Category: Notes

Notes on courses, videos, and articles I’ve consumed. When possible I’ve linked back to the source material.

UW Data Science Course Reading List

Part 0: Introduction

Data science articulated, data science examples, history and context, technology landscape

Part 1: Data Manipulation, at Scale

Databases and the relational algebra

Readings

MapReduce, Hadoop, relationship to databases, algorithms, extensions, language; key-value stores and NoSQL; tradeoffs of SQL and NoSQL Readings

Data cleaning, entity resolution, data integration, information extraction*(NOT COVERED IN LECTURES)Readings* / Talks

Part 2: Analytics

Topics in statistical modeling and experiment design Readings

Introduction to Machine Learning, supervised learning, decision trees/forests, simple nearest neighborReadings

Unsupervised learning: k-means, multi-dimensional scaling

Readings

Part 3: Interpreting and Communicating Results

Visualization, visual data analytics Readings (well, watchings)

Backlash: Ethics, privacy, unreliable methods, irreproducible results

Part 4: Graph Analytics

Readings

UW Data Science Course: Week One

Flavors of Data

Numerical This is some sort of quantitative measurement i.e. Heights of people, page load times, stocks prices

There are two types of Numerical Data: Discrete Data – Integer bases; oftne counts of some event

  • How many purchases did a customer make in a year?

  • How many times did I flip "heads"

    Continuous Data

  • Has an infinite number of possible values

    • How much time did it take for a user to check out
    • How much rain fell on a given day?

Categorical Qualitative data that has no inherent mathematical meaning

  • Gender, Yes/No (binary data), Race, State of residence, Product Category, Political Party, etc.
  • You can assign number to categories in order to represent them more compactly, but the numbers don’t have a mathematical meaning

Ordinal This is a mixture of numerical and categorical data

Ordinal data that has mathematical meaning

  • Example: movie ratings on a 1-5 scale
    • Ratings must be 1, 2, 3, 4, or 5
    • But these values have mathematical meanings; 1 means it’s a worse movie than a 2

Statistics 101

Mean

  • This is the average. Sum all the values and divide by the number of values.

Median

  • Sort the values, and take the value at the midpoint
  • if you have a odd number of data points the median might fall in between the two data points.
    • If you have an even number of samples take the average of the two in the middle.
  • Median is less susceptiable to the outliers than the mean.
    • Example: mean household income in the US is $72,641, but the mdeian is only $51,939 – because the mean is skewed by a handfull of billionaries
  • Median better repesents the "typical" American in this example.

Mode

  • The most common value in a data set
    • Not relvant to continuous numerical data
  • Back to our number of kids in each house example.

Standard Deviation and Variance – These concepts are all about the spread of the data (the shape)

Variance – measures how "spread-out" the data is.

  • Variance (sigma squared) is simply the average of the squared differences form the mean.
  • Example: What is the variance of the data set (1, 4, 5, 4, 8)?
    • First find the mean: (1+4+5+4+8)/5 = 4.4
    • Now find the differences from the mean: (-3.4, -0.4, 0.6, -0.4, 3.6)
    • Find the squared differences: (11.56, 0.16, 0.36, 0.16, 12.96)
    • Find the average of the squared differences:
      • sigma squared = (11.56 + 0.16 + 0.36 + 0.16 + 12.96) / 5 = 5.04

Standard Deviation is the the square root of the variance

This is usually used as a way to identify outliers. Data points that lie more than one standard deviation from the mean can be considered unusual.

You can talk about how extreme a data point is by talking about, "how many sigmas" away from the mean it is.

Population vs. Sample

  • If you’re working with a samepl of data instead of an entire data set (the entire population)…
    • The you wnat to use the sample variance instrad of the population variance
    • For N sameples, you just divide the squared variacnecs by N-1 instead of N.
    • So, in out example, we computed the population variance like this:
      • Sigma squared (11.56 + 0.16 + 0.36 + 0.16 + 12.96) / 5 = 5.04
    • But the sample cariance woulb be:
      • S2 = (11.56 + 0.16 + 0.36 + 0.16 + 12.96) / 4 = 6.3

The Why

Probability Density Functions

This is the probability of that range occurring. Its NOT the probability of a specific number occuring.

“Gives you the probability of a data point falling within some given range of a given value.”

Probability Mass Function – Discrete Data

Examples of Data Distributions

Uniform Distribution – there is a flat constant probability that it will happen. Basically, an equal chance that it will happen. Means there is a flat constant (equal) probability of the data occurring.

Normal / Gaussian

Exponential PDF / “Power Law” – Things fall off in an exponential manner.

UW Data Science Course

If you’re a DBA, you need to learn to deal with unstructured data

If you are a statistician, you need to learn to deal with data that does not fit in memory

If you are a software engineer, you need to learn statistical modeling and how to communicate results.

If you are a business analyst, you need to learn about algorithms and tradeoffs at scale.

Week 2

  1. Structures
    1. Rows and columns
    2. Nodes and edges
    3. Key value pairs
    4. A sequence of bytes
  2. Constraints
    1. All rows must have the same number so columns
    2. All values in one column must have the same type
    3. A child cannot have two parents
  3. Operations
    1. Find the value of key x
    2. Fine the rows where column “lastname” is “Jordan”
    3. Get the next N bytes

PWD – "print working directory”

Week 3

Descriptive – Just to describe a set of data (i.e. census data, ngram viewer)

  • Description and the interpretation are different steps
  • Description can usually not be generalized without additional statistical modeling

Exploratory – Find relationships you didn’t know about

  • Exploratory models are good for discovering new connections
  • They are also useful defining future studies
  • Exploratory analyses are usually not the final say
  • Exploratory analyses alone should not be used for generalizing / predicting
  • Correlation does not imply causation

Inferential – Use a relatively small sample of data to say something about a bigger population

  • Inference is commonly the goal of statistical models
  • Inference involves estimating both the quaintly you care about and your uncertainty about your estimate
  • Inference depends heavily on both the population and the sampling scheme

Predictive – To use the data on some objects to predict values for another object

  • If X predicts Y, it does not mean that X causes Y
  • Accurate prediction depends heavily on measuring the right variables.
  • Although there are better and worse prediction models, more data and a simple model works really well.
  • Prediction is very hard, especially about the future references.

Causal – To find out what happens to one variable when you make another variable change.

  • Usually randomized studies are required to identify causation
  • There are approaches to inferring causation in non-randomized studies, but they are complicated and sensitive to assumptions
  • Causal relationships are usually identified as average effects, but may not apply to every individual.
  • Causal models are usually the “gold standard” for data analysis.

Mechanistic – Understand the exact changes in variables that lead to changes in other variables for individual objects.

  • Incredibly harder to infer, except in simple situations
  • Usually modeled by deterministic set of equations (Physical/engineering science)
  • Generally the random component of the data is measurement error
  • If the equations are known but the parameters are not, they maybe interred with data analysis.

What is data – Data are values of qualitative or quantitative variables belonging to a set of items.

  • Set of Items: Sometimes called the populate, the set of objects you are interested in.
  • Variables: A measurement or characteristics of an item.
  • Qualitative: Country of origin, sex, treatment
  • Quantitative: Height, weight, blood pressure

Data rarely comes processed.

Data is the second most important thing

  • The most important think in data science is the question
  • The second most important is the data
  • Often the data will limit or enable the questions
  • But having data can’t save you if you don’t have a question

What about big data?

  • Collect much more data, much more cheaply. Lots of noise to signal ratio.

Big or small data “The data may not contain the answer. The combination of some data and an aching desire for an answer. The combination of some data an an aching desire for an answer does not ensure that a reasonable answer be extracted from a given body of data”

Experimental Design

What should I care about experimental design. It’s really easy to focus on the outcome and overlook an error with the numbers.

  • Care about the analysis plan.
  • It’s critical to pay attention to all aspects of the design and analysis of study. Pay attention to the data cleaning, to data analysis and the reporting so the key issues in the study don’t trip you up.

Question: Does changing the text on your website improve donations?

Experiment:

Formulate your question in advance

  1. Randomly show visitors one version or the other
  2. Measure ho much they donate
  3. Determine which is better

Data Science is a scientific discipline. Science demands you are answering a specific question when you are using data.

Compared two versions of the website. Randomly show visitor two versions. Measure how much they donate to figure out which is better.

Statistical inference – a key component of data science.

Confounding – What are the other variable that are causing a relationship.

  • Randomization and blocking
    • If you can and want to fix a variable
      • Website always says Obama 2012
    • If you don’t fix a variable, stratify it.
      • If you are testing sign up phrases and have two websites colors, use both phrases equally on both.
    • If you can’t fix a variable, randomize it.
    • Why does randomization help?
      • Because it eliminates the possibility that the non-random variable is a factor or not.

Both shoe size and literacy, the bigger the show the more literate someone is, but what’s happening is a baby and child have small feet and less literacy. Age is actually the factor not show size.

Correlation is not causation

Prediction Take a sample of people with Cancer. Take a set of data and separate out the folks that responded to chemotherapy on ones that did not. Then create a function, where you can determine who will and who won’t respond to chemotherapy.

Is challenging than inference

Prediction vs. Inference – the more separated the groupings

Prediction key quantities

  • Sensitivity
    • There probability that you have a disease, given that the test was positive
  • Specificity
    • The probability that you have no disease with a negative test
  • Postive Predictive Value
    • The probability that you have a positive test, that you have a disease
  • Negative Predictive Value
    • If you have a negative test, what is the probability that you have the disease
  • Accuracy
    • This is the probability that you were correct in the outcome.

Beware data dredging

Summary

Good experiments

  • Have replication
  • Measure variability
  • Generalize to the problem you care about
  • Are Transparent

Prediction is not inference

  • Both can be important

Beware of data dredging

  • Data dredging (also data fishing, data snooping, and p-hacking) is the use of data mining to uncover patterns in data that can be presented as statistically significant, without first devising a specific hypothesis as to the underlying causality.

Deep Learning With Python – François Chollet

Could a computer surprise us? Rather than programmers crafting data-processing rules by hand, could a computer automatically learn these rules by looking at data?

To control something, first you need to be able to observe it.

Lose Function The loss function takes the predictions of the network and the true target (what you wanted the network to output) and computes a distance score, capturing how well the network has done

Backpropagation Algorithm **** This adjustment is the job of the optimizer, which implements what’s called the Backpropagation algorithm: the central algorithm in deep learning.

Training Loop This is the training loop, which, repeated a sufficient number of times (typically tens of iterations over thousands of examples), yields weight values that minimize the loss function. A network with a minimal loss is one for which the outputs are as close as they can be to the targets: a trained network. Once again, it’s a simple mechanism that, once scaled, ends up looking like magic.
 Layer The core building block of neural networks is the layer, a data-processing module that you can think of as a filter for data. Some data goes in, and it comes out in a more useful form.

Representations Specifically, layers extract representations out of the data fed into them—hopefully, representations that are more meaningful for the problem at hand.

Data distillation Most of deep learning consists of chaining together simple layers that will implement a form of progressive data distillation. A deep-learning model is like a sieve for data processing, made of a succession of increasingly refined data filters—the layers.

The Compilation Step

  1. A loss function— How the network will be able to measure its performance on the training data, and thus how it will be able to steer itself in the right direction.
  2. An optimizer— The mechanism through which the network will update itself based on the data it sees and its loss function.
  3. Metrics to monitor during training and testing— Here, we’ll only care about accuracy (the fraction of the images that were correctly classified).

Overfitting The test-set accuracy turns out to be 97.8%—that’s quite a bit lower than the training set accuracy. This gap between training accuracy and test accuracy is an example of overfitting: the fact that machine-learning models tend to perform worse on new data than on their training data.

Tensor Numpy arrays, also called tensors. At its core, a tensor is a container for data—almost always numerical data. So, it’s a container for numbers. You may be already familiar with matrices, which are 2D tensors: tensors are a generalization of matrices to an arbitrary number of dimensions (note that in the context of tensors, a dimension is often called an axis).

Scalars (0D tensors) A tensor that contains only one number is called a scalar (or scalar tensor, or 0-dimensional tensor, or 0D tensor). In Numpy, a float32 or float64 number is a scalar tensor (or scalar array). You can display the number of axes of a Numpy tensor via the ndim attribute; a scalar tensor has 0 axes (ndim == 0). The number of axes of a tensor is also called its rank.

Vectors (1D tensors) An array of numbers is called a vector, or 1D tensor. A 1D tensor is said to have exactly one axis.

Dimensionality Dimensionality can denote either the number of entries along a specific axis (as in the case of our 5D vector) or the number of axes in a tensor (such as a 5D tensor), which can be confusing at times. In the latter case, it’s technically more correct to talk about a tensor of rank 5 (the rank of a tensor being the number of axes), but the ambiguous notation 5D tensor is common regardless.

Matrices (2D tensors) An array of vectors is a matrix, or 2D tensor. A matrix has two axes (often referred to rows and columns). You can visually interpret a matrix as a rectangular grid of numbers.

3D tensors If you pack such matrices in a new array, you obtain a 3D tensor, which you can visually interpret as a cube of numbers.

Tenors Attributes

  • Number of axes (rank)— For instance, a 3D tensor has three axes, and a matrix has two axes. This is also called the tensor’s ndim in Python libraries such as Numpy.
  • Shape— This is a tuple of integers that describes how many dimensions the tensor has along each axis. For instance, the previous matrix example has shape (3, 5), and the 3D tensor example has shape (3, 3, 5). A vector has a shape with a single element, such as (5,), whereas a scalar has an empty shape, ().
  • Data type (usually called dtype in Python libraries)—This is the type of the data contained in the tensor; for instance, a tensor’s type could be float32, uint8, float64, and so on. On rare occasions, you may see a char tensor. Note that string tensors don’t exist in Numpy (or in most other libraries), because tensors live in preallocated, contiguous memory segments: and strings, being variable length, would preclude the use of this implementation.

Types of Data

Vector Data – 2D tensors of shape (samples, features) Bach single data point can be encoded as a vector, and thus a batch of data will be encoded as a 2D tensor (that is, an array of vectors), where the first axis is the samples axis and the second axis is the features axis.

Timeseries data or sequence data— 3D tensors of shape (samples, timesteps, features) Whenever time matters in your data (or the notion of sequence order), it makes sense to store it in a 3D tensor with an explicit time axis. Each sample can be encoded as a sequence of vectors (a 2D tensor), and thus a batch of data will be encoded as a 3D tensor.

The time axis is always the second axis (axis of index 1), by convention.

Images— 4D tensors of shape (samples, height, width, channels) or (samples, channels, height, width) Images typically have three dimensions: height, width, and color depth. Although grayscale images (like our MNIST digits) have only a single color channel and could thus be stored in 2D tensors, by convention image tensors are always 3D, with a one-dimensional color channel for grayscale images.

There are two conventions for shapes of images tensors: the channels-last convention (used by TensorFlow) and the channels-first convention (used by Theano).

5D tensors of shape (samples, frames, height, width, channels) or (samples, frames, channels, height, width)

Video data is one of the few types of real-world data for which you’ll need 5D tensors. A video can be understood as a sequence of frames, each frame being a color image. Because each frame can be stored in a 3D tensor (height, width, color_depth), a sequence of frames can be stored in a 4D tensor (frames, height, width, color_depth), and thus a batch of different videos can be stored in a 5D tensor of shape (-samples, frames, height, width, color_depth).