How to fix “Your CPU supports instructions that this TensorFlow binary was not compiled to use: AVX2 FMA”

After installing Tensorflow using pip3 install:

sudo pip3 install tensorflow

I’ve received the following warning message:

I tensorflow/core/platform/cpu_feature_guard.cc:142] Your CPU supports instructions that this TensorFlow binary was not compiled to use: AVX2 FMA

Advanced Vector Extensions (AVX) are extensions to the x86 instruction set architecture for microprocessors from Intel and AMD proposed by Intel in March 2008 and first supported by Intel with the Sandy Bridge processor shipping in Q1 2011 and later on by AMD with the Bulldozer processor shipping in Q3 2011. AVX provides new features, new instructions, and a new coding scheme.

AVX introduces fused multiply-accumulate (FMA) operations, which speed up linear algebra computation, namely dot-product, matrix multiply, convolution, etc. Almost every machine-learning training involves a great deal of these operations, hence will be faster on a CPU that supports AVX and FMA (up to 300%).

We won’t ignore the warning message and we will compile TF from source.

We will start with uninstalling the default version of  Tensorflow:

sudo pip3 uninstall protobuf
sudo pip3 uninstall tensorflow

In a temp folder, clone Tensorflow:

git clone https://github.com/tensorflow/tensorflow 
git checkout r2.0

Install the TensorFlow pip package dependencies:

pip3 install -U --user pip six numpy wheel setuptools mock future>=0.17.1
pip3 install -U --user keras_applications==1.0.6 --no-deps
pip3 install -U --user keras_preprocessing==1.0.5 --no-deps

Install Bazel, the build tool used to compile TensorFlow. In my case, after downloading bazel-0.26.0-installer-darwin-x86_64.sh:

chmod +x bazel-0.26.0-installer-darwin-x86_64.sh ./bazel-0.26.0-installer-darwin-x86_64.sh --user export PATH="$PATH:$HOME/bin" bazel version

Configure your system build by running the following at the root of your TensorFlow source tree:

./configure

The Tensorflow build options expose flags to enable building for platform-specific CPU instruction sets:

Use bazel to make the TensorFlow package builder with CPU-only support:

bazel build -c opt --copt=-mavx --copt=-mavx2 --copt=-mfma --copt=-msse4.2 //tensorflow/tools/pip_package:build_pip_package

The bazel build command creates an executable named build_pip_package—this is the program that builds the pip package. Run the executable as shown below to build a .whl package in the /tmp/tensorflow_pkg directory.

To build from a release branch:

./bazel-bin/tensorflow/tools/pip_package/build_pip_package /tmp/tensorflow_pkg

Output wheel file is in: /tmp/tensorflow_pkg

You can download the file from here, and try to install it directly

pip3 install /tmp/tensorflow_pkg/tensorflow-2.0.0b1-cp37-cp37m-macosx_10_14_x86_64.whl 

cd out of that directory, and now running this should not produce any warning:

python3 -c "import tensorflow as tf;print(tf.reduce_sum(tf.random.normal([1000, 1000])))"

Enjoy!

Get started developing workflows with Apache Airflow

_images/pin_large.png

History

Airflow was started in October 2014 by Maxime Beauchemin at Airbnb. It was open source from the very first commit and officially brought under the Airbnb GitHub and announced in June 2015.

The project joined the Apache Software Foundation’s Incubator program in March 2016 and the Foundation announced Apache Airflow as a Top-Level Project in January 2019.

Apache Airflow is in use at more than 200 organizations, including Adobe, Airbnb, Astronomer, Etsy, Google, ING, Lyft, NYC City Planning, Paypal, Polidea, Qubole, Quizlet, Reddit, Reply, Solita, Square, Twitter, and United Airlines, among others.

Introduction

Airflow is a platform to programmatically author, schedule and monitor workflows.

Use airflow to author workflows as directed acyclic graphs (DAGs) of tasks. The airflow scheduler executes your tasks on an array of workers while following the specified dependencies. Rich command line utilities make performing complex surgeries on DAGs a snap. The rich user interface makes it easy to visualize pipelines running in production, monitor progress, and troubleshoot issues when needed.

When workflows are defined as code, they become more maintainable, versionable, testable, and collaborative.

Workflows

We’ll create a workflow by specifying actions as a Directed Acyclic Graph (DAG) in Python. The tasks of a workflow make up a Graph; the graph is Directed because the tasks are ordered; and we don’t want to get stuck in an eternal loop so the graph also has to be Acyclic.

The figure below shows an example of a DAG:

Installation

pip3 install apache-airflow
airflow version

AIRFLOW_HOME is the directory where you store your DAG definition files and Airflow plugins

mkdir Airflow
export AIRFLOW_HOME=`pwd`/Airflow

Airflow requires a database to be initiated before you can run tasks. If you’re just experimenting and learning Airflow, you can stick with the default SQLite option. 

airflow initdb
ls -l Airflow/

The database airflow.db is created

You can start Airflow UI by issuing the following command:

airflow webserver

Opening http://0.0.0.0:8080

Your first Airflow DAG

We’ll start by creating a Hello World workflow, which does nothing other then sending “Hello world!” to the log.

Create your dags folder, that is the directory where your DAG definition files will be stored in AIRFLOW_HOME/dags. Inside that directory create a file named hello_world.py:

mkdir dags

Add the following code to dags/hello_world.py

from datetime import datetime
from airflow import DAG
from airflow.operators.dummy_operator import DummyOperator
from airflow.operators.python_operator import PythonOperator

def print_hello():
    return 'Hello world!'

dag = DAG('hello_world', description='Simple tutorial DAG',
          schedule_interval='0 12 * * *',
          start_date=datetime(2019, 5, 29), catchup=False)

dummy_operator = DummyOperator(task_id='dummy_task', retries=3, dag=dag)

hello_operator = PythonOperator(task_id='hello_task', python_callable=print_hello, dag=dag)

dummy_operator >> hello_operator

This file creates a simple DAG with just two operators, the DummyOperator, which does nothing and a PythonOperator which calls the print_hello function when its task is executed.

Running your DAG

Open a second terminal, go to the AIRFLOW_HOME folder and start the Airflow scheduler by issuing :

export AIRFLOW_HOME=`pwd`
airflow scheduler

When you reload the Airflow UI in your browser, you should see your hello_world DAG listed in Airflow UI.

In order to start a DAG Run, first turn the workflow on, then click the Trigger Dag button and finally, click on the Graph View to see the progress of the run.

After clicking the Graph View:

You can reload the graph view until both tasks reach the status Success.

When they are done, you can click on the hello_task and then click View Log.

If everything worked as expected, the log should show a number of lines and among them something like this:

Your first Airflow Operator

Let’s start writing our own Airflow operators. An Operator is an atomic block of workflow logic, which performs a single action. Operators are written as Python classes (subclasses of BaseOperator), where the __init__ function can be used to configure settings for the task and a method named execute is called when the task instance is executed.

Any value that the execute method returns is saved as an Xcom message under the key return_value. We’ll cover this topic later.

The execute method may also raise the AirflowSkipException from airflow.exceptions. In such a case the task instance would transition to the Skipped status.

If another exception is raised, the task will be retried until the maximum number of retries is reached.

Remember that since the execute method can retry many times, it should be idempotent [it can be applied multiple times without changing the result beyond the initial application]

We’ll create your first operator in an Airflow plugin file named plugins/my_operators.py. First create the /plugins directory, then add the my_operators.py file with the following content:


import logging

from airflow.models import BaseOperator
from airflow.plugins_manager import AirflowPlugin
from airflow.utils.decorators import apply_defaults

log = logging.getLogger(__name__)

class MyFirstOperator(BaseOperator):

    @apply_defaults
    def __init__(self, my_operator_param, *args, **kwargs):
        self.operator_param = my_operator_param
        super(MyFirstOperator, self).__init__(*args, **kwargs)

    def execute(self, context):
        log.info("Hello World!")
        log.info('operator_param: %s', self.operator_param)

class MyFirstPlugin(AirflowPlugin):
    name = "my_first_plugin"
    operators = [MyFirstOperator]


In this file we are defining a new operator named MyFirstOperator. Its execute method is very simple, all it does is log “Hello World!” and the value of its own single parameter. The parameter is set in the __init__ function.

We are also defining an Airflow plugin named MyFirstPlugin. By defining a plugin in a file stored in the /plugins directory, we’re providing Airflow the ability to pick up our plugin and all the operators it defines. We’ll be able to import these operators later using the line from airflow.operators import MyFirstOperator.

Now, we’ll need to create a new DAG to test our operator. Create a dags/test_operators.py file and fill it with the following content:

from datetime import datetime
from airflow import DAG
from airflow.operators.dummy_operator import DummyOperator
from airflow.operators import MyFirstOperator

dag = DAG('my_test_dag', description='Another tutorial DAG',
          schedule_interval='0 12 * * *',
          start_date=datetime(2019, 5, 29), catchup=False)

dummy_task = DummyOperator(task_id='dummy_task', dag=dag)

operator_task = MyFirstOperator(my_operator_param='This is a test.',
                                task_id='my_first_operator_task', dag=dag)

dummy_task >> operator_task

Here we just created a simple DAG named my_test_dag with a DummyOperator task and another task using our new MyFirstOperator. Notice how we pass the configuration value for my_operator_param here during DAG definition.

At this stage your source tree looks like this:

To test your new operator, you should stop (CTRL-C) and restart your Airflow web server and scheduler. Afterwards, go back to the Airflow UI, turn on the my_test_dag DAG and trigger a run. Take a look at the logs for my_first_operator_task.

Your first Airflow Sensor

An Airflow Sensor is a special type of Operator, typically used to monitor a long running task on another system.

To create a Sensor, we define a subclass of BaseSensorOperator and override its poke function. The poke function will be called over and over every poke_interval seconds until one of the following happens:

  • poke returns True – if it returns False it will be called again.
  • poke raises an AirflowSkipException from airflow.exceptions – the Sensor task instance’s status will be set to Skipped.
  • poke raises another exception, in which case it will be retried until the maximum number of retries is reached.

As an example, SqlSensor runs a sql statement until a criteria is met, HdfsSensor waits for a file or folder to land in HDFS, S3KeySensor waits for a key (a file-like instance on S3) to be present in a S3 bucket), S3PrefixSensor waits for a prefix to exist and HttpSensor executes a HTTP get statement and returns False on failure.

To add a new Sensor to your my_operators.py file, add the following code:

from datetime import datetime
from airflow.operators.sensors import BaseSensorOperator

class MyFirstSensor(BaseSensorOperator):

    @apply_defaults
    def __init__(self, *args, **kwargs):
        super(MyFirstSensor, self).__init__(*args, **kwargs)

    def poke(self, context):
        current_minute = datetime.now().minute
        if current_minute % 3 != 0:
            log.info("Current minute (%s) not is divisible by 3, sensor will retry.", current_minute)
            return False

        log.info("Current minute (%s) is divisible by 3, sensor finishing.", current_minute)
        return True

Here we created a very simple sensor, which will wait until the the current minute is a number divisible by 3. When this happens, the sensor’s condition will be satisfied and it will exit. This is a contrived example, in a real case you would probably check something more unpredictable than just the time.

Remember to also change the plugin class, to add the new sensor to the operators it exports:

class MyFirstPlugin(AirflowPlugin):
    name = "my_first_plugin"
    operators = [MyFirstOperator, MyFirstSensor]

The final my_operators.py file is:

import logging

from airflow.models import BaseOperator
from airflow.plugins_manager import AirflowPlugin
from airflow.utils.decorators import apply_defaults

from datetime import datetime
from airflow.operators.sensors import BaseSensorOperator

log = logging.getLogger(__name__)

class MyFirstOperator(BaseOperator):

    @apply_defaults
    def __init__(self, my_operator_param, *args, **kwargs):
        self.operator_param = my_operator_param
        super(MyFirstOperator, self).__init__(*args, **kwargs)

    def execute(self, context):
        log.info("Hello World!")
        log.info('operator_param: %s', self.operator_param)

class MyFirstSensor(BaseSensorOperator):

    @apply_defaults
    def __init__(self, *args, **kwargs):
        super(MyFirstSensor, self).__init__(*args, **kwargs)

    def poke(self, context):
        current_minute = datetime.now().minute
        if current_minute % 3 != 0:
            log.info("Current minute (%s) not is divisible by 3, sensor will retry.", current_minute)
            return False

        log.info("Current minute (%s) is divisible by 3, sensor finishing.", current_minute)
        return True

class MyFirstPlugin(AirflowPlugin):
    name = "my_first_plugin"
    operators = [MyFirstOperator, MyFirstSensor]

You can now place the operator in your DAG, so the new test_operators.py file looks like:

from datetime import datetime
from airflow import DAG
from airflow.operators.dummy_operator import DummyOperator
from airflow.operators import MyFirstOperator, MyFirstSensor


dag = DAG('my_test_dag', description='Another tutorial DAG',
          schedule_interval='0 12 * * *',
          start_date=datetime(2019, 5, 29), catchup=False)

dummy_task = DummyOperator(task_id='dummy_task', dag=dag)

sensor_task = MyFirstSensor(task_id='my_sensor_task', poke_interval=30, dag=dag)

operator_task = MyFirstOperator(my_operator_param='This is a test.',
                                task_id='my_first_operator_task', dag=dag)

dummy_task >> sensor_task >> operator_task

Restart your webserver and scheduler and try out your new workflow. The Graph View looks like:

If you click View log of the my_sensor_task task, you should see something similar to this:

Have fun developing data pipelines!

References:

https://airflow.apache.org/

https://github.com/hgrif/airflow-tutorial

http://michal.karzynski.pl/blog/2017/03/19/developing-workflows-with-apache-airflow/

PyCon.DE 2017 Tamara Mendt – Modern ETL-ing with Python and Airflow (and Spark)

Recall, Precision, F1, ROC, AUC, and everything

Your boss asked you to build a fraud detection classifier, so you’ve created one.

The output of your fraud detection model is the probability [0.0-1.0] that a transaction is fraudulent. If this probability is below 0.5, you classify the transaction as non-fraudulent; otherwise, you classify the transaction as fraudulent.

To evaluate the performance of your model, you collect 10,000 manually classified transactions, with 300 fraudulent transaction and 9,700 non-fraudulent transactions. You run your classifier on every transaction, predict the class label (fraudulent or non-fraudulent) and summarise the results in the following confusion matrix:

A True Positive (TP=100) is an outcome where the model correctly predicts the positive (fraudulent) class. Similarly, a True Negative (TN=9,000) is an outcome where the model correctly predicts the negative (non-fraudulent) class.

False Positive (FP=700) is an outcome where the model incorrectly predicts the positive  (fraudulent) class. And a False Negative (FN=200) is an outcome where the model incorrectly predicts the negative (non-fraudulent) class.

Asking yourself what percent of your predictions were correct, you calculate the accuracy:

Accuracy = \frac{True}{True+False} = \frac{TP+TN}{TP+TN+FP+FN} = \frac{100+9,000}{100+9,000+700+200} = \frac{9,100}{10,000} = 0.91

Wow, 91% accuracy! Just before sharing the great news with your boss, you notice that out of the 300 fraudulent transactions, only 100 fraudulent transactions are classified correctly. Your classifier missed 200 out of the 300 fraudulent transactions!

Your colleague, hardly hiding her simile, suggests a “better” classifier. Her classifier predicts every transaction as non-fraudulent (negative), with a staggering 97% accuracy!

Accuracy =   \frac{True}{True+False} = \frac{TP+TN}{TP+TN+FP+FN} = \frac{0+9,700}{100+9,000+700+200} = \frac{9,700}{10,000} = 0.97

While 97% accuracy may seem excellent at first glance, you’ve soon realized the catch: your boss asked you to build a fraud detection classifier, and with the always-return-non-fraudulent classifier you will miss all the fraudulent transactions.

“Nothing travels faster than the speed of light, with the possible exception of bad news, which obeys its own special laws.” 

Douglas Adams

You learned the hard-way that accuracy can be misleading and that for problems like this, additional measures are required to evaluate your classifier.

You start by asking yourself what percent of the positive (fraudulent) cases did you catch? You go back to the confusion matrix and divide the True Positive (TP – blue oval) by the overall number of true fraudulent transactions (red rectangle)

Recall ( True Positive Rate ) = \frac{TP}{TP+FN} = \frac{100}{100+200} \approx 0.333

So the classier caught 33.3% of the fraudulent transactions.

Next, you ask yourself what percent of positive (fraudulent) predictions were correct? You go back to the confusion matrix and divide the True Positive (TP – blue oval) by the overall number of predicted fraudulent transactions (red rectangle)

Precision =   \frac{TP}{TP+FP} = \frac{100}{100+700} = 0.125

So now you know that when your classifier predicts that a transaction is fraudulent, only 12.5% of the time your classifier is correct.

F1 Score combines Recall and Precision to one performance metric. F1 Score is the weighted average of Precision and Recall. Therefore, this score takes both false positives and false negatives into account. F1 is usually more useful than Accuracy, especially if you have an uneven class distribution.

F1 = 2*\frac{Recall * Precision}{ Recall + Precision}=2*\frac{0.333 * 0.125}{ 0.333 + 0.125}\approx 0.182

Finally, you ask yourself what percent of negative (non-fraudulent) predictions were incorrect? You go back to the confusion matrix and divide the False Positive (FP – blue oval) by the overall number of true non-fraudulent transactions (red rectangle)

False Positive Rate = \frac{FP}{FP+TN} = \frac{700}{700+9,000} \approx 0.072

7.2% of the non-fraudulent transactions were classified incorrectly as fraudulent transactions.

ROC (Receiver Operating Characteristics)

You soon learn that you must examine both Precision and Recall. Unfortunately, Precision and Recall are often in tension. That is, improving Precision typically reduces Recall and vice versa.

The overall performance of a classifier, summarized over all possible thresholds, is given by the Receiver Operating Characteristics (ROC) curve. The name “ROC” is historical and comes from communications theory. ROC Curves are used to see how well your classifier can separate positive and negative examples and to identify the best threshold for separating them.

To be able to use the ROC curve, your classifier should be able to rank examples such that the ones with higher rank are more likely to be positive (fraudulent). As an example, Logistic Regression outputs probabilities, which is a score that you can use for ranking.

You train a new model and you use it to predict the outcome of 10 new test transactions, summarizing the result in the following table: the values of the middle column (True Label) are either zero (0) for non-fraudulent transactions or one (1) for fraudulent transactions, and the last column (Fraudulent Prob) is the probability that the transaction is fraudulent:

Remember the 0.5 threshold? If you are concerned about missing the two fraudulent transactions (red circles), then you may consider lowering this threshold.

For instance, you might lower the threshold and label any transaction with a probability below 0.1 to the non-fraudulent class, catching the two fraudulent transactions that you previously missed.

To derive the ROC curve, you calculate the True Positive Rate (TPR) and the False Positive Rate (FPR), starting by setting the threshold to 1.0, where every transaction with a Fraudulent Prob of less than 1.0 is classified as non-fraudulent (0). The column “T=1.0” shows the predicted class labels when the threshold is 1.0:

The confusion matrix for the Threshold=1.0 case:

The ROC curve is created by plotting the True Positive Pate (TPR) against the False Positive Rate (FPR) at various threshold settings, so you calculate both:

True Positive Rate (Recall) = \frac{TP}{TP+FN} = \frac{0}{0+5} =0

False Positive Rate = \frac{FP}{FP+TN} = \frac{0}{0+5} =0

You summarize it in the following table:

Now you can finally plot the first point on your ROC graph! A random guess would give a point along the dotted diagonal line (the so-called line of no-discrimination) from the left bottom to the top right corners

You now lower the threshold to 0.9, and recalculate the FPR and the TPR:

The confusion matrix for Threshold=0.9:

True Positive Rate (Recall) = \frac{TP}{TP+FN} = \frac{1}{1+4} =0.2

False Positive Rate = \frac{FP}{FP+TN} = \frac{0}{0+5} =0

Adding a new row to your summary table:

You continue and plot the True Positive Pate (TPR) against the False Positive Rate (FPR) at various threshold settings:

Receiver Operating Characteristics (ROC) curve

And voila, here is your ROC curve!

AUC (Area Under the Curve)

The model performance is determined by looking at the area under the ROC curve (or AUC). An excellent model has AUC near to the 1.0, which means it has a good measure of separability. For your model, the AUC is the combined are of the blue, green and purple rectangles, so the AUC = 0.4 x 0.6 + 0.2 x 0.8 + 0.4 x 1.0 = 0.80.

You can validate this result by calling roc_auc_score, and the result is indeed 0.80.

Conclusion

  • Accuracy will not always be the metric.
  • Precision and recall are often in tension. That is, improving precision typically reduces recall and vice versa.
  • AUC-ROC curve is one of the most commonly used metrics to evaluate the performance of machine learning algorithms.
  • ROC Curves summarize the trade-off between the true positive rate and false positive rate for a predictive model using different probability thresholds.
  • The ROC curve can be used to choose the best operating point.

Thanks for Reading! You can reach me at LinkedIn and Twitter.

References:

[1] An Introduction to Statistical Learning [James, Witten, Hastie, and Tibshirani]

How to run PySpark 2.4.0 in Jupyter Notebook on Mac

Install Jupyter notebook

$ pip3 install jupyter

Install PySpark

Make sure you have Java 8 or higher installed on your computer and visit the Spark download page

Select the latest Spark release, a prebuilt package for Hadoop, and download it directly.

Unzip it and move it to your /opt folder:

$ tar -xzf spark-2.4.0-bin-hadoop2.7.tgz
$ sudo mv spark-2.4.0-bin-hadoop2.7 /opt/spark-2.4.0

A symbolic link is like a shortcut from one file to another. The contents of a symbolic link are the address of the actual file or folder that is being linked to.

Create a symbolic link (this will let you have multiple spark versions):

$ sudo ln -s /opt/spark-2.4.0 /opt/spark̀

Check that the link was indeed created

$ ls -l /opt/spark̀

lrwxr-xr-x 1 root wheel 16 Dec 26 15:08 /opt/spark̀ -> /opt/spark-2.4.0

Finally, tell your bash where to find Spark. To find what shell you are using, type:

$ echo $SHELL
/bin/bash

To do so, edit your bash file:

$ nano ~/.bash_profile

configure your $PATH variables by adding the following lines to your ~/.bash_profile file:

export SPARK_HOME=/opt/spark
export PATH=$SPARK_HOME/bin:$PATH
# For python 3, You have to add the line below or you will get an error
export PYSPARK_PYTHON=python3

Now to run PySpark in Jupyter you’ll need to update the PySpark driver environment variables. Just add these lines to your ~/.bash_profile file:

export PYSPARK_DRIVER_PYTHON=jupyter
export PYSPARK_DRIVER_PYTHON_OPTS='notebook'

Your ~/.bash_profile file may look like this:

Restart (our just source) your terminal and launch PySpark:

$ pyspark

This command should start a Jupyter Notebook in your web browser. Create a new notebook by clicking on ‘New’ > ‘Notebooks Python [default]’.

Running PySpark in Jupyter Notebook

The PySpark context can be

sc = SparkContext.getOrCreate()

To check if your notebook is initialized with SparkContext, you could try the following codes in your notebook:

sc = SparkContext.getOrCreate()
import numpy as np
TOTAL = 10000
dots = sc.parallelize([2.0 * np.random.random(2) - 1.0 for i in range(TOTAL)]).cache()
print("Number of random points:", dots.count())
stats = dots.stats()
print('Mean:', stats.mean())
print('stdev:', stats.stdev())

The result:

Running PySpark in your favorite IDE

Sometimes you need a full IDE to create more complex code, and PySpark isn’t on sys.path by default, but that doesn’t mean it can’t be used as a regular library. You can address this by adding PySpark to sys.path at runtime. The package findspark does that for you.

To install findspark just type:

$ pip3 install findspark

And then on your IDE (I use Eclipse and Pydev) to initialize PySpark, just call:

import findspark
findspark.init()
import pyspark
sc = pyspark.SparkContext(appName="myAppName")

Here is a full example of a standalone application to test PySpark locally 

import findspark
findspark.init()
import random
from pyspark import SparkContext
sc = SparkContext(appName="EstimatePi")
def inside(p):
x, y = random.random(), random.random()
return x<em>x + y</em>y &lt; 1
NUM_SAMPLES = 1000000
count = sc.parallelize(range(0, NUM_SAMPLES)) \
.filter(inside).count()
print("Pi is roughly %f" % (4.0 * count / NUM_SAMPLES))
sc.stop()

The result:

Enjoy!

Based on this article and on this article

Error when executing `jupyter notebook` (-bash: jupiter: command not found) [Mac]

After installing jupyter

pip3 install --upgrade pip
pip3 install jupyter

and trying to launch 

jupyter notebook

the following error message appeared

-bash: jupyter: command not found

The solution:  

pip3 install --upgrade --force-reinstall --no-cache-dir jupyter 

Fighting Digital Payments Fraud with Deep Learning

Interesting presentation today at the DataScience SG meet-up

Conventional fraud prevention methods are rule based, expansive and slow to implement

Q1 2016: $5 of every $100 subject to fraud attack!

Key fraud types: account takeover, friendly fraud & fraud due to stolen card information

Consumers want: easy, instant, customized, mobile and dynamic options to suit their personal situation. Consumers do NOT want to be part of the fraud detection process.

Key technology enablers:

Historically fraud detection systems have relied on rues hand-curated by fraud experts to catch fraudulent activity.

An auto-encoder is a neural network trained to reconstruct its inputs, which forces a hidden layer to try and to learn good representations of the input

Kaggle dataset:

Train Autoencoder on normal transactions and using the Autoencoder transformation there is now a clear separation between the normal and the fraudulent transactions.

The Secret Recipe Behind GO-FOOD’s Recommendations (PyData Meetup)

The December PyData Meetup started with Luis Smith, Data Scientist at GO-JEK, sharing the Secret Recipe Behind GO-FOOD’s Recommendations:

“For GO-FOOD, we believe the key to unlocking good recommendations is to derive vector representations for our users, dishes, and merchants. This way we are able to capture our users’ food preferences and recommend them the most relevant merchants and dishes.”

How do people think about the food?

  • Flavor profile
  • Trendy
  • Value for money
  • Portion size
  • Ingredients

… and much more

The preferred approach is to let the transactional data discover the pattern.

A sample ETL workflow:

Using StarSpace to learn the vector representations:

Go-Jek formulation of the problem:

User-to-dish similarity is surfaced in the app via the “dishes you might like”. The average vector of customer’s purchases represents the recommended dish.

Due to data sparsity, item-based collaborative filtering is used for merchant recommendation.

The cold start problem is still an issue, for inactive users or users that purchase infrequently.

(published here)

Highlights of the 2018 Singapore Symposium on Natural Language Processing (SSNLP)

What a great symposium! Thank you Dr. Linlin Li, Prof. Ido Dagan, Prof. Noah Smith and the rest of the speakers for the interesting talks and thank you Singapore University of Technology and Design (SUTD) for hosting this event. Here is a quick summary of the first half of the symposium, you can learn more by looking for the papers published by these research groups:

Linlin Li: The text processing engine that powers Alibaba’s business applications

Dr. Linlin Li from Alibaba presented the mission of Alibaba’s NLP group and spoke about AliNLP, a large scale NLP technology platform for the entire Alibaba Eco-system, dealing with data collection and multilingual algorithms for lexical, syntactic, semantic, discourse analysis and distributed representation of text.

Alibaba is also helping to improve the quality of the Electronic Medical Records (EMRs) in China, traditionally done by labour intensive methods.

Ido Dagan: Consolidating Textual Information

Prof. Ido Dagan gave an excellent presentation on Natural Knowledge Consolidating Textual Information. Texts come in large multitudes, such as news story, search results, and product reviews. Search interfaces hasn’t changed much in decades, which make them accessible, but hard to consume. For example, the news tweets illustration in the slide below shows that here is a lot of redundancy and complementary information, so there is a need to consolidate the knowledge within multiple texts.

Generic knowledge representation via structured knowledge graphs and semantic representation are often being used, where both approaches require an expert to annotate the dataset, which is expansive and hard to replicate.

The structure of a single sentence will look like this:

The information can be consolidated across the various data sources via Coreference

To conclude

Noah A. Smith: Syncretizing Structured and Learned Representation

Prof. Noah described new ways to use representation learning for NLP

Some promising results

Prof. Noah presented different approaches to solve backpropagation with structure in the middle, where the intermediate representation is non-differentiable.

See you all the the next conference!

MICE is Nice, but why should you care?

Multiple Imputation by Chained Equations (MICE) 

mouse-303588_1280

As every data scientist will witness, it is rarely that your data is 100% complete. We are often taught to “ignore” missing data. In practice, however, ignoring or inappropriately handling the missing data may lead to biased estimates, incorrect standard errors and incorrect inferences.

But first we need to think about what led to this missing data, or what was the mechanism by which some values were missing and some were observed?

There are three different mechanisms to describe what led to the missing values:

  • Missing Completely At Random (MCAR): the missing observations are just a random subset of all observations, so there are no systematic differences between the missing and observed data. In this case, analysis using only complete cases will not be biased, but may have lower power.
  • Missing At Random (MAR): there might be systematic differences between the missing and observed data, but these can be entirely explained by other observed variables. For example, a case where you observe gender and you see that women are more likely to respond than men. Including a lot of predictors in the imputation model can make this assumption more plausible.
  • Not Missing At Random (NMAR): the probability of a variable being missing might depend on itself on other unobserved values. For example, the probability of someone reporting their income depends on what their income is.

MICE operates under the assumption that given the variables used in the imputation procedure, the missing data are Missing At Random (MAR), which means that the probability that a value is missing depends only on observed values and not on unobserved values

Multiple imputation by chained equations (MICE) has emerged in the statistical literature as one principled method of addressing missing data. Creating multiple imputations, as opposed to single imputations, accounts for the statistical uncertainty in the imputations. In addition, the chained equations approach is very flexible and can handle variables of varying types (e.g., continuous or binary) as well as complexities such as bounds.

The chained equation process can be broken down into the following general steps:

  • Step 1: A simple imputation, such as imputing the mean, is performed for every missing value in the dataset. These mean imputations can be thought of as “place holders.”
  • Step 2: Start Step 2 with the variable with the fewest number of missing  values. The “place holder” mean imputations for one variable (“var”) are set back to missing.
  • Step 3: “var” is the dependent variable in a regression model and all the other variables are independent variables in the regression model.
  • Step 4: The missing values for “var” are then replaced with predictions (imputations) from the regression model. When “var” is subsequently used as an independent variable in the regression models for other variables, both the observed and these imputed values will be used.
  • Step 5: Moving on to the next variable with the next fewest missing values, steps 2–4 are then repeated for each variable that has missing data. The cycling through each of the variables constitutes one iteration or “cycle.” At the end of one cycle all of the missing values have been replaced with predictions from regressions that reflect the relationships observed in the data.
  • Step 6: Steps 2 through 4 are repeated for a number of cycles, with the imputations being updated at each cycle. The idea is that by the end of the cycles the distribution of the parameters governing the imputations (e.g., the coefficients in the regression models) should have converged in the sense of becoming stable.

To make the chained equation approach more concrete, imagine a simple example where we have 3 variables in our dataset: age, income, and gender, and all 3 have at least some missing values. I created this animation as a way to visualize the details of the following example, so let’s get started.

MICE Animation

The initial dataset is given below, where missing values are marked as N.A.

Step00

In step 1 of the MICE process, each variable would first be imputed using, e.g., mean imputation, temporarily setting any missing value equal to the mean observed value for that variable.

Step01

Then in the next step the imputed mean values of age would be set back to missing (N.A).

Step02

In the next step Bayesian linear regression of age predicted by income and gender would be run using all cases where age was observed.

Step03

In the next step, prediction of the missing age value would be obtained from that regression equation and imputed. At this point, age does not have any missingness.

Step04

The previous steps would then be repeated for the income variable. The originally missing values of income would be set back to missing (N.A).

Step05

A linear regression of income predicted by age and gender would be run using all cases with income observed.

Step06

Imputations (predictions) would be obtained from that regression equation for the missing income value.

Step07

Then, the previous steps would again be repeated for the variable gender. The originally missing values of gender would be set back to missing and a logistic regression of gender on age and income would be run using all cases with gender observed. Predictions from that logistic regression model would be used to impute the missing gender values.

Step08

This entire process of iterating through the three variables would be repeated until some measure of convergence, where the imputations are stable; the observed data and the final set of imputed values would then constitute one “complete” data set.

We then repeat this whole process multiple times in order to get multiple imputations.

* Let’s connect on Twitter (@ofirdi), LinkedIn or my Blog

Resources

What is the difference between missing completely at random and missing at random? Bhaskaran et al https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4121561/

A Multivariate Technique for Multiply Imputing Missing Values Using a Sequence of Regression Models, E. Raghunathan et al http://www.statcan.gc.ca/pub/12-001-x/2001001/article/5857-eng.pdf

Multiple Imputation by Chained Equations: What is it and how does it work? Azur et al https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3074241/

Recent Advances in missing Data Methods: Imputation and Weighting – Elizabeth Stuart https://www.youtube.com/watch?v=xnQ17bbSeEk

Introduction to Survival Analysis

Introduction

Survival analysis is generally defined as a set of methods for analysing data where the outcome variable is the time until the occurrence of an event of interest. For example, if the event of interest is heart attack, then the survival time can be the time in years until a person develops a heart attack. For simplicity, we will adopt the terminology of survival analysis, referring to the event of interest as ‘death’ and to the waiting time as ‘survival’ time, but this technique has much wider applicability. The event can be death, occurrence of a disease, marriage, divorce, etc. The time to event or survival time can be measured in days, weeks, years, etc.

The specific difficulties relating to survival analysis arise largely from the fact that only some individuals have experienced the event and, subsequently, survival times will be unknown for a subset of the study group. This phenomenon is called censoring.

In longitudinal studies exact survival time is only known for those individuals who show the event of interest during the follow-up period. For others (those who are disease free at the end of the observation period or those that were lost) all we can say is that they did not show the event of interest during the follow-up period. These individuals are called censored observations. An attractive feature of survival analysis is that we are able to include the data contributed by censored observations right up until they are removed from the risk set.

Survival and Hazard

T  –  a non-negative random variable representing the waiting time until the occurrence of an event.

The survival function, S(t), of an individual is the probability that they survive until at least time t, where t is a time of interest and T is the time of event.

F001

The survival curve is non-increasing (the event may not reoccur for an individual) and is limited within [0,1].

survival-graph-crop

F(t) – the probability that the event has occurred by duration t:

F002

the probability density function (p.d.f.) f(t):

F003

An alternative characterisation of the distribution of T is given by the hazard function, or instantaneous rate of occurrence of the event, defined as

F004

The numerator of this expression is the conditional probability that the event will occur in the interval [t,t+dt] given that it has not occurred before, and the denominator is the width of the interval. Dividing one by the other we obtain a rate of event occurrence per unit of time. Taking the limit as the width of the interval goes down to zero, we obtain an instantaneous rate of occurrence.

Applying Bayes’ Rule

F005

on the numerator of the hazard function:

F006

Given that the event happened between time t to t+dt, the conditional probability of this event happening after time t is 1:

F007

Dividing by dt and passing to the limit gives the useful result:

F008

In words, the rate of occurrence of the event at duration t equals the density of events at t, divided by the probability of surviving to that duration without experiencing the event.

We will soon show that there is a one-to-one relation between the hazard and the survival function.

The derivative of S(t) is:

F009

We will now show that the hazard function is the derivative of -log S(t):

F010

If we now integrate from 0 to time t:

F011

F012

F013

 and introduce the boundary condition S(0) = 1 (since the event is sure not to have occurred by duration 0):

F014

F015

we can solve the above expression to obtain a formula for the probability of surviving to duration t as a function of the hazard at all durations up to t:

F016

One approach to estimating the survival probabilities is to assume that the hazard function follow a specific mathematical distribution. Models with increasing hazard rates may arise when there is natural aging or wear. Decreasing hazard functions are much less common but find occasional use when there is a very early likelihood of failure, such as in certain types of electronic devices or in patients experiencing certain types of transplants. Most often, a bathtub-shaped hazard is appropriate in populations followed from birth.

The figure below hows the relationship between four parametrically specified hazards and the corresponding survival probabilities. It illustrates (a) a constant hazard rate over time (e.g. healthy persons) which is analogous to an exponential distribution of survival times, (b) strictly increasing (c) decreasing hazard rates based on a Weibull model, and (d) a combination of decreasing and increasing hazard rates using a log-Normal model. These curves are illustrative examples and other shapes are possible.

different_hazard_functions

Example

The simplest possible survival distribution is obtained by assuming a constant risk over time:

survival-constant-risk

Censoring and truncation

One of the distinguishing feature of the field of survival analysis is censoring: observations are called censored when the information about their survival time is incomplete; the most commonly encountered form is right censoring.

censor_truncation

Right censoring occurs when a subject leaves the study before an event occurs, or the study ends before the event has occurred. For example, we consider patients in a clinical trial to study the effect of treatments on stroke occurrence. The study ends after 5 years. Those patients who have had no strokes by the end of the year are censored. Another example of right censoring is when a person drops out of the study before the end of the study observation time and did not experience the event. This person’s survival time is said to be censored, since we know that the event of interest did not happen while this person was under observation.

Left censoring is when the event of interest has already occurred before enrolment. This is very rarely encountered.

In a truncated sample, we do not even “pick up” observations that lie outside a certain range.

Unlike ordinary regression models, survival methods correctly incorporate information from both censored and uncensored observations in estimating important model parameters

Non-parametric Models

The very simplest survival models are really just tables of event counts: non-parametric, easily computed and a good place to begin modelling to check assumptions, data quality and end-user requirements etc. When no event times are censored, a non-parametric estimator of S(t) is 1 − F(t), where F(t) is the empirical cumulative distribution function.

Kaplan–Meier

When some observations are censored, we can estimate S(t) using the Kaplan-Meier product-limit estimator. An important advantage of the Kaplan–Meier curve is that the method can take into account some types of censored data, particularly right-censoring, which occurs if a patient withdraws from a study, is lost to follow-up, or is alive without event occurrence at last follow-up.

Suppose that 100 subjects of a certain type were tracked over a period of time to determine how many survived for one year, two years, three years, and so forth. If all the subjects remained accessible throughout the entire length of the study, the estimation of year-by-year survival probabilities for subjects of this type in general would be an easy matter. The survival of 87 subjects at the end of the first year would give a one-year survival probability estimate of 87/100=0.87; the survival of 76 subjects at the end of the second year would yield a two-year estimate of 76/100=0.76; and so forth.

But in real-life longitudinal research it rarely works out this neatly. Typically there are subjects lost along the way (censored) for reasons unrelated to the focus of the study.

Suppose that 100 subjects of a certain type were tracked over a period of two years determine how many survived for one year and for two years. Of the 100 subjects who are “at risk” at the beginning of the study, 3 become unavailable (censored) during the first year and 3 are known to have died by the end of the first year. Another 2 become unavailable during the second year and another 10 are known to have died by the end of the second year.

KM_experiment_table_died

Kaplan and Meier proposed that subjects who become unavailable during a given time period be counted among those who survive through the end of that period, but then deleted from the number who are at risk for the next time period.

The table below shows how these conventions would work out for the present example. Of the 100 subjects who are at risk at the beginning of the study, 3 become unavailable during the first year and 3 die. The number surviving the first year (Year 1) is therefore 100 (at risk) – 3 (died) = 97 and the number at risk at the beginning of the second year (Year 2) is 100 (at risk) – 3 (died) – 3 (unavailable) = 94. Another 2 subjects become unavailable during the second year and another 10 die. So the number surviving Year 2 is 94 (at risk) – 10 (died) = 84.

KM_experiment_table_survived

As illustrated in the next table, the Kaplan-Meier procedure then calculates the survival probability estimate for each of the t time periods, except the first, as a compound conditional probability.

KM_experiment_table

The estimate for surviving through Year 1 is simply 97/100=0.97. And if one does survive through Year 1, the conditional probability of then surviving through Year 2 is 84/94=0.8936. The estimated probability of surviving through both Year 1 and Year 2 is therefore (97/100) x (84/94)=0.8668.

Incorporating covariates: proportional hazards models

Up to now we have not had information for each individual other than the survival time and censoring status ie. we have not considered information such as the weight, age, or smoking status of individuals, for example. These are referred to as covariates or explanatory variables.

Cox Proportional Hazards Modelling

The most interesting survival-analysis research examines the relationship between survival — typically in the form of the hazard function — and one or more explanatory variables (or covariates).

F017

where λ0(t) is the non-parametric baseline hazard function and βx is a linear parametric model using features of the individuals, transformed by an exponential function. The baseline hazard function λ0(t) does not need to be specified for the Cox model, making it semi-parametric. The baseline hazard function is appropriately named because it describes the risk at a certain time when x = 0, which is when the features are not incorporated. The hazard function describes the relationship between the baseline hazard and features of a specific sample to quantify the hazard or risk at a certain time.

The model only needs to satisfy the proportional hazard assumption, which is that the hazard of one sample is proportional to the hazard of another sample. Two samples xi and xj satisfy this assumption when the ratio is not dependent on time as shown below:

F018

The parameters can be estimated by maximizing the partial likelihood.

 

Sources:
https://www.cscu.cornell.edu/news/statnews/stnews78.pdf
https://www.nature.com/articles/6601118#t2
http://blog.applied.ai/survival-analysis-part1/#fn:3
http://data.princeton.edu/wws509/notes/c7s1.html
https://en.wikipedia.org/wiki/Kaplan%E2%80%93Meier_estimator
http://www.stats.ox.ac.uk/~mlunn/lecturenotes1.pdf
Kaplan-Meier methods and Parametric Regression methods, Kristin Sainani Ph.D.
http://vassarstats.net/survival.html
http://www.mas.ncl.ac.uk/~nmf16/teaching/mas3311/week09.pdf