Estadísticas y predicciones de Tercera Division RFEF Group 14

Introducción al Fútbol en la Tercera División RFEF Grupo 14

La Tercera División RFEF representa uno de los escenarios más emocionantes y competitivos del fútbol español. El Grupo 14, en particular, es conocido por su intensa rivalidad y por ser cuna de talentos que aspiran a llegar a las ligas superiores. Mañana, el apasionante mundo del fútbol nos regalará una jornada llena de emociones, donde cada equipo dará lo mejor de sí para asegurar puntos vitales en la clasificación.

Programación de Partidos para Mañana

La jornada futbolística promete ser vibrante con encuentros que captarán la atención de todos los aficionados. Aquí te presentamos el calendario de partidos programados para mañana en el Grupo 14:

• 10:00 AM: Club Deportivo Linares vs. Real Jaén
• 12:30 PM: Atlético Malagueño vs. Marbella FC
• 03:00 PM: CD Roquetas vs. UD Melilla
• 05:30 PM: CD El Ejido vs. CD Almería B
• 08:00 PM: Vélez CF vs. Lorca FC

Análisis de Equipos y Estrategias

Cada equipo trae consigo una estrategia específica diseñada para maximizar sus posibilidades de victoria. Analicemos algunos aspectos clave que podrían influir en el resultado de los partidos:

Club Deportivo Linares vs. Real Jaén

El Club Deportivo Linares ha mostrado una solidez defensiva impresionante durante las últimas jornadas. Su capacidad para mantener la portería a cero podría ser un factor decisivo ante un Real Jaén que busca capitalizar cualquier error defensivo.

Atlético Malagueño vs. Marbella FC

Atlético Malagueño ha destacado por su poderío ofensivo, con un ataque liderado por jóvenes promesas que han demostrado gran capacidad goleadora. Sin embargo, Marbella FC no se queda atrás, ya que su juego colectivo y la experiencia de sus jugadores veteranos podrían inclinar la balanza a su favor.

CD Roquetas vs. UD Melilla

CD Roquetas ha trabajado en mejorar su presión alta durante los entrenamientos, lo que podría complicar las cosas para UD Melilla, que depende mucho de su juego desde atrás para construir ataques efectivos.

CD El Ejido vs. CD Almería B

CD El Ejido ha sido consistentemente uno de los equipos más equilibrados del grupo, con una mezcla perfecta entre defensa y ataque. Frente a ellos, CD Almería B buscará explotar cualquier debilidad defensiva para sumar puntos importantes.

Vélez CF vs. Lorca FC

Vélez CF viene de una racha positiva que le ha permitido subir posiciones en la tabla. Lorca FC, por otro lado, tendrá que mostrar su mejor versión para detener el ímpetu ofensivo del Vélez CF.

Pronósticos y Predicciones de Apuestas

Más allá del puro espectáculo deportivo, las apuestas ofrecen un panorama interesante sobre cómo podrían desarrollarse los partidos. A continuación, presentamos algunas predicciones basadas en análisis estadísticos y expertos en apuestas deportivas:

Pronósticos para Club Deportivo Linares vs. Real Jaén

• Ganador: Club Deportiv<|repo_name|>edwardchenfeng/ntu-ml-course<|file_sep|>/README.md # NTHU Machine Learning Course This repo contains the source codes for the machine learning course offered by the Department of Computer Science and Information Engineering (CSIE) in National Tsing Hua University (NTHU). ## Syllabus The syllabus can be found [here](https://sites.google.com/site/ntucomputerscience/2021-fall-courses/csie-608-8-machine-learning) ## Code and Material All code and material can be found in the `./lecture` folder. ## License [MIT](https://choosealicense.com/licenses/mit/) <|repo_name|>edwardchenfeng/ntu-ml-course<|file_sep|>/lecture/lecture06/code/plot.py import matplotlib.pyplot as plt import numpy as np def plot_loss(loss): plt.figure(figsize=(10,6)) plt.plot(loss) plt.xlabel('Iteration') plt.ylabel('Loss') plt.title('Loss') plt.show() def plot_boundary(x_train, y_train): x1 = np.linspace(-4,4) x2 = np.linspace(-4,4) xx1, xx2 = np.meshgrid(x1,x2) x = np.vstack((xx1.ravel(), xx2.ravel())).T z = model.predict(x) z = z.reshape(xx1.shape) plt.figure(figsize=(10,6)) plt.contourf(xx1, xx2,z,cmap=plt.cm.Paired) for i in range(np.max(y_train)+1): plt.scatter(x_train[y_train==i][:,0],x_train[y_train==i][:,1]) plt.xlabel('$x_1$') plt.ylabel('$x_2$') plt.title('Decision Boundary') plt.show() <|file_sep|>documentclass[12pt]{article} usepackage{amsmath} usepackage{amssymb} usepackage{graphicx} usepackage{listings} usepackage{xcolor} usepackage{float} usepackage{hyperref} % newcommand{norm}[1]{leftlVert#1rightrVert} % newcommand{abs}[1]{left|#1right|} % newcommand{inner}[2]{left<#1,#2right>} % DeclareMathOperator*{argmin}{argmin} % DeclareMathOperator*{argmax}{argmax} % page layout setlength{parindent}{0pt} setlength{parskip}{0pt plus 0.5ex} % code style lstset{ basicstyle=ttfamily, columns=fullflexible, keywordstyle=color{blue}, commentstyle=color{gray}, numbers=none, numberstyle=tiny, numbersep=5pt, tabsize=4, showstringspaces=false, frame=single, breaklines=true, breakatwhitespace=false } % title title{CSIE608-8 Machine Learning\Lecture Notes} % author author{Chen-Feng Edward Chen\Department of Computer Science and Information Engineering\National Tsing Hua University\[email protected]} % date date{today} begin{document} maketitle section{Introduction} In this lecture we will cover the following topics: % begin{itemize} item Introduction to Linear Regression; % item The Least Square Method; % item Gradient Descent. % noindent And we will work on the following problems: % begin{itemize} item Exercise (Lecture Note): Linear Regression. % noindent And we will use the following software: % noindent Python (with Jupyter Notebook). % end{itemize} % end{itemize} vspace*{0.5cm} noindent In this lecture we will start our journey to machine learning! We will learn how to build our first machine learning model - linear regression. vspace*{0.5cm} noindent In this lecture we will also learn how to build our first machine learning model using Python and Jupyter Notebook. vspace*{0.5cm} noindent Please follow along with the notebook `lecture01.ipynb` on Google Colab url{https://colab.research.google.com/drive/1T8-KwZB6Xzr7KtI5ePbQyL4CJ7dJNQ7D?usp=sharing}. Or you can download the notebook from this GitHub repository url{https://github.com/chencf-edward/ntu-ml-course}. vspace*{0.5cm} noindent In this lecture we will learn about linear regression which is one of the most basic supervised machine learning models for regression problems. vspace*{0.5cm} noindent We assume that you have some background in linear algebra and calculus. vspace*{0.5cm} noindent For more information about linear algebra and calculus please refer to: % % noindent Linear Algebra: % noindent https://en.wikipedia.org/wiki/Linear_algebra \ https://www.khanacademy.org/math/linear-algebra \ https://www.mathsisfun.com/algebra/matrix-multiplying.html \ https://en.wikipedia.org/wiki/Determinant \ https://en.wikipedia.org/wiki/Eigenvalue \ https://en.wikipedia.org/wiki/Singular_value_decomposition \ https://en.wikipedia.org/wiki/Matrix_inversion \ https://en.wikipedia.org/wiki/Multivariate_normal_distribution \ % noindent Calculus: % noindent https://www.khanacademy.org/math/calculus-home \ https://www.mathsisfun.com/calculus/index.html \ https://en.wikipedia.org/wiki/Gradient_descent \ https://en.wikipedia.org/wiki/Stochastic_gradient_descent vspace*{0.5cm} noindent If you are interested in more advanced topics in machine learning please refer to: % % noindent Andrew Ng's Machine Learning Course on Coursera: https://www.coursera.org/learn/machine-learning vspace*{0.5cm} noindent If you are interested in more advanced topics in linear algebra please refer to: % % noindent Gilbert Strang's Linear Algebra on YouTube: https://www.youtube.com/user/professorsgordon/videos vspace*{0.5cm} noindent If you are interested in more advanced topics in deep learning please refer to: % % noindent Deep Learning Specialization on Coursera by Andrew Ng and his colleagues: https://www.coursera.org/specializations/deep-learning vspace*{0.5cm} noindent In this lecture we will use Python and Jupyter Notebook to build our first machine learning model - linear regression. vspace*{0.5cm} noindent Python is a general purpose programming language that is widely used in data science and machine learning. vspace*{0.5cm} noindent Jupyter Notebook is an open source web application that allows you to create and share documents that contain live code, equations, visualizations and narrative text. vspace*{0.5cm} noindent The combination of Python and Jupyter Notebook provides a powerful tool for building machine learning models. vspace*{0.5cm} In this lecture we will use the following Python libraries: % begin{itemize} item numpy; % noindent A library for scientific computing with Python. % noindent https://numpy.org/ item matplotlib; noindent A plotting library for creating static, animated, and interactive visualizations in Python. noindent https://matplotlib.org/ item pandas; noindent A library providing high-performance data structures and data analysis tools for Python. noindent https://pandas.pydata.org/ % item scikit-learn; % % noindent A library for machine learning in Python. % % noindent https://scikit-learn.org/stable/ % item tensorflow; % % noindent An open-source software library for dataflow and differentiable programming across a range of tasks. % % noindent https://www.tensorflow.org/ % item keras; % % noindent An open-source software library for neural networks. % % noindent https://keras.io/ %item seaborn; %noindent A statistical data visualization library based on matplotlib. %noindent https://seaborn.pydata.org/ %end{itemize} In this lecture we will learn about linear regression which is one of the most basic supervised machine learning models for regression problems. vspace*{0.5cm} In supervised learning we have a dataset consisting of input-output pairs $(x,y)$ where $x$ is an input vector and $y$ is the corresponding output value. vspace*{0.5cm} In regression problems the output value $y$ is a real number. vspace*{0.5cm} In classification problems the output value $y$ is a discrete label. vspace*{0.5cm} For example consider the following dataset: vspace*{-10pt} $$ (x_1,y_1) = ((1,1),3) \ (x_2,y_2) = ((2,4),6) \ (x_3,y_3) = ((3,-1),4) $$ vspace*{-10pt} In this example each input vector $x_i$ has two features $x_{i1}$ and $x_{i2}$. vspace*{-10pt} We can visualize this dataset as follows: vspace*{-10pt} $$ x_1 = (x_{11},x_{12}) = (1,1) \ x_2 = (x_{21},x_{22}) = (2,4) \ x_3 = (x_{31},x_{32}) = (3,-1) $$ vspace*{-10pt} $$ y_1 = f(x_1) + epsilon_1 = w^T x_1 + b + epsilon_1 = w_1 x_{11} + w_2 x_{12} + b + epsilon_1 = w^T x + b + epsilon \ y_2 = f(x_2) + epsilon_2 = w^T x_2 + b + epsilon_2 = w_1 x_{21} + w_2 x_{22} + b + epsilon_2 = w^T x + b + epsilon \ y_3 = f(x_3) + epsilon_3 = w^T x_3 + b + epsilon_3 = w_1 x_{31} + w_2 x_{32} + b + epsilon_3 = w^T x + b + epsilon $$ where $w$ is a vector of weights $(w_1,w_2)$ and $b$ is a bias term. We want to find the best values of $w$ and $b$ such that $f(x)$ approximates $y$ as closely as possible. In other words we want to minimize the error between the predicted values $hat y$ and the true values $y$: $$ E(w,b) = |y-hat y |^{2}_{F} = |y-f(X)|^{2}_{F} $$ where $|cdot |_{F}$ denotes the Frobenius norm. The Frobenius norm of a matrix $A$ is defined as: $$ |A |^{2}_{F} := tr(A^TA) $$ where $tr(cdot)$ denotes the trace operator. The trace operator of a matrix $A$ is defined as: $$ tr(A):=sum^{n}_{i=1} A_{ii} $$ where $A_{ii}$ denotes the diagonal elements of matrix $A$. Therefore we can rewrite our objective function as follows: $$ E(w,b)=tr((y-f(X))^T(y-f(X)))=tr((y-WX-b)^T(y-WX-b)) $$ where we have defined: $$ W:=diag(w)\ X:= [vec{x}_{i}]^T=[[vec{x}_{i}]^T]^T=[[(x_{i})]_{j}]^T=[[(x_{ij})]]^T=[(x_{ij})] $$ and $vec{x}_i$ denotes the input vector corresponding to example $i$, i.e., $vec{x}_i=x_i=(x_{i1},...,x_{id})$, where $d$ denotes the number of features. Let us expand our objective function: $$ E(w,b)=tr((y-WX-b)^T(y-WX-b))\= tr(y^Ty-y^TXW-y^Tb-WX^Ty+WXX^TW+bX^Ty+b^Ty+b^Tb) $$ Note that: $$ tr(WX^Ty)=tr((WX^Ty)^T)=tr(YXW)=YXW\ tr(bX^Ty)=tr((bX^Ty)^T)=tr(YXb)=YXb\ tr(b^Ty)=tr((b^Ty)^T)=tr(Yb)=Yb\ tr(b^Tb)=tr((b^Tb)^T)=tr(b^{T}b)=bb^{T}=bb=b^{2}\ WXX^{T}W=Wdiag(vec{x}_{i}vec{x}_{j}^{T})W=Wdiag(sum^{d}_{k=1}