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 BLOG >> August 2013

Complex Decision Trees [Decision Trees
Posted on August 21, 2013 @ 01:13:00 PM by Paul Meagher

In my last blog I offered up a video tutorial on how to construct simple decision trees and analyze them using expected values. It is easy to object that these binary decision trees are too simple to represent the complex decision problems that we are confronted with each day. Before you object too loudly, you should examine what a more complex decision tree might look like and the issues that arise when we add more complexity to our decision trees.

A decision tree can become more complex in two basic ways. We can add more intermediate acts or we can add more intermediate events. In simple decision trees we have a binary set of Actions (apply 90 lb nitrogen, apply 110 lb nitrogen) leading to a binary set of Events (e.g., probability of low rainfall, probability of high rainfall) and each combination of Actions and Events lead to an Outcome. See my blog, Representing Decisions with Graphviz, for more details.

So one way we can add complexity to a decision tree, beyond just adding more than 2 branches for each action and event node, is to add intermediate actions and/or events to our decision tree. So, for example, our decision problem might involve the act of either applying 90lbs or 110lbs of Nitrogen per acre to our wheat crop. We might also have to choose between the actions of applying the Nitrogen at time X or at time Y. The combination of these actions can then lead into a season with either a low summer rainfall event or a high summer rainfall event. We can represent a fragment of this decision tree generically with the following diagram:

The diagram was constructed using Graphviz and the dot file I used to construct it looks like this:

digraph MultiStep {

  rankdir=LR;

  Decision -> Action_Step_1A;
  Decision -> Action_Step_1B;

  Action_Step_1A -> Action_Step_2A;
  Action_Step_1A -> Action_Step_2B;

  Action_Step_2A -> Event_1;
  Action_Step_2A -> Event_2;

  Action_Step_2B -> Event_3;
  Action_Step_2B -> Event_4;

}

This is just a fragment of a multistep decision problem. As you can see, the number of terminal branches in this decision problem explodes as we add more intermediate action or event nodes. This does not prevent us from using decision trees to help us make better decisions, but it does give us advance warning that we should be very sure that it is necessary to introduce intermediate actions or events into our decision tree before we do so as they add considerable complexity to the decision tree. Decision trees are not meant to capture the minute details of a decision problem, just the high level actions and events that impact upon the decision. The choice of action and event nodes, just like the assignment of probabilities to event nodes, involves alot of subjective judgement. The process of formalizing it all into a decision tree, however, brings the whole exercise out of subjective reality into consensus reality where others can comment, disagree, or agree with the manner in which you have framed the decision problem.

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Computing Expected Values [Decision Trees
Posted on August 20, 2013 @ 12:47:00 PM by Paul Meagher

So you have a simple decision tree leading from actions, to events, to outcomes. You have labelled the probability of your events, the costs and payoffs associated with actions and outcomes, and you are wondering how you can use all this information to pick a course of action. One answer is that you can compute the expected value associated with each outcome and make your decision based upon the course of action that yields the highest expected value (e.g., highest average profit).

Fortunately, I do not have to explain what an expected value is or how to compute it because there is an excellent tutorial available that explains it all. So, sit back, and learn from MBA Bullshit how to use a decision tree to compute expected values and how you can use expected values to help you decide on a course of action.

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A Theory of Entrepreneurship [Entrepreneurship
Posted on August 15, 2013 @ 07:59:00 AM by Paul Meagher

There are a few theories out there that try to explain successful entrepreneurship. Currently, the best candidate explanation is called the "Lean Startup" theory. It has many useful things to say about how to adapt a service to a market base in a reliable and cost-effective manner. Universities looking to offer courses on entrepreneurship now use Lean Startup Theory as part of the foundational framework for their curriculum. It has some traction.

It is a difficult task to try to explain why some entrepreneurs are successful while others are not. The very definition of what an entrepreneur is fuzzy. Are small business owners entrepreneurs? Or, is that title reserved only for those are trying to bring an innovative product to market? Is the mother who sells Avon on the side an entrepreneur? What about farmers tending to their crops and animals? Or those who fish the oceans? An actor looking for gigs? In my view, entrepreneurship pervades all of these activities and a theory of entrepreneurship should explain why some mothers, farmers, fishers, and actors are more financially successful than others. While being "lean" may be part of the explanation, I conjecture that a factor that has more explanatory weight is how many lines-of-business they have established and are in the process of realistically establishing.

Lines-Of-Business Theory

My theory on successful entrepreneurship can be most easily understood using a farming business as an example. Farmer Joe and Farmer Sally both own farms of equal size and capacity to raise crops and animals. It turns out, however, that Farmer Sally is more successful than Farmer Joe as measured by the amount of profit generated at the end of the year. How might we explain the difference?

If we examine Joe's operation, we might observe that he is raising beef cattle and spends most of his time doing all the chores required to raise his animals. Some years Joe does well and other years not so well, much depends on the price of beef when he is ready to sell. Sally also has some animals, some hens and sheep, and also vegetable gardens, an orchard, and rents out rooms in her house as a bed and breakfast. Sally has not placed all of her eggs in one basket. Instead she has diversified into several lines of business which generate separate streams of income (e.g., sells eggs, lamb, vegetables, apples, and rooms). Her cashflow is also more regular than Joe's. Sally is not making millions of dollars but she is making a comfortable living, is not worrying about how to pay her bills, and has saved money to buy plants and equipment for a new line of business for next year (growing blueberries). Sally is growing her business each year by adding a new line of business each year. Some years, one of her lines of business might do better (room rentals) than another one (pests damage to crops) but overall they compensate for each other because they are fairly separate lines of business.

It is easy to see that having multiple profitable lines-of-business can explain why Sally is more successful than Joe. At the very least, we could use the lines-of-business theory to explain why some farmers are more successful than other farmers - they have more than one line of business, they have chosen lines of business that can compensate each other, they have chosen profitable lines of business, they are investing in new lines-of-business each year, and they are able to manage all of these lines-of-business without a marital, health or stress breakdown.

So does this line-of-business theory explain why some entrepreneurs are successful? It would suggest that they are successful because they have more than one profitable line-of-business, that they have used one line-of-business to bootstrap another line-of-business, that their focus is always divided between expanding existing lines-of-business while also exploring and investing in new lines-of-business. This theory, if true, would have some explanatory force in explaining differential success of entrepreneurs and also offers some suggestions as to what to look for when trying to explain entrepreneur success (define, count, and measure each line of business and see if there is a difference among entrepreneurs that correlates with profit level). It also explains why some mothers, farmers, and actors are more entrepreneurial than others - it has to do with wanting to setup new lines of business (another stream of income). This theory says that successful entrepreneurs do not just do one thing well, they do multiple things well and are always engaged in finding and establishing profitable new lines-of-business.

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Layout, Weights, and Highlighting with Graphviz [Decision Trees
Posted on August 8, 2013 @ 03:56:00 AM by Paul Meagher

I introduced the Graphviz program in my last blog. In today's blog I want to go a little deeper into the DOT language to show how you can achieve three useful effects using the DOT language. The three effects are:

  • Change the overall layout of the graph. Instead of starting our decision tree from the top, I would prefer to start it from the left side of the canvas and expand it towards the right side of the canvas (i.e., left-to-right reading order). I can do this by adding the command rankdir=LR; to my dot file.
  • Would be nice to show probability values on links going into event nodes. For example, the probability of high rain fall this season. We do this by adding a bracket next to link commands and specifying the value for the "label" attribute (e.g., Action -> HighRainFall[label="0.6"];).
  • If you are trying to highlight a path through a decision tree, then there are ways to highlight a path in graphviz. One way would be to thicken the line and add red coloration to each link in the path (e.g., Action -> LowRainFall[label="0.4",color=red,penwidth=3.0]; ).

If we put all these elements together in one dot program file, it would look like this:

digraph { 
  
  rankdir=LR;

  Action -> LowRainFall[label="0.4",color=red,penwidth=3.0]; 
  Action -> HighRainFall[label="0.6"]; 

}

If we load this dot file into the graphviz program "dot", it will generate this graph:

What we have here is a fragment of a graph. A fragment like this might appear in your decision tree leading from an action node to an event node. This is how we can get probabilities to appear on our graphical representations of a decision problem. Also, I like to orient the tree from left-to-right because if you have a large branchy tree it can more easily be printed off whereas top-to-bottom trees are hard to print off and involve alot of horizontal scrolling to view. Finally, when you make a decision to pursue a particular course of action, you can highlight that course of action graphically with a thick red pen effect.

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