hackmd-github-sync-badge Note: See Sect. 3 of cl_en.pdf in Computational Intelligence course for introduction on Linear Regression. 1. Linear Regression Linear regression is a statistical method used in supervised learning where the goal is to predict the value of a dependent variable $t$ based on the values of one or more independent variables $x$. The relationship between the dependent variable and the independent variables is assumed to be linear, i.e., it can be described using a linear function. The general form of a linear regression model is given by: $$

In this Section, we will organize and summarize key concepts about fully recurrent networks, the forward pass, derivatives, and visualization of computational graphs. We'll also provide mathematical equations, explanations, and illustrations for better understanding. A fully recurrent network (RNN) is a type of neural network designed for processing sequences of data, such as time-series data or text. Unlike traditional feed-forward networks, RNNs have connections that loop back on themselves, allowing the network to remember information from previous time steps. This property makes RNNs well-suited for sequential tasks like language modeling and speech recognition. The basic equations for a fully recurrent network are: $s(t) = W x(t) + R a(t-1)$ $a(t) = \tanh(s(t))$

Recommender systems are algorithms and software applications that suggest products, services, or information to users based on analysis of data. Typically, these systems predict user preferences based on various inputs, which can include past behavior (such as previously viewed products or purchased items), user profiles, or item information. Why Do We Need Recommender Systems? The necessity for recommender systems arises from several key challenges and opportunities in digital environments: Information Overload: As the amount of available information and the number of available products increase, it becomes overwhelming for users to sift through all possible options to find what they like or need. Recommender systems help by filtering out the noise and presenting a subset of items likely to be of interest. Personalization: In the digital world, where user experience is paramount, personalization is crucial. Recommender systems provide personalized experiences by delivering content or product suggestions tailored to individual users' preferences. Improved User Engagement: By showing users items that are more relevant to their tastes and needs, recommender systems increase the likelihood of user engagement, whether through longer sessions on a platform or through increased likelihood of purchase in e-commerce scenarios. Increase Sales and Revenue: For commercial platforms, such as online retailers and streaming services, recommender systems drive sales by suggesting relevant products or content to users, thereby increasing conversion rates and customer retention. Discovery of New Products: Recommender systems help users discover products or content that they may not have come across by themselves, enhancing user satisfaction and stickiness to the platform.

hackmd-github-sync-badge Central Limit Theorem The Central Limit Theorem (CLT) is a fundamental result in the field of statistics and probability theory. It provides a foundation for understanding why many distributions in nature tend to approximate a normal distribution under certain conditions, even if the original variables themselves are not normally distributed. The theorem states that, given a sufficiently large sample size, the distribution of the sample means will be approximately normally distributed, regardless of the shape of the population distribution, provided the population has a finite variance. The formula or the mathematical formulation of the CLT can be derived from the concept of convergence in distribution of standardized sums of independent random variables. Let's consider the classical version of the CLT to understand where the formula comes from: Consider a sequence of $n$ independent and identically distributed (i.i.d.) random variables, $X_1, X_2, ..., X_n$, each with a mean $\mu$ and a finite variance $\sigma^2$. The sample mean $\bar{X}$ of these $n$ random variables is given by: $$

Basics Understanding the concepts of expectation, bias, and variance is crucial for grasping fundamental statistical principles in machine learning. Here’s a beginner-friendly explanation: 1. Expectation The expectation (or expected value) is a core concept in probability theory and statistics, reflecting the average outcome one can expect from a random variable. Mathematically, it's the weighted average of all possible values that this random variable can take on, with the weights being the probabilities of each outcome. For Discrete Random Variables: If you have a discrete random variable $X$ that can take on values $x_1, x_2, ..., x_n$ with probabilities $P(X=x_1), P(X=x_2), ..., P(X=x_n)$, the expectation is given by: $$ E[X] = \sum_{i=1}^{n}x_iP(X=x_i) $$ For Continuous Random Variables: If $X$ is continuous with a probability density function $f(x)$, the expectation is: $$E[X] = \int_{-\infty}^{\infty} x f(x) dx $$