Preface
Contents
Preface¶
Imports¶
# Install packages that are not installed in colab
try:
import google.colab
IN_COLAB = True
except:
IN_COLAB = False
if IN_COLAB:
!pip install watermark
%load_ext watermark
# Core
import numpy as np
import arviz as az
import pandas as pd
import tensorflow as tf
import tensorflow_probability as tfp
2022-01-19 18:53:11.553766: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcudart.so.11.0'; dlerror: libcudart.so.11.0: cannot open shared object file: No such file or directory
2022-01-19 18:53:11.553804: I tensorflow/stream_executor/cuda/cudart_stub.cc:29] Ignore above cudart dlerror if you do not have a GPU set up on your machine.
%watermark -p numpy,tensorflow,tensorflow_probability,arviz,pandas
numpy : 1.21.5
tensorflow : 2.7.0
tensorflow_probability: 0.15.0
arviz : 0.11.4
pandas : 1.3.5
Code 0.1¶
print( "All models are wrong, but some are useful." )
All models are wrong, but some are useful.
Code 0.2¶
x = np.arange(1, 3)
# see how I have to cast it to make tensorflow happy
# remove the cast to see the result yourself
x = tf.cast(x * 10, dtype=tf.float32)
x = tf.math.log(x)
x = tf.reduce_sum(x)
x = tf.exp(x)
x
2022-01-19 18:53:14.194683: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcuda.so.1'; dlerror: libcuda.so.1: cannot open shared object file: No such file or directory
2022-01-19 18:53:14.194719: W tensorflow/stream_executor/cuda/cuda_driver.cc:269] failed call to cuInit: UNKNOWN ERROR (303)
2022-01-19 18:53:14.194747: I tensorflow/stream_executor/cuda/cuda_diagnostics.cc:156] kernel driver does not appear to be running on this host (fv-az272-145): /proc/driver/nvidia/version does not exist
2022-01-19 18:53:14.195067: I tensorflow/core/platform/cpu_feature_guard.cc:151] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations: AVX2 FMA
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
<tf.Tensor: shape=(), dtype=float32, numpy=200.00002>
Code 0.3¶
print(tf.math.log(0.01 ** 200))
print(200 * tf.math.log(0.01))
tf.Tensor(-inf, shape=(), dtype=float32)
tf.Tensor(-921.03406, shape=(), dtype=float32)
The second line is the right answer. This problem arises because of rounding error, when the computer rounds very small decimal values to zero. This loses precision and can introduce substantial errors in inference. As a result, we nearly always do statistical calculations using the logarithm of a probability, rather than the probability itself