Data Science Decisions in Time:Sequential Hypothesis Testing

Overview

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This is part of our specialization on Making Decision in Time. For this second course we start with a landmark paper from Chernoff and build new insights into the ideas that his paper sparked. The ending point should bring new code and new algorithm insights into perspective, and use, by many computer and data scientists.

Syllabus

Chernoff and Active Hypothesis Testing

We extend Wald's ideas for sequential hypothesis testing to a new -- and closely related -- problem. In this second course we evaluate how best to choose from a set of hypothesis for sequentially arriving data. This has many modern applications, for example how best to set a price for a new product, what is the best therapy for a patient, how to determine the rare events in a stream of visual images and many many more. We begin by examining a type of visual search for the 'odd one out' and then build from that first week.

Hierarchical Searching for Alternative Hypothesis

Searching within an ordered hierarchical setting can improve the search. But, it is not immediately obvious how to setup the data structure to support this type of search. In this part of the course we explore how to define a biased walk, based on information, to quickly find an 'odd one out'. From this concept of walking along a tree structure, we then move into thinking about how to best setup that tree structure.

Large Hypothesis and/or Action Spaces

Many real-world applications have extremely large action and/or hypothesis spaces. For the application of Chernoff's ideas there has to be a way to apply the algorithms quickly at scale. In this set of material we examine how approximations may work and how Chernoff's ideas have been extended to different types of problems.

Sequential Hypothesis for Biology and Medicine

The ideas that we have been exploring can also be applied to data slices collected at disparate windows in time, can be applied to improving MRI scans and can be applied to molecular protein design. These applications all share the concept of using sequential hypothesis testing to improve understanding. In addition, all three of these ideas are under active code development.

Putting it together: testing on visual images

In our fifth week we explore how to move beyond the 'odd one out' and into multiple hypothesis testing for streams of data. This could be for setting a dosage level on a medication or on how to identify objects in a set of images.