Time series analysis and forecasting have many applications, because of its “claimed” capability in predicting the future. This blog covers some of the most classic statistical time series models. It is intended to remind myself of some important concepts. Therefore, apologize for any unclearness. The essential goal of time series…

Model for systems that change over time in a random manner A Markov chain is a special type of stochastic process, defined in terms of the conditional distributions of future states given the present and past states. If the current state only depends on the previous state. A sequence of random variables 𝑋1, 𝑋2,… is called a stochastic process or random process with discrete time parameter. Homogeneous Markov Chain

Definition

Probability mass function -> Discrete (finite number of different values) Probability density function -> Continuous (every value in an interval) Both have cumulative distribution function, where f(x) = P(X<x) The inverse of the CDF is called quantile function, and it is useful for indicating where the probability is located in a distribution. Discrete Distributions f(x) are all probability mass function(pmf)

Conditional Probability & Bayes Theorem Conditional probability is important because a lot of supervised learning problem is structured in a way like what is Y given features X. And conditional probability is an intuitive way to construct it.

Permutation & Combination Probability is based on events, which is a set of possible outcomes of a experiment. Each event is a subset of sample space. Pr(A) is the probability that A event will occur, given a experiment. Permutations The number of distinct orderings of k items selected without replacement from…

How to know if the model is working? We’ve reviewed some of the most representative modern machine learning algorithms in the previous series. These can get us a good start to build supervised predictive models. Only learning about the models is not enough, since you can’t manage something you can’t measure. This post will focus on the performance measure, how good is the model and how to understand it.

A Theoretically Beautiful Algorithm 🎆 Pre 1980s, almost all learning methods learned linear decision surfaces, and they have nice theoretical properties. In 1980s, decision trees and neural networks have allowed efficient learning of non-linear decision surfaces, but has little theoretical basis and suffer from local minima. …

🔥The most popular category of learning algorithms The idea of Ensemble learning also referred to as a multi-classifier system, and committee-based learning is to build a prediction model by combining the strengths of a collection of simpler models. Like the old saying, “Unity is strength!”🥊. In general, when mixing a…