Grammar School Inspirations

My kid is nearing the end of her tenure in our local public elementary school. However, for some reason they have had trouble mastering required elements of the language art. After I struggle to answer some of her homework questions, I felt giving up. I had to read some of the text 4-5 times before coming up with very tenuous answers.

Finally, I decided to dispense my massive wisdom instead of trying to demonstrate the correct.

Child, there are several different things you are learning here. In the least you have expression. Expression is the minimum you must do to in the context of speaking, writing, and other performances—let’s just call all these activities performances. Expression can be very basic, chicken scratches, a whole page filled by pencil, a hand print, a foot print, a bark, a cry, Hayden’s Trumpet Concerto performed on a Eb. there are no limits to what constitutes as expression. In America we have laws that protect human vocal expression as a basic rights. Modern arts have taken these to the limits of our imagination. Therefore the minimum is that you must express.

Next thing the teachers teach you is the skill of information communication. An idea in your head, be it information you know to be factual or a feeling, can be communicated to others through performances. Some of the skills in information communication include: summarization, listing information, relating information, serialization, causation etc. the skill of information communication is one of human’s proudest achievements. We can do it efficiently and to great precision. Therefore it is vital that you learn how to do this for both simple and implicit information.

Another purpose of performances is one of affectation. (Here we use it in the first person and speak to skills of affectation, later in a different perspective.) Many of the devices and techniques the school teach are methods of affectation. “How do I grab the readers’ attention?” One often hears echos of classes past… “How do I prepare the reader for this complex concept?” And “How do I surprise/scare/alert/depress the reader/listener/viewer(consumer)?” These skills, for performance learners are geared towards achieving specific goals affecting the consumers. Their successful application reasonably leads to manifestation of intended changes.

So then, for elementary school, you can focus on learning skills and identifying which of expression, communication, and affectation each skill element aims to accomplish….

Me

Now, then, I realized I digressed so much that it is now bed time and her homework is unfinished—because of me. But these thoughts are racing through my head unstoppable.

In truth grammar school performance skill classification actually helped me understand a mess of confusing things. For starters, the fact that expression, as in the freedom of expression, is actually a very nebulous… err… expression. But viewed from a complexity or mental effort to produce, it does not require much. It would appear that freedom of expression is an upper bound on permissible performances. It says that our system of thinking imposes no upper limit to speech or other forms of expression.

EXCEPT, we actually can and indeed do impose restrictions on performances. What comes to mind immediately are NDA’s, trade secrets, government secrets, passwords, etc. There are also lower bounds such as real estate mandatory disclosure rules and SEC filings where specific fields of information are required to be included in any performance. It would appear that we have (or that we have expressed, ala functional relativism—adopting relativistic view to enable computability/functionality/operability) indeed put restrictions on performances that communicate. Even though they are expressive performances, due to their informative functions. The detailed consideration of this type of expression can partially be taken up by a new branch of law covering information property which I proposed as a different type of property from those that we already have laws for, e.g real estate, chattel etc, due to the advancing and emerging science and technology of information. Briefly, we want to quantify it quality information communication using modern and future formal theories of information(such as the idea of information gain). That would enable us to make more precise statements about what we want/can/should communicate.

FURTHERMORE, performances with affectatious nature can further be restricted. Most prominently, in many professional circumstances (teacher, doctor, CPA, police) and in the court of law, it is never permitted for a person to perform so as to (mis)lead the consumer to believe information that is false. They are not permitted to perform so as to induce a damaging or undesirable action of the consumer.

Aside from expression, communication and affectation can be subjective. Whether a person has mislead and whether the performance as intentional or inadvertent, these are determinations that we do not have objective criterion’s for. In the future we may have the technology to measure them, but right now, our society tend to resort to functional relativism by identifying authorities on matters of lying and manipulation—judges in the court system, managers in the professional environment, etc. We, as a society, tend to agree with the judgement of these authorities. “Judge xyz has ruled on such and such matter.” says xyz made a decision , but it also says we hold that decision to be good or true enough to proceed.

I really enjoy my conversations with my children. They make me think hard about what I know and believe. They ask “why” and “what” so much that it trains me to have more critical assessment of the nature of my realities…. and spelling. I can’t wait to talk to them again and again…

Equality of Utility II

Some time ago we investigated the equality of benefits. Roughly speaking let us consider degenerate real world actions into discretely selectable choices of action a\in A given individual x, who has observable features f(x) and protected feature p(x). Suppose the company has to choose among a set of actions to take a \in A. What is a workable definite of fairness or equality in such a decision making effort with respect to protected properties p?

Let god bestow us, a neutral third party, with a utility functor u whose evaluation on the individual u(x) results in a function u(x)(a) is the utility of company taking action a to individual x, u(x)(b) is the utility to individual x of company taking action b.
Let f be the decision process of company g, g(x) is the decision company makes, some a for the individual x. Then the right thing to do
g(f(x)) = argmax_{a\in A}(u(x)(a)) = g(f(x), p(x))
Simple, we do as god says, act as if we have the knowledge of an oracle–even when knowing some discriminable information that we then chose to ignore.

This is not as easy as it looks in a formula. Think of a person with a clown nose and one without, your behavior will likely be very different between those two persons, even if you decide that a clown nose has absolutely nothing to do with the task at hand.

Additionally, the nature of our imperfection dictates that our systems that we build are imperfect. What if we cannot achieve God’s will? What if we fail to do the virtuous even when we know what the right thing to do is?

What could a neutral thirdparty reasonably demand of a faulty company? One suggested approach is to establish probabilistic equality among protected classes. Suppose there are some number of classes, m\in M which corresponds to values of p(x), between which we must protect their utility. (So for example M could be cartesian product of age, sex, race, birthplace, religion and political party)

E(u(x)(g(f(a)))| m) = c\ \forall m\in M

That the customer utility for each class is identically some value c. This is a simplification as there are other classes of equivalence in stochastic variables.

Note this framework has some slight benefit over traditional machine learning framework evaluating equality on confusion matrix of classifier performance g. There two most inspiring examples that I suffer from:

Situation 1: I noticed that my coworker was getting Tesla car advertisements while I do not receive one. Even though my utility in not receiving the advertisement was a negligibly loss–because I cannot afford a tesla, I still feel angry. I may even be tempted to find a protected attribute of mine to claim that tesla discriminated against me in its advertisement campaign: What! they think mid-aged Asian man can’t have a midlife crisis or can’t afford to splurge on a Tesla? In this case a true negative for prediction regarding response/conversion through a Tesla car Ad but offensive enough to cause problems. In retrospect this would have had positive utility for me, when I reached out to Tesla I learned more about how the car would work for me. But the decision seem to produce a negative sentiment from its subject.(The company has, since my drafting of this blog entry, sent me repeated invitation to test drive the S, perhaps due to recent but small increase in my disposable cash, which I may consider calling upon by taking the offer to test drive, at a suitable time. this is just an example)

Situation 2: I am offended when I do receive an advertisement for STD testing, and in particular for hepatitis family of diseases. For gods sake, there’s a Asian Liver Center at Stanford whose purpose for establishment is to check me for hepatitis or other Liver problems present in Asian livers. In this case, god bless me, that I am free of hepatitis and other liver problems of any kind, and that this is a false positive in advertising. I am offended. And in reality one may argue that the benefit of this advertisement, to me, to increase my chances of early detection is positive–E(u(huan)g(f(huan)))>0 I still feel offended. This case is a false positive to advertisement conversion. It is a positive utility to have shown it to me. And yet it produced negative sentiment.

Situation 3: I just received a piece of snail mail from a Redwood City mortuary advertising their service to Mr. And Mrs. Chang. I am terrified. I feel this is a death threat of some form. Putting the idea of me dying in Redwood City in my head. The letter has hand addressed envelope. This is a false positive for advertising relevance(I did not die, not yet any ways, and I am not planning on dying) it has zero utility for me, and I am definitely feeling very negative sentiment.

These are but several of many possible situations where the company could do the right thing in front of God, and in front of the board, by still be erring and thereby producing very negative sentiment. At risk of running out of numbers to enumerate all of them, I have not numbered all the types starting at 1.

To summarize, there are several factors that ultimately factor into a company’s decision making process, nonexclusively they are:

  • The E.u.g.f for x, whether it is defensible in front of an oracle, God, or court of law;
  • how will any action make the subject individual feel, the sentiment it produces, irrespective of objective utility;
  • is utility function universally accepted;
  • and finally the company’s bottom line.

With these considerations in mind, we can now continue with our exploration of fairness.

Equality of Benefit

I’ve been involved in a lot of discussion around bias, equality and fairness regarding algorithmic decision making. Without going into excessive amount of background and detail the gist of my believe at the current moment is that equality of utility is the safest thing for companies to aspire to.

What is equality of utility? Let’s degenerate into binary decision making: given individual x, who has observable features f(x) and protected feature p(x). Suppose the company has to choose among two actions to take {a,b}. What is a workable definite of fairness or equality in such a decision making effort with respect to protected properties p?

Let god bestow us, a neutral third party, with a utility functor u whose evaluation on the individual u(x) results in a function u(x)(a) is the utility of company taking action a to individual x, u(x)(b) is the utility to individual x of company taking action b.

Let g be the decision process of company, g(•) is the decision company makes either a or b for the situation. Then the right thing to do

g(f(x)) = argmax_{i\in{a,b}}(u(x)(i)) = g(f(x), p(x))

Simple, we do as god says is best for the customer, act as if we have the knowledge of an oracle–even when we know of some reason for discrimination.