Daniel Daza

Visualizing sequential Bayesian learning

In this notebook we will examine the problem of estimation given observed data from a Bayesian perspective. We start by gathering a dataset $\mathcal{D}$ consisting of multiple observations. Each observation is independent and drawn from a parametric probability distribution with parameter $\mu$. We can thus write the probability of the dataset... Read more

Neural networks from scratch with NumPy

Neural networks are very popular function approximators used in a wide variety of fields nowadays and coming in all kinds of flavors, so there are countless frameworks that allow us to train and use them without knowing what is going on behind the scenes. So I set out to reinvent the wheel and decided to write a post deriving the math for backpr... Read more

Sequential Bayesian linear regression

When we perform linear regression using maximum likelihood estimation, we obtain a point estimate of the parameters $\mathbf{w}$ of the linear model. The Bayesian approach to this problem is to treat the parameters of the model as random variables for which we have a prior belief on their uncertainty, corresponding to the distribution $p(\mathbf... Read more

Maximum a posteriori signal detection

Digital signals are all around us. From the phone in our pockets to the massive infrastructure behind the Internet, they have enabled a wide variety of technologies, yet it is easy to take them for granted. We sometimes think of them as strings of zeros and ones traveling in a clear stream of data, but the truth is that as there are digital sign... Read more

Dimensionality reduction and classification with Fisher's linear discriminant

In this notebook we will deal with two interesting applications of Fisher’s linear discriminant: dimensionality reduction, and classification. This discriminant is formulated so that an appropriate projection of the data is found, so that the distance between points of different classes is maximized and the distance between points of the same cl... Read more