Can you read my post?

Is the phrase “can you [do X]?” considered a polite way to request something in written communication on the internet, or perhaps even in American English more generally?

It is a common phrase I encounter in semi-professional communication through e-mails, Slack, etc. It almost always appears without an associated “please”. The most confusing aspect is that, in its typical usage “can you [do X]” is hardly a question with a reasonable yes/no answer (e.g. “can you send me this file?”), it is instead a straightforward request. Unless it easy to replace “can you” by “are you able to” without sounding overly sarcastic, a more accurate way to ask “can you [do X]?” is instead to say “please [do X]”.

I hypothesize that “can you [do X]?” is indeed intended to sound like a less demanding way to request something, by situating the request as a question rather than a command. However, the phrase has a few shortcomings:

  • regardless of intent, it still is missing “please”, (which is important when many small requests add up and eat away at time!);

  • in most contexts it is not really a question and can be interpreted as a frustrated statement, lamenting the inability of the receiver to do simple/trivial tasks.

Can you leave a comment below?

Why Is America Experiencing A Frenzy of Russophobia?

There has been an upward trend of anti-Russian sentiment among the American public, growing at an unstoppable pace since news first broke last June of Russia hacking the DNC. Morning shows, newspaper front-pages, hashtags on social networks: the propaganda machine is at full-steam driving the renewed national phobia of the great threat and evil known as Putin’s Russia.

Note: While writing this post I came across Cathy Young’s op-ed at Forward.com: Red Scare: Trump and Democrats Alike Fan Paranoia Regarding Russia. Ms. Young is an excellent writer and I suggest reading her thoughts on the issue for an alternative analysis. I will weigh in below with my own perspective on the Russia affair.

There are at least three largely overlapping but distinct interest-groups which are central to the anti-Russia info-wars.

Democrats. Sorely bitter after being obliterated in last November’s election, Democrats are engaging in an all-out campaign to undermine the legitimacy of the Trump administration. Democrats are also upset at being hacked, with emails revealing the level of corruption at the core of the DNC and their shameful treatment of Sen. Bernie Sanders. (As an aside: if I were a Democrat supporter I would be rather thankful to Russia for exposing the corruption, fraud, and deception of my leaders, rather than live in la-la land under the doctrine of “good guys” and “bad guys”).

Antagonizing Russia to undermine Trump is an interesting and understandable political strategy, but is neither new nor likely to be particularly fruitful. The Tea Party (and previously, Hillary Clinton’s campaign during the 2008 primaries) played a similar card when questioning Obama’s legitimacy with the birther movement circa 2010. Conspiracies about his Kenyan/Islamic/Martian origins, led in no small part by Trump himself, were endless. Birtherism became a national amusement; Republican media and staunch supporters thrived by fostering a culture of mean-spirited and destructive accusations toward Obama. Well, at least this pattern of undermining political opponents contributes more to the American partisan divide, which is exactly what our country is missing right now.

The foreign policy establishment. The Trump administration has surprised Washington’s foreign policy establishment, which for decades has been led by neoconservative politicians and lobby groups, by significantly marginalizing the State Department. Neocons, who count both prominent Democrats (think Victora Nuland, Obama’s great choreographer of the Ukrainian theatre) and Republicans (Sen. John McCain has been leading the fear-mongering recently) among their ranks, are finding themselves playing second fiddle to Trump’s military generals over at the Pentagon. My sense is that they are fabricating a foreign policy crisis with Russia in an attempt to revitalize their political relevance.

In the meantime, the Americans, Russians, and Turks are engaging in unprecedented levels of security coordination in the fight against ISIS and Syria’s civil war. While coverage of the deployment of 400 Marines into Manbij, Syria has been scant in US media, it is a significant military and diplomatic breakthrough signalling a change in US attitudes toward a solution in Syria.

The national news media. I hypothesize that people enjoy hating on Russia. At least, it gives us external enemy to vent against, and confirm the exceptionalism of our democratic principles and moral character of our leaders. Under Orwellian philosophy, this is exactly the type of sentiment which the system would program its proles to engage in. And under the capitalist system, where media are for-profit corporations acting in their own financial interest and political agendas, if stories about Russia continue to sell pageviews and drive up viewer numbers, then they are guaranteed non-stop coverage. The longevity of the Russia focus is tied only to how long the media can keep up interest, and draw out the saga via unexpected twists and turns. Only then can our attention be moved to worry about the next earth-ending crisis.

I am not an expert on Russian culture, principles, or ways-of-life. As a non-citizen of Russia, and having no connection to the country or daily experiences of its regular people, I do not believe I am empowered to make value judgements about their political system, government, and/or president Vladimir Putin. It is tempting in Western thinking to label other regimes as dictatorial and antagonistic, but I believe that is a judgement only for people to make about themselves.

A Thought Experiment With The Bayesian Posterior Predictive Distribution

Let $\pi(\theta)$ be a prior for parameter $\Theta$, and $p(x|\theta)$ a likelihood which generates an exchangeable sequence of random variables $(X_1,X_2,X_3\dots)$.

Given a set of observations $D := \lbrace X_0=x_0, X_1=x_1, \dots, X_{N-1}=x_{N-1}\rbrace$, the posterior predictive distribution for the next random variable in the sequence $X_N$ is defined as $$p(X_{N}=s | D) = \int p(X_{N}=s | D,\theta) \pi(\theta|D)d\theta = \int p(X_{N}=s|\theta) \pi(\theta|D)d\theta, $$

where the second equality follows from assuming the data is exchangeable (or i.i.d conditioned on latent parameter $\theta$). The posterior predictive density evaluated at ${X_{N}=s}$ is an expectation under the posterior distribution $\pi(\theta|D)$. Define the function $g(s,\theta) := p(X_{N}=s|\theta)$, (note that $g$ does not depend on the index $N$ of the random variable since $\theta$ is known), and then compute the expectation of the random variable $g(s,\Theta)$ under $\pi(\theta|D)$, $$ p(X_N=s | D) = \mathbb{E}_{\pi(\cdot|D)}\left[ g(s,\Theta) \right]. $$

Now consider the case where each random variable $X_i$ is a two-dimensional vector $X_i = (X_{[i,1]}, X_{[i,2]}).$ The data $D = \lbrace X_0=x_0, X_1=x_1, \dots, X_{N-1}=x_{N-1}\rbrace$ is thus an exchangeable sequence of bivariate observations. (Assume for simplicity that marginalizing and conditioning the joint distribution $p(X_{[i,1]},X_{[i,2]}|\theta)$ are easy operations.) We again perform inference to obtain the posterior $\pi(\theta|D)$.

Suppose we wish to evaluate the probability (density) of the event $\lbrace X_{[N,1]}=s \mid X_{[N,2]}=r \rbrace$ under the posterior predictive. I am in two minds about what this quantity could mean:

Approach 1

Define the conditional probability density again as an expectation of a function of $\Theta$ under the posterior distribution. In particular, let the probe function $g(s,r,\theta) := p(X_{[N,1]}=s|X_{[N,2]}=r,\theta)$ (recalling that $g$ does not depend on $N$ when $\theta$ is known) and then compute the expectation of $g(s,r,\Theta)$ under $\pi(\theta|D)$, $$ p_{\text{approach 1}}(X_{[N,1]}=s|X_{[N,2]}=r,D) = \mathbb{E}_{\pi(\cdot|D)}\left[ g(s,r,\Theta) \right]. $$

Approach 2

Define the desired conditional probability density by application of the Bayes Rule. Namely, separately compute two quantities

joint density:
$ p(X_{[N,1]}=s,X_{[N,2]}=r|D) = \int p(X_{[N,1]}=s,X_{[N,2]}=r|\theta) \pi(\theta|D)d\theta $

marginal density:
$ p(X_{[N,2]}=r|D) = \int p(X_{[N,2]}=r|\theta) \pi(\theta|D)d\theta $

and then return their ratio, $$ p_{\text{approach 2}}(X_{[N,1]}=s|X_{[N,2]}=r,D) = \frac{p(X_{[N,1]}=s,X_{[N,2]}=r|D)}{p(X_{[N,2]}=r|D)}. $$

Note that Approach 2 is equivalent to appending the condition $\lbrace X_{[n,2]}=r \rbrace$ to the observation set $D$ so that $D’ := D \cup \lbrace X_{[N,2]}=r \rbrace$ and the new posterior distribution is $\pi(\theta|D’)$. It then computes the expectation of $g(s,r,\Theta)$ under $\pi(\cdot|D’)$, $$ p_{\text{approach 2}}(X_{[N,1]}=s|X_{[N,2]}=r,D) = \mathbb{E}_{\pi(\cdot|D’)}\left[ g(s,r,\Theta) \right] $$

Exercise: Show why the two expressions for $p_{\text{approach 2}}$ are equivalent (or let me know if I made a mistake!)

Thoughts

The question is thus, does the Bayesian reasoner update their beliefs about $\theta$ based on the condition ${X_{[N,2]}=r}$? I think both approaches can make sense:

In Approach 1, we do not treat $\lbrace X_{[N,2]}=r \rbrace$ as a new element of the observation sequence $D$; instead we define the probe function $g(s,r,\theta)$ based on the conditional probability (which is a function of the population parameter), and then compute its expectation.

Approach 2 follows more directly from the “laws of probability” but is less interpretable from the Bayesian paradigm. Why? Because if ${\Theta = \theta}$ is known, then $p(X_{[N,1]}=s|X_{[N,2]}=r,\theta)$ is just a real-number — since the Bayesian does not know $\theta$, they marginalize over it. But it is unclear why the probe function $g(s,r,\theta)$ should influence the distribution of $\pi(\theta|D)$, regardless of whether it happens to represent a density parameterized by $\theta$.

Next Steps

Perhaps I should numerically/analytically compute the difference between Approach 1 and Approach 2 for a bivariate Gaussian with known covariance and unknown mean. For simplicity, just use the prior predictive, letting $D=\varnothing$.

Trump Knew It, Hillary Blew It

Election season has come and gone. Donald Trump pulled off what has been repeatedly characterized as “stunning upset” over bitter rival Hillary Clinton. The web has gone rampant with post-mortem analysis about the failures of election polling. But was it really that stunning?

Several polls conducted in the lead up to the election reported on the virtually deadlocked race, all well-within any reasonable margin of error:

Quinnipiac University reported on the situation in key battleground states (Nov 2)

Democrat Hillary Clinton’s October momentum comes to a halt as she clings to a small lead in Pennsylvania, while Republican Donald Trump moves ahead in Ohio, leaving Florida and North Carolina too close to call.

Probability forecast models on the other hand were remarkably off-mark and predicted Clinton well-ahead just the night before the election:

  • New York Times Upshot: Clinton 84%, Trump 16%
  • FiveThirtyEight: Clinton 66.9%, Trump 33%
  • PredictWise: Clinton 89%, Trump 11%

I was watching the blitz of last-ditch rallies held by Trump and Clinton the night before election day, to learn about the sentiments they were expressing about their chances. Here is a revealing segment from Trump’s penultimate war cry in New Hampshire (8pm on Nov 7):

We are going right after this to Michigan, because Michigan is in play… The polls just came out: we are leading in Michigan; we are leading in New Hampshire; we are leading in Ohio; we are leading in Iowa; leading in North Carolina; I think we are doing really, really well in Pennsylvania; and I do believe we are leading in Florida.

In the meantime, according to the New York Times:

Mrs. Clinton’s campaign was so confident in her victory that her aides popped open Champagne on the campaign plane early Tuesday.

Either way, each candidate and their popular base was clearly happy to live in their own reality right up to the wire. Some personal take-aways from this whole affair:

  • Polling and forecasting is a messy, complex, empirical problem which next-to-nobody understands. I doubt it is statistical.

  • Well-informed voters do not derive the bulk of their information from cursory reading of social or national news media. They are vigilant about critiquing every aspect of information they consume. Otherwise, they are very, very sad.

Everything You Need To Know About … Headlines!

There used to be a time when journalism was a profession. In the information age, however, the production and consumption of public media has become a long gone art. Data streams chaotically and continuously from all directions through the social networks — Facebook, Witter, Slacks, SMS — and it is a mystery how anyone can distill a meaningful signal from the noise. One might rather call it the mis-information age.

One can also write a volume, critiquing the sloppiness in today’s written content. For this post, let us focus right at the start; headlines. The purpose of a headline is to serve as a useful, succinct summary for the content of an article.

Many headlines on the web are instead extremely predictable, repetitive, and often appear to be pulled right out of a book called “Click Bait 101”. I recently browsed through the front page of Google News, and selected an assortment of representative headlines that echo some of the most recurring motifs.

Everything you need to know about …

These articles are a hold-my-hand guide through a dangerously oversimplified presentation of some complex issue. They usually receive very high number of comments and page views. I attribute most the blame for the success of this headline to the intellectual laziness of readers, who wish to quickly be knowledgeable and form opinions about a topic that society agrees is important.

It is also troubling that the writer is confident that they are telling you “everything you need to know about…” It would be more honest and accurate to rephrase as “some things we want you to know about…” Here are some examples.

  • Everything You Need to Know About Britain’s New Prime Minister. ABC
  • Everything You Need to Know About K2, the Drug Linked to Mass Overdose. NBC
  • Everything You Need to Know About Today’s GOP Rules Committee Meeting. ABC
  • Everything you need to know about the net neutrality debate in India. India Times
  • Everything you need to know about Theresa May’s Brexit nightmare in five minutes. Politics UK

The last one is the exemplar — promising a comprehensive coverage of the Brexit in five minutes of your valuable time.

[someone] just did [something shocking]!

Intended for maximum shock and urgency. The [something shocking] event is typically a straight-out-deception of something trivial. The primary purpose of the headline is rather to make a statement about, or build a persona for, the [someone]. Examples:

  • Bernie Sanders Just Made Jill Stein The Most Powerful Woman In American Politics. Huffington Post
  • The FDA Just Declared War on Cookie Dough. Smithsonian
  • Putin Just Created His Own Personal Army. Daily Caller
  • Vladimir Putin just invited Kim Jong Un to visit Russia. Really. Washington Post

Even though a given reader may not read much about Putin, glancing through enough headlines like these work to build the negative, dictatorial character that is widespread in the West today. And who has the remotest idea about who is Jill Stein? Maybe she is too busy working in the Earth’s core and shifting tectonic plates…

[Yes, No, Sorry], …

These headlines sound like bitter responses in an argument on a Youtube comment forum. For each of these examples, consider how much more readable and professional the title would be, without the silly bolded words.

  • No, Bernie Sanders Did Not Sell Out by Endorsing Hillary Clinton — Just the Opposite. Forward
  • Sorry, You’re Just Going To Have to Save More Money.​ Wall St. Journal
  • Sorry 538, La Taqueria is delicious — but it’s also fatally flawed.​ Vox
  • Yes, Clinton is sinking in the polls. No, you should not panic. Here’s why.​ Washington Post

Some similar prefixes to look out for the future are “Right,” and “Wait,”. It is pretty surprising they have not been picked up already.

Conclusion

The next time you come across a headline along these lines, think about why the writer chose that particular pattern, what emotional or intellectual reaction they are trying to evoke, and how it contributes to their propaganda.

May I borrow your name?

Although quite simple, my name is not easy to pronounce in English (even for me). Older people sometimes say “ferris” like a ferris wheel (perhaps in reference to the famous 80s movie Ferris Bueller’s Day Off). I am not particularly bothered by the different permutations either way, but it can be inconvenient at times.

When visiting a coffee shop, or engaging in any other unimportant event where a name is required for reference, I typically give the simplest two-letter name: “Jo”. It is impossible to cause any confusion or unnecessary back-and-forth exchange. The strategy usually works fine (although on rare occasion I stare blank-faced at the poor barista, yelling repetitively for “Jo” and wondering why I am ignoring them).

More recently I have decided to have a bit more fun with using names. The last few times I was grabbing a coffee with a friend, I would use their name at the counter instead. What I found most surprising is the unexpected response it stirred — a mix of confusion, defensiveness, and a feeling of being insulted:

Friend: “That is my name! What is wrong with you?

Me: Relax. (Always fun to tell someone getting worked up to relax)

Friend: “No! You cannot just use my name!

A name is a highly personal matter. I wonder what set of experiments one can design to formally study the question: to what extent do people feel their names are related to their “identity”? Why does casually using someone else’s name (not even posing as that person, which is creepy, but using a general first name which they happen to have) suddenly make them uncomfortable?

I think Shakespeare said it right. Try it with your friends, and see what reactions it invokes.

Enough Urban Legends About QWERTY

Over the past few years there has been much on and off talk about the origins of the QWERTY keyboard. Here is a Google Trends plot showing the “interest” (based on search volume?) of the term qwerty vs dvorak. 

Screenshot from 2016-02-14 21:51:47

I am not sure why Google believe that internet users were suddenly interested in this topic for one day in August 2010 after zero search traffic for half a decade. But the key point is, news headlines (and sometimes “tidbits” at a dinner conversation) now and again keep reminding us of some fables about the much maligned keyboard layout.

Some of the best anecdotes are

  • Bars collided and jammed together in early typewriters, so qwerty designer Christopher Sholes arranged the most common letters in the worst possible locations to slow down typists.
  • The qwerty keyboard arose from telegraph operators who used morse code (a Japanese study looks into the whole prehistory) and found it to be the best arrangement, in comparison to earlier keyboards based on alphabetical order.
  • Salespeople pushed for qwerty because they could type the word T-Y-P-E-W-R-I-T-E-R without having to cross their fingers over one another (a key selling point, of course, because typewriter is a very common English word and our tools need to be specially optimized to type it …)
  • The Illuminati popularized qwerty, in collaboration with the CIA, to slow down Russian spies infiltrating NASA during in the Space Race.

Regardless of the “true” history (which probably is not that interesting) the worst part about all this coverage is the portrayal of qwerty as an historic tragedy which we are now doomed to suffer with forever.

Some studies look into the efficacy of keyboard layout and suggest that the current design is not optimal. College students who are experts with dvorak smirk at their classmates with pride for their superior typing abilities.

It is time to put an end to all this boring droll. So what if we type 3 fewer words per minute? Let us eliminate this great inefficiency for once and for all, and watch as labor productivity, youth employment, and gender equality rise to unprecedented levels, while crime rates, the GINI coefficient and CO2 emissions plummet.

The next time Google News suggest an article about qwerty I am changing news sources.

Metropolis-Hastings With Gaussian Drift Proposal On Bounded Support

Professor Darren Wilkinson has an excellent blog post on a common implementation issue that arises when the standard random-walk Metropolis Hastings algorithm, with a Gaussian proposal, is modified to sample from a target distribution $p(x)$ where

$$\text{supp}(p) = \{ x : p(x) > 0 \} = (0, \infty).$$

In this blog post, we are going to briefly review the setup, the problem, and then generalize the solution proposed by Wilkinson to the situation where $\text{supp}(p) = (a,b)$ (instead of the non-negative reals). We will also allow the Gaussian proposal to have a general variance $\sigma^2$ (rather than just $\sigma^2 = 1$).

The purpose of this blog post is

  • to illustrate that small programmatic changes in a probabilistic algorithm can violate correctness,
  • to hope someone implementing this sampler will find the general derivation informative and useful for their own purposes.

Sampling From A Gamma

To reuse the example from Wilkinson, suppose we are interested in sampling from a gamma with shape $\alpha = 2$ and scale $\theta =1$,

$$p(x) = \frac{1}{Z} x\exp(-x), x > 0$$

by implementing random walk MH. The proposal $N(\cdot | x_i, \sigma^2)$ is a Gaussian with mean at the current sample $x_{i}$, and known variance $\sigma^2$ (aside: the gamma can be sampled much more efficiently). The standard MH algorithm proceeds as

        1. initialize $x_0$ to some value in $(0, \infty)$

        2. for $i = 0,1,2,\dots$

            2.1 sample from the proposal, $x’ \sim N(\cdot|x_i,\sigma^2)$

            2.2 compute the acceptance ratio $A(x’, x_i) = \frac{ p(x’)N(x_i| x’, \sigma^2) }{ p(x_{i})N(x’| x_i, \sigma^2) } = \frac{p(x’)}{p(x_{i})}$

            2.3 if $U[0,1] \le A(x’, x_{i})$

                    then $ x_{i+1} \leftarrow x’$ (accept)

                    else $ x_{i+1} \leftarrow x_{i}$ (reject)

In the sample step 2.1, it is possible that we obtain $x’ < 0$ (for instance, if $x_{i}$ is near 0 or $\sigma^2$ is large). One intuitive approach is to automatically reject samples that are outside $\text{supp}(p)$ and repeat until $x>0$. In the case of $Ga(2,1)$, this rejection would be enforced anyway since the acceptance ratio $A(x’,x_{i})$ will be negative when $x’ < 0$ (if we ignore the fact that $p$ is defined on the positive reals and evaluate $p(x’)$ anyway).

However, Wilkinson observes that if we were sampling from $Ga(3,1)$ for instance, then

$$p(x) = \frac{1}{Z} x^2\exp(-x), x > 0$$

which is positive even when $x < 0$ (again, when ignoring the positive constraint on $x$). Our rejection step would not have been guaranteed to occur in 2.3 had we decided to keep the bad sample $x’ < 0$ in step 2.1. So we were just lucky with the $Ga(2,1)$ example, and need a more robust sampling strategy for the general case.

Rejection Sampling Changes The Proposal Distribution

By discarding samples outside the target support in step 2.1, we are rejection sampling the Gaussian proposal $N(\cdot|x_i,\sigma^2)$ for all values $x’ < 0$. This strategy is equivalent to sampling from a truncated Gaussian, which is not symmetric in its mean and argument. Therefore, we cannot cancel terms in the acceptance ratio (step 2.2) anymore.

A Correct Sampler Needs A Correct Acceptance Ratio

Generalizing the results from Wilkinson, suppose that the target $p(x)$ has $\text{supp}(p) = (a,b)$ and the Gaussian has variance $\sigma^2$ (typically, this variance is adapted during runtime to achieve a desired acceptance rate). We will still reject samples $x’ \notin (a,b)$ in 2.1, and keep sampling until $x’ \in (a,b)$. We need to account for all the previous rejections.

The proposal density is now

$$N_{(a,b)}(x’ | x_i, \sigma^2) = \frac{ \frac{1}{\sigma} \phi (\frac{x’-x_i}{\sigma}) } {\Phi(\frac{b-x_i}{\sigma}) – \Phi(\frac{a-x_i}{\sigma})} \mathbf{I}_{(a,b)}(x’),$$

where $\phi$ is the standard Gaussian density, and $\Phi$ is the standard Gaussian cumulative distribution function. While the numerator is symmetric in $(x’,x_i)$, the denominator is not. It follows that with our new strategy, the correct acceptance ratio for step 2.2

$$A(x’,x_i) = \frac{p(x’) ( \Phi(\frac{b-x_i}{\sigma}) – \Phi(\frac{a-x_i}{\sigma}) ) }{ p(x_{i}) ( \Phi(\frac{b-x’}{\sigma}) – \Phi(\frac{a-x’}{\sigma})) } $$

A good step is to check we agree with Wilkinson in the special case that $a=0,b=\infty,\sigma^2=1$. In this case, the term $\Phi(\frac{b-x_i}{\sigma}) – \Phi(\frac{a-x_i}{\sigma}) = 1-\Phi(-x_i) = \Phi(x_i)$, and similarly for the term in the numerator. This result cross-checks with Wilkinson.

Also remember to change the initialize step 1 to choose $x_0$ from the range of interest.

The Rejection Rate and Numerical Stability

The good news for this sampler is that the mean of the truncated normal $N_{(a,b)}(\cdot|x_i,\sigma^2)$ is guaranteed to remain in the truncation interval, which means the rejection rate is not going to be problematic (unless for some reason $\sigma^2$ is unusually large, which should be designed in tandem with $\text{supp}(p)$ to avoid this issue).

The rejection rate is a problem when the mean $x_i$ of the underlying, non-truncated normal is not in the interval $(a,b)$, and more elaborate algorithms exist (or use a different proposal). Another critical issue in this case is that $\Phi(\frac{b-x_i}{\sigma}) – \Phi(\frac{a-x_i}{\sigma})$ becomes numerically unstable, tends to zero. We would be able to get away with $x/0$ or $0/x$ in $A$, but we might also have the numerically disastrous $0/0$. Thankfully, we do not have these problems.

Conclusion

Samplers are delicate probabilistic objects, treat them with care.

Hello world!

Welcome to Random Seed. A good proportion of implementors of probabilistic computation fail to address two key issues relating to entropy control in their software

  • Keeping track of the state of the random number generator.
  • Permuting the random seed.

We will look into these two issues, as well as many other topics, throughout future blog posts.