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probml
GitHub Repository: probml/pyprobml
 Path: blob/master/notebooks/book1/02/centralLimitDemo.ipynb
1193 views
Kernel: Python 3

Central Limit Theorem 

import jax
import jax.numpy as jnp
import matplotlib.pyplot as plt
import seaborn as sns

try:
    from probml_utils import savefig, latexify
except ModuleNotFoundError:
    %pip install -qq git+https://github.com/probml/probml-utils.git
    from probml_utils import savefig, latexify
Collecting git+https://github.com/probml/probml-utils.git Cloning https://github.com/probml/probml-utils.git to /tmp/pip-req-build-mc62jfr2 Running command git clone -q https://github.com/probml/probml-utils.git /tmp/pip-req-build-mc62jfr2 Installing build dependencies ... done Getting requirements to build wheel ... done Preparing wheel metadata ... done Requirement already satisfied: firebase-admin in /usr/local/lib/python3.7/dist-packages (from probml-utils==0.1.dev50+g413eabd) (4.4.0) Requirement already satisfied: scikit-learn in /usr/local/lib/python3.7/dist-packages (from probml-utils==0.1.dev50+g413eabd) (1.0.2) Requirement already satisfied: graphviz in /usr/local/lib/python3.7/dist-packages (from probml-utils==0.1.dev50+g413eabd) (0.10.1) Requirement already satisfied: jaxlib in /usr/local/lib/python3.7/dist-packages (from probml-utils==0.1.dev50+g413eabd) (0.3.7+cuda11.cudnn805) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from 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/root/.cache/pip/wheels/2b/8e/c6/7ee3f9f9776fd18c0ccb04492902ed42225b6dfab3c68f14c0 Successfully built probml-utils TexSoup Installing collected packages: chex, TexSoup, distrax, probml-utils Successfully installed TexSoup-0.3.1 chex-0.1.3 distrax-0.1.2 probml-utils-0.1.dev50+g413eabd 
latexify(width_scale_factor=2, fig_height=1.85)
/usr/local/lib/python3.7/dist-packages/probml_utils/plotting.py:26: UserWarning: LATEXIFY environment variable not set, not latexifying warnings.warn("LATEXIFY environment variable not set, not latexifying") 
def calcMean(keys, N):
    # Generates N random numbers from 1 to 5 and calculates their mean.
    x = jnp.mean(jax.random.beta(keys, 1, 5, [1, N]))
    return x

def plot_convolutionHist(mean_list, N, sampleSize, bins):
    counts, nbinslocation = jnp.histogram(mean_list, bins=20)
    counts = counts / (sampleSize / bins)

    plt.figure()
    plt.title(f"N = {N}")
    plt.bar(nbinslocation[:-1], counts, width=0.02, color="black", align="edge")

    plt.xticks(jnp.linspace(0, 1, 3))
    plt.yticks(jnp.linspace(0, 3, 4))
    plt.xlim(0, 1)
    plt.ylim(0, 3)
    plt.xlabel("$bins$")
    plt.ylabel("$Frequency\ (\mu)$")
    sns.despine()
    savefig(f"clt_N_{N}")

key = jax.random.PRNGKey(1)
keys = jax.random.split(key, num=10000)

sampleSize = 10000
bins = 20
N_array = [1, 5]
for N in N_array:
    means = jax.vmap(calcMean, in_axes=(0, None), out_axes=0)
    out = means(keys, N)
    plot_convolutionHist(out, N, sampleSize, bins)
/usr/local/lib/python3.7/dist-packages/probml_utils/plotting.py:79: UserWarning: set FIG_DIR environment variable to save figures warnings.warn("set FIG_DIR environment variable to save figures")
Image in a Jupyter notebookImage in a Jupyter notebook
from ipywidgets import interact


@interact(N_value=(1, 10))
def generate_random(N_value):
    sampleSize = 100000
    bins = 20
    means = jax.vmap(calcMean, in_axes=(0, None), out_axes=0)
    out = means(keys, N_value)
    plot_convolutionHist(out, N_value, sampleSize, bins)