Data Science Overview
Statistics is the discipline of analyzing data. As such it intersects heavily with data science, machine learning and, of course, traditional statistical analysis. These are:
- Descriptive statistics
- Experimental Design
Descriptive statistics includes exploratory data analysis, unsupervised learning, clustering and basic data summaries. Descriptive statistics have many uses, most notably helping us get familiar with a data set. Descriptive statistics usually are the starting point for any analysis. Often, descriptive statistics help us arrive at hypotheses to be tested later with more formal inference.
Inference is the process of making conclusions about populations(群体) from samples. Inference includes most of the activities traditionally associated with statistics such as: estimation, confidence intervals, hypothesis tests and variability. Inference forces us to formally define targets of estimations or hypotheses. It forces us to think about the population that we’re trying to generalize to from our sample.
Prediction overlaps quite a bit with inference, but modern prediction tends to have a different mindset. Prediction is the process of trying to guess an outcome given a set of realizations of the outcome and some predictors. Machine learning, regression, deep learning, boosting, random forests and logistic regression are all prediction algorithms. If the target of prediction is binary or categorical, prediction is often called classification. In modern prediction, emphasis shifts from building small, parsimonious, interpretable models to focusing on prediction performance, often estimated via cross validation. Generalizability is often given not by a sampling model, as in traditional inference, but by challenging the algorithm on novel datasets. Prediction has transformed many fields include e-commerce, marketing and financial forecasting.
Experimental design is the act of controlling your experimental process to optimize the chance of arriving at sound conclusions. The most notable example of experimental design is randomization. In randomization a treatment is randomized across experimental units to make treatment groups as comparable as possible. Clinical trials and A/B testing both employ randomization. In random sampling, one tries to randomly sample from a population of interest to get better generalizability of the results to the population. Many election polls try to get a random sample.
Machine learning has been a revolution in modern prediction and clustering. Machine learning has become an expansive field involving computer science, statistics and engineering. Some of the algorithms have their roots in artificial intelligence (like neural networks and deep learning). For data scientists, we decompose two main activities of machine learning. (Of course, this list is non-exhaustive.) These are are
- Unsupervised learning - trying to uncover unobserved factors in the data. It is called “unsupervised” as there is no gold standard outcome to judge against. Some example algorithms including hierarchical clustering, principal components analysis, factor analysis and k-means.
- Supervised learning - using a collection of predictors, and some observed outcomes, to build an algorithm to predict the outcome when it is not observed. Some examples include: neural networks, random forests, boosting and support vector machines.
We give a famous early example of unsupervised clustering in the computation of the g-factor. This was postulated to be a measure of intrinsic intelligence. Early factor analytic models were used to cluster scores on psychometric questions to create the g-factor. Notice the lack of a gold standard outcome. There was no true measure of intrinsic intelligence to train an algorithm to predict it.
For supervised learning, we give an early example, the development of regression. In this, Francis Galton wanted to predict children’s heights from their parents. He developed linear regression in the process. Notice that having several children with known adult heights along with their parents allows one to build the model, then apply it to parents who are expecting.
It is worth contrasting modern machine learning and prediction with more traditional statistics. Traditional statistics has a great deal of overlap with machine learning, including models that produce very good predictions and methods for clustering. However, there is much more of an emphasis in traditional statistics on modeling and inference, the problem of extending results to a population. Modern machine learning was somewhat of a revolution in statistics not only because of the performance of the algorithms for supervised and unsupervised problems, but also from a paradigm shift away from a focus on models and inference. Below we characterize some of these differences.和传统统计学视角不一样的地方：
For this discussion, I would summarize (focusing on supervised learning) some characteristics of ML as:
- the emphasis on predictions;
- evaluating results via prediction performance;
- having concern for overfitting but not model complexity per se;
- emphasis on performance;
- obtaining generalizability through performance on novel datasets;
- usually no superpopulation model specified;
- concern over performance and robustness.
In contrast, I would characterize the typical characteristics of traditional statistics as:
- emphasizing superpopulation inference;
- focusing on a-priori hypotheses;
- preferring simpler models over complex ones (parsimony), even if the more complex models perform slightly better;
- emphasizing parameter interpretability;
- having statistical modeling or sampling assumptions that - connect data to a population of interest;
- having concern over assumptions and robustness.
In recent years, the distinction between both fields have substantially faded. ML researchers have worked tirelessly to improve interpretations while statistical researchers have improved the prediction performance of their algorithms.
The Structure of a Data Science Project
- 5 Phases
- EDA(Exploratory Data Analysis)
- Are the data suitable for the question
- Sketch the solution
- Formal Modeling
The outputs of a data science experiment
- Clearly written
- Concise conclusions
- Omit the unnecessary
- Reproducible result
- Web pages and apps
- Easy to use
- Code commented
- Version control
Defining Success in data science
Defining success is a crucial part of managing a data science experiment. Of course, success is often context specific. However, some aspects of success are general enough to merit discussion. My list of hallmarks of success includes:
- New knowledge is created.
- Decisions or policies are made based on the outcome of the experiment.
- A report, presentation or app with impact is created.
- It is learned that the data can’t answer the question being asked of it.
Some more negative outcomes include: decisions being made that disregard clear evidence from the data, equivocal results that do not shed light in one direction or another, uncertainty prevents new knowledge from being created.
Let’s discuss some of the successful outcomes first.
New knowledge seems ideal to me (especially since I’m an academic). However, new knowledge doesn't necessarily mean that it's important. If it produces actionable decisions or policies, that’s even better. (Wouldn’t it be great if there was an evidence-based policy like the evidence-based medicine movement that has transformed medicine.) That our data science products have great (positive) impact is of course ideal. Creating reusable code or apps is great way to increase the impact of a project.
Finally, the last point is perhaps the most controversial. I view it as a success if we can show that the data can’t answer the questions being asked. I am reminded of a friend who told a story of the company he worked at. They hired many expensive prediction consultants to help use their data to inform pricing. However, the prediction results weren’t helping. They were able to prove that the data couldn’t answer the hypothesis under study. There was too much noise and the measurements just weren’t accurately measuring what was needed. Sure, the result wasn’t optimal, as they still needed to know how to price things, but it did save money on consultants. I have since heard this story repeated nearly identically by friends in different industries.
Data Scientist Toolbox
- iPython Notebook
- R markdown
Sperating Hype from Value
- What is the question you are trying to answer with data?
- Do you have the data to answer that question?
- If you could answer the question? Could you use the answer?