Parametric model A statistical model is parametric if the probability distribution of $X$ belongs to some family of distributions indexed by some parameter $\theta$ of finite dimension. Definition: Parametric model A parametric model is a set of probability distributions $\mathcal{P} = \{P_\theta, \theta \in \Theta\}$ with $\Theta \subset \mathbb{R}^d$ for some finite dimension $d$. Our main goal is to use the observations $X_1, \dots, X_n$ to learn the value of $\theta$. Note that it is possible to do so only if each probability distribution $P_\theta \in \mathcal{P}$ is defined by a unique parameter $\theta$. ...

The pinhole model The first very simple way to acquire images is with the pinhole model. Here, part of the light coming from the object passes through a small aperture $O$ and is projected onto the focal plane. We do this so that each point of the object is represented by a ray. Otherwise, the image would not be formed. The distance $f$ is called the focal length. Let’s suppose we have the following model to describe the pinhole: ...

Page Rank Let $G = (V, E)$ be a web graph. Each node $v \in V$ represents a web page, while there is a directed edge from $u \in V$ to $v \in V$ if $u$ has a hyperlink to $v$. The importance of $v$ is proportional to the importance of nodes linking to $v$. Let $\delta_\text{in}(v)$ and $\delta_\text{out}(v)$ be the in and out degrees of $v$ in $G$. Then we can define the matrix $M$ as follows: ...

The problem For some time, I’ve had the premium subscription of Spotify and it has been great. However, often times there are songs that I wish I could listen to which are simply not available in Spotify’s library. Fortunately for us, Spotify has this nice feature where you can use its client to listen to local files. In other words, we can listen to music that is not available on Spotify by simply downloading and importing it. Of course, using this feature has its own problems, like syncing the local files between your devices. I will not be discussing these issues here, though. ...

Warning If the LaTeX below does not render correctly, please refresh the page. Also, do not forget to set the math renderer in MathJax configurations, as shown in the figure below. The configurations window can be accessed by right-clicking on any LaTeX element. Introduction Currently the exponential advance of technology is no longer a surprise, but rather an inherent characteristic of the modern world. Even though this evolution constantly enhances devices, it does not do so in a homogeneous way, creating a world where the distribution of computational power is asymmetric. In this scenario, the ability to safely delegate hard computations to a powerful third party becomes very attractive. Studies in Verifiable Computation address this problem seeking to provide a series of important guarantees. The most important and intuitive one is that the verification must be easier than the computation of the function delegated (if this was not the case, the client should just perform the computation himself). Depending on the scheme implemented, other interesting qualities may be provided, such as public verification (in contrast, some settings may require a designated verifier that is trusted with secret information). ...