CS PhD student in the Laboratory of Computational Neuroscience at EPFL || Personal website: https://sites.google.com/view/modirsha

To compare researchers with each other¹, we need to have a measure that can represent how influential and successful they have been by a single number. One way to do so is to look at how many times their articles have been cited and count their total number of citations (*N*). A more complex way is to calculate their h-index (*h*) which is supposed to also take into account how these *N *citations are distributed across papers of a researcher.

A recent discussion with a few of my friends made me think about the h-index and what it really means…

*WARNING:** This article is not supposed to be scientifically precise. Rather, it is a playful discussion about an imaginary scenario inspired by scientific findings*

It is generally believed that dopamine is what makes us feel happy and pleased, and there is scientific evidence for the release of dopamine at the time of accomplishing something or receiving rewards. …

In a finite Markov Decision Process (MDP), the optimal policy is defined as a policy that maximizes the value of all states at the same time¹. In other words, if an optimal policy exists, then the policy that maximizes the value of state *s *is the same as the policy that maximizes the value of state *s'.*²* *But why should such a policy exist?

The famous introductory book of Sutton and Barto on reinforcement learning¹ takes the existence of optimal policies for granted and let this question unanswered. …

A lady claims that she can find out whether tea or milk is added first to a cup of milk-tea, only by tasting it. How can we evaluate her claim? Through solving this problem, known as the lady tasting tea problem, Sir Ronald Fisher introduced the notions of hypothesis testing and p-value for the first time.

In this article, I revisit Fisher's solution (i.e. the frequentist approach), use a Bayesian approach for the problem of lady tasting tea, and compare their results.

Given a cup of milk-tea, we assume that the lady would guess the right answer (i.e. whether tea…

In the absence of a distance, “close” and “far” are meaningless. To define these notions over a set of abstract mathematical objects, we need to be able to measure the distance between each pair of them. The question is: If the abstract mathematical objects are random variables, then how should we measure the distance between them?

Correlation distance is a popular way of measuring the distance between two random variables with finite variances¹. If the correlation² between two random variables is *r*, then their correlation distance is defined as *d=1-r*. However, a proper distance measure needs to have a few…

*“X₂ *and *X₃* both increase when *X₁ *increases”; if there is a deterministic relation between these variables, then such a statement logically implies that “*X₂* increases also when *X₃ *increases”*. *However, as soon as we move to a probabilistic setting and add the adverb “on average” to the first statement, the implication is not true anymore!

In a probabilistic setting, *Xi'*s are random variables, and “on average increase” is equivalent to a positive correlation. Consider a simple exemplar setting and assume that the correlation between *X₁* and *X₂* and the correlation between *X₁ *and* X₃ *are the same and equal…