Book Review: The Lean Startup

TBH, I skipped the second half of Part Three: Accelerate and jumped straight into the Epilogue. After reading Innovator's Dilemma, I was expecting a lot from this book. I was disappointed. The Lean Startup is highly laudable; but, I thought some descriptions such as the three "A"s metrics can be more thoroughly discussed. Examples would be great. I try to summarize the book as best as I can...

Summary

Because startups face high risks and extreme uncertainties, a core principle of Lean Startup is to apply scientific approaches to learn, experiment, and test hypotheses as early and as often as possible. Both validated learning and the build-measure-learn loop help startups to learn quickly and make progress. Startup owners and teams should use actionable, accessible, and auditable (three "A"s) metrics, cohort analysis, split-test experiments, and innovation accounting in evaluating performance. "Keep learning" is the thesis of the book (IMO, "adaptive learning" is the thesis).

Two takeaways from the book:

• Build a MVP product early and test market hypotheses.  A MVP (Minimum Viable Product) is a product that lacks some features because it is developed in a relatively short time with minimal effort. With customer feedback from MVP, startups obtain meaningful indicators to make improvements in product. Startups should always target the riskiest assumption first.
• Have a plan? Good: Remember: "Everyone has a plan until they get punched in the face." Think like an experimentalist. Test your hypotheses smartly and frequently. Don't get blinded by "vanity metrics" (see here for definition) that mislead you. Use split tests (A/B tests), cohort analysis, and innovation accounting to interpret data for improvements. Look for actionable, accessible, and auditable metrics like registration and conversion rates. 

Who should read the book:

I don't know.

Finding Convergence, Part III: Fixed Point Iteration

The generalization of our square-root problem in Part I and Part II is that of finding the root of a non-linear function. Given a continuous and differentiable function \(f(x)\), we want to find a value of \(x\) such that

$$\ f(x) = 0$$

1. The first step in the application of the Fixed Point Iteration method is to algebraically manipulate \(f(x)\) so that we can rewrite the underlying relationship in the form of

$$\ x = g(x)$$

2. The second step is making a guess for a starting point, \(x_{0}\). In nearly all cases, the closer the initial guess is to the answer, the more likely the fixed point iteration will converge, and the faster the method will converge.

3. The main step in the algorithm is then expressed as an iterative application of

$$\ x_{n+1} = g(x_{n})$$

which we repeat until the change in \(x\) from one iteration to the next is insignificant in the context of our problem. In a computer implementation, it is often convenient to simply carry out a fixed number of iterations that we know to be more than enough iterations.

Example

Given the function below, let's perform steps 1 to 3:

$$\ f(x) = cos(x) - x$$

Step 1: Arrange the function so that \(x\) is on the left hand side. We want the form of \(f(x)=0\).

$$\ x = cos(x)$$

Step 2: Make an initial guess of  \(x\). 

We know that \(cos(x=0)=1\) and \(cos(x=\frac{\pi}{2})=0\). Therefore, the root must fall in somewhere between 0 and \(\frac{\pi}{2}\). Let's pick the middle,

$$\ x_{0} = \frac{\pi}{4}$$

The results are shown as below. We see that convergence takes place after around 15 iterations. However, it takes 29 iterations to get  \(f(x)\) to \(10^{-7}\).

 

                xn        g(x)                f(x)

0	0.785398	0.707107	-7.829138e-02
1	0.707107	0.760245	5.313782e-02
2	0.760245	0.724667	-3.557712e-02
3	0.724667	0.748720	2.405240e-02
4	0.748720	0.732561	-1.615904e-02
...	...	...	...
26	0.739087	0.739084	-2.715506e-06
27	0.739084	0.739086	1.829198e-06
28	0.739086	0.739085	-1.232170e-06
29	0.739085	0.739085	8.300044e-07
30	0.739085	0.739085	-5.591009e-07

Babylonian Method

Now, if we modify Step 3 using the Babylonian method described in Part II.

$$\ x_{n+1} = \frac{1}{2}(g(x_{n})+x_{n})$$

The result is shown as below. Clearly, the modified method converges much quicker compared to the original method, i.e. 15 iterations vs. 7 iterations.