{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introducción a los métodos de Monte-Carlo con Python" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Esta notebook fue creada originalmente como un blog post por [Raúl E. López Briega](http://relopezbriega.com.ar/) en [Matemáticas, análisis de datos y python](http://relopezbriega.github.io). El contenido esta bajo la licencia BSD.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"Métodos" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introducción\n", "\n", "En el cierre de mi [artículo anterior](http://relopezbriega.github.io/blog/2016/11/26/introduccion-a-la-teoria-de-probabilidad-con-python/), comentaba sobre la sorprendente influencia que han tenido los [números aleatorios](https://es.wikipedia.org/wiki/N%C3%BAmero_aleatorio), que junto con el poder de cálculo que nos proporcionan las computadoras modernas; nos han ayudado a resolver muchos de los problemas numéricos más complejos en ciencia, ingeniería, [finanzas](http://relopezbriega.github.io/category/finanzas.html) y [estadísticas](http://relopezbriega.github.io/category/pobabilidad-y-estadistica.html). En esencia, detrás de cada una de esas soluciones encontramos una familia de métodos que se conocen bajo el nombre de [Métodos de Monte-Carlo](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Montecarlo).\n", "\n", "## ¿Qué son los métodos de Monte-Carlo?\n", "\n", "Los [Métodos de Monte-Carlo](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Montecarlo) son técnicas para analizar fenómenos por medio de [algoritmos computacionales](https://es.wikipedia.org/wiki/Algoritmo), que utilizan y dependen fundamentalmente de la generación de [números aleatorios](https://es.wikipedia.org/wiki/N%C3%BAmero_aleatorio). El término Monte-Carlo, hace referencia al [casino de Montecarlo](https://es.wikipedia.org/wiki/Casino_de_Montecarlo), una de las capitales de los juegos de azar; y se utilizó como denominación para estás técnicas por la [aleatoriedad](https://es.wikipedia.org/wiki/Aleatoriedad) inherente que poseen. El estudio de los [Métodos de Monte-Carlo](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Montecarlo) requiere un conocimiento detallado en una amplia gama de campos; por ejemplo, la *[probabilidad](http://relopezbriega.github.io/tag/probabilidad.html)* para describir los experimentos y procesos aleatorios, la *[estadística](http://relopezbriega.github.io/tag/estadistica.html)* para analizar los datos, las [ciencias de la computación](https://es.wikipedia.org/wiki/Ciencias_de_la_computaci%C3%B3n) para implementar eficientemente los [algoritmos](https://es.wikipedia.org/wiki/Algoritmo) y la *programación matemática* para formular y resolver problemas de optimización.\n", "\n", "Como los [Métodos de Monte-Carlo](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Montecarlo) dependen en gran medida de la posibilidad de producir, con una computadora, un flujo infinito de [variables aleatorias](https://es.wikipedia.org/wiki/Variable_aleatoria) para todo tipo de [distribuciones](http://relopezbriega.github.io/blog/2016/06/29/distribuciones-de-probabilidad-con-python/); no podemos hablar de los [Métodos de Monte-Carlo](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Montecarlo), sin antes explicar los [números aleatorios](https://es.wikipedia.org/wiki/N%C3%BAmero_aleatorio) y como podemos generarlos con la ayuda de una computadora.\n", "\n", "## Números aleatorios y Monte-Carlo\n", "\n", "En el corazón de los [Métodos de Monte-Carlo](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Montecarlo) encontramos un *[generador de números aleatorios](https://es.wikipedia.org/wiki/Generador_de_n%C3%BAmeros_aleatorios)*, es decir un procedimiento que produce un flujo infinito de [variables aleatorias](https://es.wikipedia.org/wiki/Variable_aleatoria), que generalmente se encuentran en el intervalo (0, 1); los cuales son independientes y están uniformemente distribuidos de acuerdo a una [distribución de probabilidad](http://relopezbriega.github.io/blog/2016/06/29/distribuciones-de-probabilidad-con-python/). La mayoría de los lenguajes de programación hoy en día contienen un [generador de números aleatorios](https://es.wikipedia.org/wiki/Generador_de_n%C3%BAmeros_aleatorios) por defecto al cual simplemente debemos ingresarle un valor inicial, generalmente llamado **seed** o semilla, y que luego en cada invocación nos va a devolver un secuencia uniforme de [variables aleatorias](https://es.wikipedia.org/wiki/Variable_aleatoria) independientes en el intervalo (0, 1). \n", "\n", "### Números pseudoaleatorios\n", "\n", "El concepto de una secuencia infinita de [variables aleatorias](https://es.wikipedia.org/wiki/Variable_aleatoria) es una abstracción matemática que puede ser imposible de implementar en una computadora. En la práctica, lo mejor que se puede hacer es producir una secuencia de números *pseudoaleatorios* con propiedades estadísticas que son indistinguibles de las de una verdadera secuencia de [variables aleatorias](https://es.wikipedia.org/wiki/Variable_aleatoria). Aunque actualmente métodos de generación física basados en la radiación de fondo o la mecánica cuántica parecen ofrecer una fuente estable de números verdaderamente [aleatorios](https://es.wikipedia.org/wiki/N%C3%BAmero_aleatorio) , la gran mayoría de los [generadores de números aleatorios](https://es.wikipedia.org/wiki/Generador_de_n%C3%BAmeros_aleatorios) que se utilizan hoy en día están basados en algoritmos simples que pueden ser fácilmente implementados en una computadora; por lo que en realidad son [generadores de números pseudoaleatorios](https://es.wikipedia.org/wiki/Generador_de_n%C3%BAmeros_pseudoaleatorios).\n", "\n", "\n", "### Números aleatorios en Python\n", "\n", "En [Python](http://python.org/) el módulo `random` nos proporciona un rápido [generador de números pseudoaleatorios](https://es.wikipedia.org/wiki/Generador_de_n%C3%BAmeros_pseudoaleatorios) basado en el algoritmo [Mersenne Twister](https://en.wikipedia.org/wiki/Mersenne_Twister); el cual genera números con una distribución casi uniforme y un período grande, haciéndolo adecuado para una amplia gama de aplicaciones. Veamos un pequeño ejemplo." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.36352835585530807" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Utilizando random para genera números aleatorios.\n", "import random\n", "\n", "random.seed(1984) # semilla para replicar la aleatoriedad\n", "random.random() # primer llamado a random" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.49420568181919666" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "random.random() # segundo llamado a random" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.33961008717180197\n", "0.21648780903913534\n", "0.8626522767441037\n", "0.8493329421213219\n", "0.38578540884489343\n" ] } ], "source": [ "for i in range(5):\n", " print(random.random()) # 5 números aleatorios" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.36352835585530807\n", "0.49420568181919666\n", "0.33961008717180197\n", "0.21648780903913534\n", "0.8626522767441037\n", "0.8493329421213219\n", "0.38578540884489343\n" ] } ], "source": [ "# volviendo a llamar a seed para replicar el mismo resultado aleatorio.\n", "random.seed(1984) \n", "for i in range(7):\n", " print(random.random()) # Mismos resultados que arriba." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "En este ejemplo podemos ver como la función `random` genera números aleatorios entre 0 y 1, también podemos ver como con el uso de `seed` podemos replicar el comportamiento aleatorio. \n", "\n", "### Elegir un buen generador de números aleatorios\n", "\n", "Existe una gran variedad de [generadores de números aleatorios](https://es.wikipedia.org/wiki/Generador_de_n%C3%BAmeros_aleatorios) que podemos elegir; pero elegir un buen [generador de números aleatorios](https://es.wikipedia.org/wiki/Generador_de_n%C3%BAmeros_aleatorios) es como elegir un coche nuevo: para algunas personas o aplicaciones la velocidad es primordial, mientras que para otros la robustez y la fiabilidad son más importantes. Para la [simulación de Monte-Carlo](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Montecarlo) las propiedades distributivas de los [generadores aleatorios](https://es.wikipedia.org/wiki/Generador_de_n%C3%BAmeros_aleatorios) es primordial, mientras que en la criptografía la imprevisibilidad es crucial. Por tal motivo, el generador que vayamos a elegir dependerá de la aplicación que le vayamos a dar.\n", "\n", "## Monte-Carlo en acción\n", "\n", "Los [Métodos de Monte-Carlo](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Montecarlo) se basan en la analogía entre [probabilidad](http://relopezbriega.github.io/tag/probabilidad.html) y volumen. Las *matemáticas de las medidas* formalizan la noción intuitiva de [probabilidad](http://relopezbriega.github.io/tag/probabilidad.html), asociando un evento con un conjunto de resultados y definiendo que la [probabilidad](http://relopezbriega.github.io/tag/probabilidad.html) del evento será el volumen o medida relativa del universo de posibles resultados. [Monte-Carlo](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Montecarlo) usa esta identidad a la inversa, calculando el volumen de un conjunto interpretando el volumen como una [probabilidad](http://relopezbriega.github.io/tag/probabilidad.html). En el caso más simple, esto significa muestrear aleatoriamente un universo de resultados posibles y tomar la fracción de muestras aleatorias que caen en un conjunto dado como una estimación del volumen del conjunto. La [ley de grandes números](https://es.wikipedia.org/wiki/Ley_de_los_grandes_n%C3%BAmeros) asegura que esta estimación converja al valor correcto a medida que aumenta el número de muestras. El [teorema del límite central](https://es.wikipedia.org/wiki/Teorema_del_l%C3%ADmite_central) proporciona información sobre la magnitud del probable error en la estimación después de un número finito de muestras. \n", "En esencia podemos decir que el [Método de Monte-Carlo](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Montecarlo) consiste en calcular o aproximar ciertas expresiones a través de adivinarlas con la ayuda de dibujar una cantidad normalmente grande de números aleatorios. \n", "Veamos como funciona con un ejemplo, calculemos el área de un círculo de radio 1; lo que es lo mismo a decir que aproximemos el valor de [$\\pi$](http://relopezbriega.github.io/blog/2015/03/14/el-dia-pi/)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# \n", "# importando modulos necesarios\n", "import matplotlib.pyplot as plt \n", "import numpy as np # importando numpy\n", "import pandas as pd # importando pandas\n", "from scipy import stats\n", "\n", "np.random.seed(1984) # para poder replicar el random\n", "\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YAIAdi8PDuWQcjS9+yPdeqPn6pcbDsGRIXX8/QE+P+2ghVnJua9ak45wo7ojg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sabzs5yZY1gouLCY4Cg6lV771H3qltT7+M4ZeYK4zVUVw3aNaCqKMscABUBMP47C59IMbAl+f3v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arNfTcC7SVa2Ff29rqnjV6nyyF3l5uTHiV6s2zAGeIUsn4tyiS46qci4zvheLcQXDajXuoIZz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\n4UdkC7Jxscth4oI7HHPZMadNT0+n38G/IzBa6cAK7b2/R34A+xx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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Ejemplo: Aproximando el valor de pi - área de un círculo de\n", "# radio = 1.\n", "\n", "def mc_pi_aprox(N=10000):\n", " plt.figure(figsize=(8,8)) # tamaño de la figura\n", " x, y = np.random.uniform(-1, 1, size=(2, N))\n", " interior = (x**2 + y**2) <= 1\n", " pi = interior.sum() * 4 / N\n", " error = abs((pi - np.pi) / pi) * 100\n", " exterior = np.invert(interior)\n", " plt.plot(x[interior], y[interior], 'b.')\n", " plt.plot(x[exterior], y[exterior], 'r.')\n", " plt.plot(0, 0, label='$\\hat \\pi$ = {:4.4f}\\nerror = {:4.4f}%'\n", " .format(pi,error), alpha=0)\n", " plt.axis('square')\n", " plt.legend(frameon=True, framealpha=0.9, fontsize=16)\n", "\n", "mc_pi_aprox()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6r3+15iL/ZNky9j/6aB6dPZuzx4+H+nqCjY0MGT2agf368WLLAnDab35DeWkp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\nKf/xSy/lLlN+ejP6vXuLYYyoeSXlD8U0uvA3fBJj8K4/0cKcQpI4ocKTT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# con 1000000 experimentos\n", "mc_pi_aprox(N=100000)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Como vemos en este ejemplo, para calcular el área del círculo realizamos un gran número de experimentos aleatorios, en el primer ejemplo utilizamos 10,000 experimentos; y luego calculamos el área obteniendo una [media aritmética](https://es.wikipedia.org/wiki/Media_aritm%C3%A9tica) de los valores que caen dentro de la superficie del círculo. Debemos hacer notar que incluso utilizando un gran número de experimentos aún así en el primer ejemplo no logramos obtener los primeros dos decimales correctos; recién en el segundo ejemplo, cuando utilizamos 100,000 experimentos logramos obtener los primeros dos dígitos correctos; esto demuestra que el [Método de Monte-Carlo](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Montecarlo) en su versión más cruda tarda bastante en [converger](https://es.wikipedia.org/wiki/Convergencia_en_probabilidad).\n", "\n", "### Técnicas de reducción de varianza\n", "\n", "Existen varias técnicas generales para la [reducción de la varianza](https://en.wikipedia.org/wiki/Variance_reduction), estos métodos mejoran la precisión y la tasa de [convergencia](https://es.wikipedia.org/wiki/Convergencia_en_probabilidad) de la [integración](https://es.wikipedia.org/wiki/Integraci%C3%B3n) por medio del [Método de Monte-Carlo](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Montecarlo) sin aumentar el número de experimentos. Algunas de estas técnicas son:\n", "\n", "* **[Muestreo de importancia](https://en.wikipedia.org/wiki/Importance_sampling)**: La idea principal detrás del [Muestreo de importancia](https://en.wikipedia.org/wiki/Importance_sampling) es simplemente encontrar una distribución para la variable aleatoria subyacente que asigne una alta probabilidad a aquellos valores que son importantes para calcular la cantidad que nos interesa determinar.\n", "* **[Muestreo estratificado](https://es.wikipedia.org/wiki/Muestreo_estratificado)**: El principal principio subyacente al [Muestreo estratificado](https://es.wikipedia.org/wiki/Muestreo_estratificado) es natural: tomar una muestra de una pequeña subpoblación que refleje las propiedades del total de la población tanto como sea posible.\n", "* **[Variantes de control](https://en.wikipedia.org/wiki/Control_variates)**: El método de las [Variantes de control](https://en.wikipedia.org/wiki/Control_variates) explota la información sobre los errores en las estimaciones de las cantidades conocidas para reducir el error de una estimación de una cantidad desconocida. \n", "* **[Variaciones antitéticas](https://en.wikipedia.org/wiki/Antithetic_variates)**: El método de las [Variaciones antitéticas](https://en.wikipedia.org/wiki/Antithetic_variates) es el método de [reducción de la varianza](https://en.wikipedia.org/wiki/Variance_reduction), más fácil. Se basa en la idea de combinar una selección aleatoria de puntos con una opción sistemática. Su principal principio es la [reducción de la varianza](https://en.wikipedia.org/wiki/Variance_reduction), mediante la introducción de la simetría.\n", "\n", "Excede al alcance de este artículo el profundizar en cada una de estas técnicas, pueden encontrar un análisis más detallado de las mismas en el siguiente [enlace](http://iacs-courses.seas.harvard.edu/courses/am207/blog/lecture-4.html) (en inglés). \n", "\n", "## Métodos de Monte-Carlo via cadenas de Markov \n", "\n", "El desarrollo de los [métodos de Monte-Carlo via cadenas de Markov](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo), o [MCMC](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo) por sus siglas en inglés, es sin duda uno de los mayores avances en el enfoque computacional de la [estadística](http://relopezbriega.github.io/tag/estadistica.html). Muchos de los problemas que son intratables utilizando un enfoque *analítico* a menudo pueden ser resueltos utilizando alguna forma de [MCMC](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo), incluso aunque se trate de problemas en varias [dimensiones](https://es.wikipedia.org/wiki/Dimensi%C3%B3n). \n", "Las técnicas [MCMC](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo) se aplican para resolver problemas de [integración](https://es.wikipedia.org/wiki/Integraci%C3%B3n) y optimización en grandes [espacios dimensionales](https://es.wikipedia.org/wiki/Espacio_de_Hilbert). Estos dos tipos de problemas desempeñan un papel fundamental en [machine learning](http://relopezbriega.github.io/category/machine-learning.html), [física](https://es.wikipedia.org/wiki/F%C3%ADsica), [estadística](http://relopezbriega.github.io/tag/estadistica.html), [econometría](https://es.wikipedia.org/wiki/Econometr%C3%ADa) y el [análisis de decisiones](https://es.wikipedia.org/wiki/An%C3%A1lisis_de_decisi%C3%B3n).\n", "\n", "### ¿Qué es una cadena de Markov?\n", "\n", "Una [cadena de Markov](https://es.wikipedia.org/wiki/Cadena_de_M%C3%A1rkov) es un objeto matemático que consiste en una secuencia de estados y un conjunto de [probabilidades](http://relopezbriega.github.io/tag/probabilidad.html) que describen las *transiciones entre esos estados*. La característica principal que tiene esta cadena es que la probabilidad de moverse a otros estados **depende solamente del estado actual**. Dada una cadena, se puede realizar una [caminata aleatoria](https://es.wikipedia.org/wiki/Camino_aleatorio) eligiendo un punto de partida y moviéndose a otros estados siguiendo las *[probabilidades](http://relopezbriega.github.io/tag/probabilidad.html) de transición*. Si de alguna manera encontramos una [cadena de Markov](https://es.wikipedia.org/wiki/Cadena_de_M%C3%A1rkov) con *transiciones proporcionales* a la distribución que queremos probar, el muestreo se convierte simplemente en una cuestión de moverse entre los estados de esta cadena.\n", "\n", "#### Caminata aleatoria en un grafo\n", "\n", "Una [cadena de Markov](https://es.wikipedia.org/wiki/Cadena_de_M%C3%A1rkov) puede ser ilustrada con el siguiente [grafo](https://es.wikipedia.org/wiki/Grafo), el cual representa una [cadena de Markov](https://es.wikipedia.org/wiki/Cadena_de_M%C3%A1rkov) de cuatro estados.\n", "\n", "\"Cadena\n", "\n", "Los estados de la cadena se representan como los nodos del [grafo](https://es.wikipedia.org/wiki/Grafo), una arista de dirección se extiende de un nodo $x$ hacia otro nodo $y$ si la transición de $x$ hacia $y$ es posible en una iteración. Cada una de estas aristas de dirección tienen una [probabilidad](http://relopezbriega.github.io/tag/probabilidad.html) asociada $P_{xy}$; esta es la [probabilidad](http://relopezbriega.github.io/tag/probabilidad.html) de que el nodo sea elegido en la siguiente iteración cuando la cadena se encuentra en el estado $x$. La cadena comienza en algún estado, digamos $X_0$, que puede ser elegido en forma [aleatoria](https://es.wikipedia.org/wiki/Aleatoriedad) de acuerdo con una [distribución](http://relopezbriega.github.io/blog/2016/06/29/distribuciones-de-probabilidad-con-python/) inicial o simplemente asignado en forma arbitraria. Desde allí, la cadena se mueve de un estado a otro en cada iteración según las [probabilidades](http://relopezbriega.github.io/tag/probabilidad.html) de transición del nodo vecino.\n", "\n", "#### Representación matricial\n", "\n", "Como alternativa a la representación en forma de [grafo](https://es.wikipedia.org/wiki/Grafo), la cadena antes descripta también puede ser representada por una matriz $P = (p_{xy})$ de las [probabilidades](http://relopezbriega.github.io/tag/probabilidad.html) $p_{xy}$ de transición de un estado $x$ a un estado $y$ en una iteración de la cadena. Esta matriz es llamada [matriz de transición](https://es.wikipedia.org/wiki/Matriz_estoc%C3%A1stica) y tiene la característica que todas sus filas deben sumar 1. Por ejemplo, la [matriz de transición](https://es.wikipedia.org/wiki/Matriz_estoc%C3%A1stica) de nuestro ejemplo sería la siguiente:\n", "\n", "$$ P = \\begin{bmatrix}\n", "p_{11} & p_{12} & 0 & p_{14} \\\\ \n", "p_{21} & 0 & p_{23} & 0 \\\\\n", "p_{31} & 0 & 0 & p_{34} \\\\\n", "0 & 0 & p_{43} & p_{44} \n", "\\end{bmatrix}\n", "$$\n", "\n", "Esta formulación de matriz es mucho más que una descripción tabular de la cadena; también es una herramienta de cálculo. Ya que si por ejemplo definimos a $p_t$ como el *vector de probabilidad* de una [variable aleatoria](https://es.wikipedia.org/wiki/Variable_aleatoria) $X_t$; entonces podemos calcular $p_{t + 1}$ como una [multiplicación de matrices](https://es.wikipedia.org/wiki/Multiplicaci%C3%B3n_de_matrices)\n", "\n", "$$ p_{t + 1} = p_t \\cdot P, \\hspace{1cm} t= 1, 2, \\dots \n", "$$\n", "\n", "#### La distribución invariante\n", "\n", "Una de las características generales de las [cadenas de Markov](https://es.wikipedia.org/wiki/Cadena_de_M%C3%A1rkov) es que pueden poseer una [distribución invariante](https://en.wikipedia.org/wiki/Stationary_distribution), tomemos por ejemplo la siguiente representación matricial de una [cadena de Markov](https://es.wikipedia.org/wiki/Cadena_de_M%C3%A1rkov):\n", "\n", "$$ P = \\begin{bmatrix}\n", "0.3 & 0.2 & 0.5 \\\\ \n", "0.4 & 0.3 & 0.3 \\\\ \n", "0.3 & 0.4 & 0.3 \n", "\\end{bmatrix}\n", "$$\n", "\n", "Si comenzamos en el primer estado de la cadena, podemos obtener $p_1$ del siguiente modo:\n", "\n", "$$ p_1 = \\begin{bmatrix}\n", "1 & 0 & 0 \n", "\\end{bmatrix} \\cdot \\begin{bmatrix}\n", "0.3 & 0.2 & 0.5 \\\\ \n", "0.4 & 0.3 & 0.3 \\\\ \n", "0.3 & 0.4 & 0.3 \n", "\\end{bmatrix} = \\begin{bmatrix}\n", "0.3 & 0.2 & 0.5 \n", "\\end{bmatrix}\n", "$$\n", "\n", "Ahora que ya obtuvimos $p_1$, podemos continuar y obtener $p_2$:\n", "\n", "$$ p_2 = p_1 P = \\begin{bmatrix}\n", "0.3 & 0.2 & 0.5 \n", "\\end{bmatrix} \\cdot \\begin{bmatrix}\n", "0.3 & 0.2 & 0.5 \\\\ \n", "0.4 & 0.3 & 0.3 \\\\ \n", "0.3 & 0.4 & 0.3 \n", "\\end{bmatrix} = \\begin{bmatrix}\n", "0.32 & 0.22 & 0.36\n", "\\end{bmatrix}\n", "$$\n", "\n", "Si continuamos con este proceso en forma recursiva, veremos que la distribución tiende hacía un *límite*, este límite es su [distribución invariante](https://en.wikipedia.org/wiki/Stationary_distribution). \n", "\n", "$$ p_3 = p_2 P = \\begin{bmatrix}\n", "0.332 & 0.304 & 0.364 \n", "\\end{bmatrix}, \\\\ \n", "p_4 = p_3 P = \\begin{bmatrix}\n", "0.3304 & 0.3032 & 0.3664 \n", "\\end{bmatrix}, \\\\ \n", "p_5 = p_4 P = \\begin{bmatrix}\n", "0.33032 & 0.3036 & 0.36608 \n", "\\end{bmatrix}, \\\\ \n", "\\dots \\hspace{1cm} \\dots \\\\\n", "p_{10} = p_9 P = \\begin{bmatrix}\n", "0.330357 & 0.303571 & 0.366072 \n", "\\end{bmatrix}\n", "$$\n", "\n", "Veamos el ejemplo con la ayuda de [Python](https://www.python.org/) para que quede más claro." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.3, 0.2, 0.5],\n", " [ 0.4, 0.3, 0.3],\n", " [ 0.3, 0.4, 0.3]])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Ejemplo distribución invariante\n", "P = np.array( [[0.3, 0.2, 0.5],\n", " [0.4, 0.3, 0.3 ],\n", " [0.3, 0.4, 0.3]] )\n", "P" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "p_1 = [ 0.3 0.2 0.5]\n", "p_2 = [ 0.32 0.32 0.36]\n", "p_3 = [ 0.332 0.304 0.364]\n", "p_4 = [ 0.3304 0.3032 0.3664]\n", "p_5 = [ 0.33032 0.3036 0.36608]\n", "p_6 = [ 0.33036 0.303576 0.366064]\n", "p_7 = [ 0.3303576 0.3035704 0.366072 ]\n", "p_8 = [ 0.33035704 0.30357144 0.36607152]\n", "p_9 = [ 0.33035714 0.30357145 0.36607141]\n", "p_10 = [ 0.33035714 0.30357143 0.36607143]\n", "p_11 = [ 0.33035714 0.30357143 0.36607143]\n" ] } ], "source": [ "p1 = np.array( [1, 0, 0] )\n", "for i in range(1, 12):\n", " p_i = p1 @ P\n", " print('p_{0:} = {1:}'.format(i, p_i))\n", " p1 = p_i " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Como vemos, luego de 12 iteraciones la distribución alcanza su *límite* y ya no cambian los resultados. Hemos alcanzado la [distribución invariante](https://en.wikipedia.org/wiki/Stationary_distribution)!\n", "\n", "### El algoritmo Metropolis-Hastings\n", "\n", "Uno de los métodos [MCMC](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo) más populares es el [algoritmo Metropolis-Hastings](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm); de hecho la mayoría de los algoritmos de [MCMC](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo) pueden ser interpretados como casos especiales de este algoritmo. El [algoritmo Metropolis-Hastings](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm) esta catalogado como **uno de los 10 algoritmos más importantes y más utilizados en ciencia e ingeniería** en los últimos veinte años.Se encuentra en el corazón de la mayoría de los métodos de muestreo [MCMC](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo).\n", "El problema básico que intenta resolver el [algoritmo Metropolis-Hastings](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm) es proporcionar un método para generar muestras de alguna distribución genérica, $P(x)$. La idea es que en muchos casos, podemos saber cómo escribir la ecuación para la [distribución de probabilidad](http://relopezbriega.github.io/blog/2016/06/29/distribuciones-de-probabilidad-con-python/) $P(x)$, pero no sabemos cómo generar muestras aleatorias de la misma. Entonces la idea básica detrás de este algoritmo es la de construir una [cadena de Markov](https://es.wikipedia.org/wiki/Cadena_de_M%C3%A1rkov) cuya [distribución invariante](https://en.wikipedia.org/wiki/Stationary_distribution) sea la distribución de muestreo que deseamos, es decir $P(x)$. En principio, esto puede parecer bastante complicado, pero la flexibilidad inherente en la elección de las [probabilidades](http://relopezbriega.github.io/tag/probabilidad.html) de transición lo hacen más simple de lo que parece.\n", "\n", "\n", "#### ¿Cómo funciona el algoritmo?\n", "\n", "El algoritmo funciona del siguiente modo. Supongamos que el estado actual de la [cadena de Markov](https://es.wikipedia.org/wiki/Cadena_de_M%C3%A1rkov) es $x_n$, y queremos generar $x_{n + 1}$. De acuerdo con el [algoritmo Metropolis-Hastings](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm), la generación de $x_{n + 1}$ **es un proceso en dos etapas**. La **primera etapa** consiste en generar un *candidato*, que denominaremos $x^*$. El valor de $x^*$ se genera a partir de la *[distribución](http://relopezbriega.github.io/blog/2016/06/29/distribuciones-de-probabilidad-con-python/) propuesta*, denotada $Q (x^* | x_n)$, la cual depende del estado actual de la [cadena de Markov](https://es.wikipedia.org/wiki/Cadena_de_M%C3%A1rkov) , $x_n$. Existen algunas limitaciones técnicas menores sobre la *[distribución](http://relopezbriega.github.io/blog/2016/06/29/distribuciones-de-probabilidad-con-python/) propuesta* que podemos utilizar, pero en su mayor parte puede ser cualquier cosa que deseemos. Una forma típica de hacerlo es utilizar una [distribución normal](https://es.wikipedia.org/wiki/Distribuci%C3%B3n_normal) centrada en el estado actual $x_n$. Es decir,\n", "\n", "$$ x^*|x_n \\sim Normal(x_n, \\sigma^2)$$\n", "\n", "La **segunda etapa** es la de *aceptación-rechazo*. Lo primero que debemos hacer en este paso es calcular la [probabilidad](http://relopezbriega.github.io/tag/probabilidad.html) de aceptación $A(x_n \\rightarrow x^*)$, la cual estará dada por:\n", "\n", "$$A(x_n \\rightarrow x^*) = \\min \\left(1, \\frac{P(x^*)}{P(x_n)} \\cdot \\frac{Q(x_n | x^*)}{Q(x^* | x_n)} \\right)\n", "$$\n", "\n", "Muy bien. Ahora que tenemos el *candidato* $x^*$ y hemos calculado la [probabilidad](http://relopezbriega.github.io/tag/probabilidad.html) de aceptación $A(x_n \\rightarrow x^*)$, es tiempo de decidir *aceptar* al candidato (en cuyo caso se establecemos $x_{n + 1} = x^*$); o *rechazar* al candidato (en cuyo caso estableceremos $x_{n + 1} = x_n$). Para tomar esta decisión, generamos un número aleatorio (uniformemente distribuido) entre 0 y 1, que denominaremos $u$. Entonces:\n", "\n", "$$x_{n + 1} = \\left\\{\n", " \\begin{array}{ll}\n", " x^* & \\mbox{si } u \\leq A(x_n \\rightarrow x^*)\\\\\n", " x_n & \\mbox{si } u > A(x_n \\rightarrow x^*)\n", " \\end{array}\n", "\\right.\n", "$$\n", "\n", "Y esto es en esencia como funciona el [algoritmo Metropolis-Hastings](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm)!\n", "\n", "Veamos un pequeño ejemplo en [Python](https://www.python.org/):" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Ejemplo algoritmo metropolis\n", "def metropolis(func, steps=10000):\n", " \"\"\"A very simple Metropolis implementation\"\"\"\n", " muestras = np.zeros(steps)\n", " old_x = func.mean()\n", " old_prob = func.pdf(old_x)\n", " \n", " for i in range(steps):\n", " new_x = old_x + np.random.normal(0, 0.5)\n", " new_prob = func.pdf(new_x)\n", " aceptacion = new_prob / old_prob\n", " if aceptacion >= np.random.random():\n", " muestras[i] = new_x\n", " old_x = new_x\n", " old_prob = new_prob\n", " else:\n", " muestras[i] = old_x\n", " \n", " return muestras" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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k5GQbPHiwPf/8834T2cy8k+pOOeUUS05OtvT0dBs0aJDt2LHD97UfeVne+PHj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\nPzqHH/pRY7LtCazgdm7ibN7wW38AeJp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# distribución beta\n", "func = stats.beta(0.4, 2)\n", "samples = metropolis(func=func, steps=100000)\n", "x = np.linspace(0.01, .99, 100)\n", "y = func.pdf(x)\n", "plt.figure(figsize=(8,8))\n", "plt.xlim(0, 1)\n", "plt.plot(x, y, 'r-', lw=3, label='Distribución verdadera')\n", "plt.hist(samples, bins=30, normed=True, label='Distribución estimada con MCMC')\n", "plt.xlabel('$x$', fontsize=14)\n", "plt.ylabel('$pdf(x)$', fontsize=14)\n", "plt.legend(fontsize=14)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Vjxkzhho1ajB+/HjWr1/PvHnz+POf/xxynA4dOrBixQrmzJnD5s2beeCBB054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\njTKz0xKHTQH2MLOPgUHANYn9XYF3zOwt4DGgv3N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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# distribución normal\n", "func = stats.norm(0.4, 2)\n", "samples = metropolis(func=func)\n", "x = np.linspace(-6, 10, 100)\n", "y = func.pdf(x)\n", "plt.figure(figsize=(8,8))\n", "plt.xlim(-6, 6)\n", "plt.plot(x, y, 'r-', lw=3, label='Distribución verdadera')\n", "plt.hist(samples, bins=30, normed=True, label='Distribución estimada con MCMC')\n", "plt.xlabel('$x$', fontsize=14)\n", "plt.ylabel('$pdf(x)$', fontsize=14)\n", "plt.legend(fontsize=14)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "como vemos, las [distribuciones](http://relopezbriega.github.io/blog/2016/06/29/distribuciones-de-probabilidad-con-python/) estimadas utilizando [MCMC](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo) se acercan bastante a las [distribuciones](http://relopezbriega.github.io/blog/2016/06/29/distribuciones-de-probabilidad-con-python/) reales.\n", "\n", "### Otros métodos MCMC\n", "\n", "Además del [algoritmo Metropolis-Hastings](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm) existen otros algoritmos de muestreo que utilizan los métodos [MCMC](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo). Algunos de ellos son:\n", "\n", "* **[Muestreo de Gibbs](https://es.wikipedia.org/wiki/Muestreo_de_Gibbs)**, el cual es un caso especial del [algoritmo Metropolis-Hastings](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm).\n", "\n", "* **[Monte-Carlo Hamiltoniano o híbrido](https://en.wikipedia.org/wiki/Hybrid_Monte_Carlo)**, el cual reduce la correlación entre los sucesivos estados de muestreo usando una evolución [Hamiltoniana](https://es.wikipedia.org/wiki/Mec%C3%A1nica_hamiltoniana). \n", "\n", "* **[Muestreo de rebanada o Slice sampler](https://en.wikipedia.org/wiki/Slice_sampling)**, este método se basa en la observación de que para muestrear una [variable aleatoria](https://es.wikipedia.org/wiki/Variable_aleatoria) se pueden tomar muestras en forma uniforme de la región debajo del gráfico de su [función de densidad](https://es.wikipedia.org/wiki/Funci%C3%B3n_de_densidad_de_probabilidad).\n", "\n", "* **[NUTS o No U turn sampler](https://arxiv.org/abs/1111.4246)**, el cual es una extensión del algoritmo [híbrido de Monte-Carlo](https://en.wikipedia.org/wiki/Hybrid_Monte_Carlo) que logra incluso mayor eficiencia.\n", "\n", "Con esto concluye este paseo por los [Métodos de Monte-Carlo](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Montecarlo) y la [estadística](http://relopezbriega.github.io/category/pobabilidad-y-estadistica.html) computacional, espero que les haya parecido interesante y les sea de utilidad en sus proyectos.\n", "\n", "Saludos!\n", "\n", "*Este post fue escrito utilizando IPython notebook. Pueden descargar este [notebook](https://github.com/relopezbriega/relopezbriega.github.io/blob/master/downloads/MCpy.ipynb) o ver su version estática en [nbviewer](http://nbviewer.ipython.org/github/relopezbriega/relopezbriega.github.io/blob/master/downloads/MCpy.ipynb).*" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }