∫ntegrabℓε ∂iﬀerentiαℓs · unorganised notes, code, and writings of random topics

Arpa's trick explained

April 27, 2022 blog code

Recently I encountered with the problem of range minimum query (RMQ) and there are many ways to solve it, depending on the trade off between preprocessing complexity and per-query runtime complexity. Block-paritioning and a sparse table would be clever techniques. A hybrid of both would need some more code but... [more]

Dash, Flask, and WebSocket

April 26, 2022 blog system

In Python, Django is the most popular web framework. Second comes to Flask. What Flask is handy to do is to create some RESTful APIs by defining the web endpoints and the handlers. The frontend, however, is not something Django or Flask can provide to you. The best they can... [more]

Bengio et al (2003) A Neural Probabilistic Language Model

April 8, 2022 paper

Language model has the curse of dimensionality, namely, if we want to model the joint distribution of 10 words in a vocabulary of \(10^5\), there are \(10^{5\times 10} = 10^{50}\) parameters. But if the variables are continuous, we can use fewer parameters. [more]

Sampling and Visualizing Copulae

April 2, 2022 blog code math

Copula is a multivariate CDF defined over \(C: [0,1]^d \mapsto [0,1]\), [more]

Gaussian Process Regression

March 15, 2022 blog math

Gaussian process regression is an interesting method of function regression. It is non-parametric, meaning not to assume anything (linear, polynomial, etc.) about the objective function. Let’s consider a function of \(\mathbb{R}\mapsto\mathbb{R}\). Without knowing anything or assuming anything, the fuction \(f(x)\) can take, and maps to, any value in \(\mathbb{R}\). We... [more]