color and light perception. We are able to extract features and find patterns with ease.

It is interesting that on a higher level of visual perception (visual cognition), our brains are able to highlight colors and shapes to focus on certain aspects. If we search for red-colored highways on a road map, we can use our visual cognition to highlight the red roads and put the other colors in the background. (Ware 2021)

#data-visualization #gestalt-principles #visualization #data-science #visual-variables

Critiquing DataVisualization

Visualization is an interactive representation of (abstract, complex) data that can help human to perform the task more effectively. It helps us see patterns in broader contexts that specific statistical questions do not reveal. Also, it helps us drive insights and questions that even predefined analytical queries do not elicit.

In this blog post, I will critique one good and one bad visualization.

Good Visualization:

In the below visualization, the three maps accurately show the life expectancy in the years 1800, 1950 and 2015. We can easily interpret how life expectancy has changed over the last three centuries. In the year 1800, people could expect a life span of only 25–40 years, irrespective of the location of their birth. As the new century (1950) began, newborns had the chance of longer life (over 60 years) but it is highly dependent on the location of their birth. People in continents like North America have a higher life expectancy as compared to people born in Asia. In recent decades every country has made very substantial progress in health and many other aspects.

Image for post

Life Expectancy in 1800, 1950 and 2015 [source]

Globally the life expectancy increased from less than 30 years to over 72 years; after two centuries of the progress, we can expect to live even twice as long as our ancestors.

#visualization #data-visualization #visual studio code #visual studio