The easier the problem, the poorer the solution

Source: Google Images

The predictions from logistic regression seem to be pretty unstable for training sets obtained from the same population!!! To introduce the issue let me first bring in the context where I faced it.

1. Context:

I was performing logistic regression on a dataset — response was credit default status (yes/no) for given credit balance (varying from 0–20000). The training sets were generated (simulated) via a governing logistic function itself. It was noticed that for the same simulating function, the fit scores for the training sets generated in different attempts were varying between 50% and…


Comparing two methods to keep your balance in classification

Source: Google Images

Context:

Handling dataset imbalance in classification problems is a very hot topic in the machine learning (ML) community. Here we refer to the imbalance in the proportion of samples for each response class. While going through ISLR by James, Witten, Hastie, Tibshirani — I came across this point and the approach to handle the adverse effects of such imbalances is by manipulating the threshold probability limit that decides the prediction decision boundary. The documentation of Logistic Regression in sklearn, however, introduced me to the concept of class-weights which seems to serve the…


A glance into the reality behind

Source: Google images

Abstract:

Categorical variables can be encoded either through ordinal (1, 2, 3, …) or one-hot (001, 010, 100, …) encoding schemes. For categorical variables that do not have any relevant ordering present, for e.g., (male, female and other) where none is greater than the other in any sense, using ordinal encoding might lead to issues because, the ordering inherent in (1, 2, 3) might find its way into the calculations. We will try to find out how real of a problem this is, does it have similar effects on both feature and response variables and what is the cause for this…


In the context of Linear Regression - a geometrical insight

Source: Google Images

Abstract:

Our assumption is that collinearity amongst the features, in the context of Linear Regression, does not affect the fit much. However it makes the coefficients of the fit tremendously uncertain and hence adversely affects the interpretability of the model. We will verify this assumption and then also provide a justification as to why is it so. The justification will contain a geometric insight into the reality behind.

Context:

This question rise from a Linear Regression that was being performed on a dataset. I observed that after I removed a perfectly collinear…


A geometrical interpretation of its inner workings

Image source: Google images and http://firsttimeprogrammer.blogspot.com/2015/04/fourier-series-and-square-wave.html

What this post is about? What you need to know?

In this post I will try to explain the intuition behind Fourier series expansion — why does it at all work, what is the motivation behind it. So I assume a certain knowledge about the basics of Fourier expansion, at least its principle, as a pre-requisite. A little exposure to vectors and their projections will also do (particularly that found in linear algebra courses although linear algebra is not needed). The motivation for writing this post comes from a portion of the book “Linear Algebra And Its Application” by Gilbert Strang.

A little context

Fourier series expansion is one of the ubiquitous tools…


Source: Google images

The recent event of Covid-19 in India and the Amphan cyclone storm in West Bengal have brought forth extreme suffering for the poor and under-privileged. The images of migrant labourers engaged in an endless walk and the homeless people shedding tears of despair speak of their plight. Along with these the word “empathy” seems to have become more frequent. However, before I start using, abusing or misusing that word I feel there is a need to understand that word in all its depth.

Hence I would take this opportunity to explore the word by taking a deeper look within myself…


Source: Google Images

Hello Readers,

Today’s journey will be, as the title suggests, “Mr. Newton’s journey to the gravitational law” — an imaginary journey with Mr. Newton as our guide. So you must be wanting to know what all we will face in this little adventure of ours. Hence, first some travel plans for you.

When in high-school, physics text books stated that prior to Newton there were Kepler’s laws of planetary motion. Based on these laws Newton discovered his celebrated “Universal theory of gravitation”. And one very common exercise of the text books was to derive Kepler’s laws out of Newton’s law…


Dear Readers,

After a long time I am writing to you. Another experience of mine to share with you; another one of my personal opinions to bring forth for your critical evaluation. And hope this turns out to be an enjoyable read for you.

For a long time I have wondered what is the proper way to study the basic sciences. In my very limited exposure to the vast field of science, I have struggled a lot. Struggled to find out what truly the dry equations or complexly phrased laws really mean. Struggled to imagine what train of thought leads…


How was an infinite number system created? A child’s musings

Dear Readers,

This will be an investigation into the number system becoming infinite. Just to warn any mathematics enthusiasts, this is an outcome of childish inquiry. So please do not expect any genuine mathematics here.

As a prologue to this journey, I have the habit of creating a story in my mind as to how the scientific community reached various conclusions. Whether this story has anything to do with historical reality, I never cared. You might find resonances of this habit in the journey we will be taking together shortly. After all it’s just for fun.

In order to board…


Dear Readers,

Please do not let the title intimidate you or get your hopes too high. This is not a hardcore scientific article; nor is the author a scientist himself.

We will just reflect on the way human beings have applied reason in their grand and age-old quest into science. Once we grasp the real nature of our scientific reasoning methodology, we will try to speculate its eventual fate.

Such a grand task attempted by someone not involved in any scientific endeavour is bound to have certain immature conclusions. …

Anirban Chakraborty

A science enthusiast and passionate philosopher in pursuit of truth.

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