Archive for the ‘Wally Xie’ Category

Qchain: Blockchain Advertising and Analytics Platform

Friday, June 2nd, 2017

I am presently working on a project called Qchain, which is focused focused on facilitating efficient and cost-effective transactions between digital advertisers and content publishers using blockchain technology, with a wonderfully scrappy and resourceful team. The development and rise of cryptocurrency has fascinating me over the past few years, and I am excited to finally be a part of it in a more intimate and front-line fashion.

Bitcoin started snaking its way into the global consciousness while I was in college. I remember chuckling about the pizzas being sold for $10,000. And then, from pizzas, we moved on to dark net markets, Mt. Gox, the rise and fall of a million microcosms in the mining scene, from CPUs, to GPUs, to ASICs. And where are we at now? Proof of stake, proof of importance, proof of contribution, proof of covfefe.

Increasing speculative awareness of cryptocurrency has certainly outstripped day-to-day enterprise and civilian use cases of blockchain technology, and I have my doubts about whether blockchain technology is good for certain things at all, given that the decentralization facilitated by blockchain tech is not a be-all, end-all. Indeed, certain things function better centralized; the spectrum of trade-offs on the decentralization-centralization scale varies for different things. However, there is no doubt that blockchain solutions will come to prove their use for several markets and industry sectors. They have already more than proved themselves for dark net markets. For all the joking about the impracticality and triviality of cryptocurrency, I’d say that changing how humans buy drugs is a massive feat.

I have no doubt that blockchains will (eventually) become used for the record keeping and resolution of insurance claims, the shipment and verification of goods, and the verification and tracking of tax payments. And perhaps (I and my team obviously hope), blockchain solutions could become useful for advertising. Let us see how this all plays out! I definitely welcome you to read more about the Qchain project proposal in our white paper located on our website.

LaTeX Poster — “Bayesian Evaluation of Earth System Models Using Soil Respiration Data”

Saturday, January 28th, 2017

Download (PDF, 373KB)

Poster presented at regional conference today, SoCal Sysbio at my home institution, UCI.

LaTeX .tex file and beamerposter style file for the poster are included here. The template is based off of Philippe Dreuw and Thomas Deselaers’ original beamerposter template available at this link. Where my style file differs is that with some modifications, it no longer is limited to the Tango color palette and now also accepts dvipsnames and svgnames color names to increase the breadth of available colors.

I’ve been having a lot of fun with this project. Some details already on the poster, of course. An even briefer TLDR; of this is that I am trying to compare Earth System models (ESMs) in a Bayesian fashion to see which models are consistent with historical soil carbon dioxide flux data and are worth the effort to refine. I eyeballed some fits of the conventional and AWB soil carbon models under informative and realistic priors, and am proceeding to quantify the fits using Bayesian goodness of fit metrics. I will take a look at Bayes factors and posterior predictive p-values.

Arranging a Beta Distribution into Exponential Family Form

Sunday, November 20th, 2016

A family of PMFs or PDFs is an exponential family if it can be arranged into the form

$f(x|\theta) = h(x)c(\theta)\exp\left(\sum_{i=1}^kw_i(\theta)t_i(x)\right)$

where $\theta$ is the vector of parameters.

The Beta distribution PDF takes the form

$f_X(x) = \frac{x^{\alpha – 1}(1 – x)^{\beta – 1}}{\textrm{B}(\alpha, \beta)}$

Given that the $\alpha$ and $\beta$ parameters are unknown, we now arrange $f_X(x)$ into an exponential family form:

$f(x|\alpha,\beta) = \frac{x^{\alpha – 1}(1 – x)^{\beta – 1}}{\textrm{B}(\alpha, \beta)}$
$= \frac{e^{(\alpha – 1)\ln(x)}e^{(\beta – 1)\ln(1 – x)}}{\textrm{B}(\alpha, \beta)}$
$= \frac{e^{(\alpha – 1)\ln(x) + (\beta – 1)\ln(1 – x)}}{\textrm{B}(\alpha, \beta)}$
$= \frac{1}{\textrm{B}(\alpha, \beta)}e^{(\alpha – 1)\ln(x) + (\beta – 1)\ln(1 – x)}$

The log identity $x^b = e^{b\ln(x)}$ is a very useful logarithmic identity to remember when trying to arrange PDFs into exponential family form.

We observe:
$h(x) = I_{x \in (0,1)}(x)$ (If you see that h(x) = 1, that is a cue to use an indicator function that ranges through the support of $x$.)
$c(k,\beta) = \frac{1}{\textrm{B}(\alpha, \beta)$
$w_1(k,\beta) = \alpha – 1$
$w_2(k,\beta) = \beta – 1$
$t_1(x) = \ln(x)$
$t_2(x) = \ln(1-x)$

Hence, the Beta distribution given unknown parameters $\alpha$ and $\beta$ is an exponential family with a two-dimensional parameter vector $\theta$.

A similar process will apply for showing that a Beta PDF with one unknown parameter, $\beta$ or $\alpha$ is an exponential family.

Regarding Identity Politics And Their Guaranteed Persistence

Sunday, November 20th, 2016

I absolutely hate this talk of “we must end identity politics” that has become pervasive after the election, especially as people are trying to prescribe Democrats solutions for how to recover from this election. First off, how are people defining “identity politics”? It appears that a lot of people are using it as a blanket term for political organization and mobilization by gender, race, or ethnic group. Identity politics exist and will not go away because your geographic origins, gender, phenotypes, genotypes determine your lot in life, the hand you’ve been dealt, et cetera (insert favored idiom here). Your predetermined traits (like those of an RPG character class) come with a set of pros and cons that relate to your probabilities of success in life as defined by societal and cultural values. People are motivated to maintaining or improving their probabilities, so it is easy to motivate people to advocate for the blocs they belong to. Yes, identity politics make it easy to hate on another group of people as The Others, but it has also mobilized mass sectors of the American population to advocate for egalitarian goals, such as women’s suffrage, desegregation, and elimination of sodomy laws, which allowed members of one American bloc to live significantly more comfortably at little or no cost (and perhaps benefit) to opposing blocs.

As an alternative, people are promoting an emphasis on “class politics.” But how are identity politics so different from class politics? You are still slicing a population into sub-groups, and then trying to get them to oppose the interests of another group. Yes, having no hive-mind sub-group jousting would be ideal, but it is a platonic ideal that is impossible given human brain heuristics. Identity politics will survive the 2016 election and persist as humans continue to exist in their current form.

Arranging a Gamma Distribution Family into Exponential Family Form

Sunday, November 20th, 2016

A family of PMFs or PDFs is an exponential family if it can be arranged into the form

$f(x|\theta) = h(x)c(\theta)\exp\left(\sum_{i=1}^kw_i(\theta)t_i(x)\right)$

where $\theta$ is the vector of parameters.

Now, the shape-scale parameterization of the Gamma distribution PDF takes the form

$f_X(x) = \frac{1}{\Gamma(k)\beta(k)}x^{k-1}e^{-\frac{x}{\beta}}$

$\beta$ is typically used as the symbol for the rate parameter in the shape-rate parameterization of the Gamma PDF, but the default symbol for the scale parameter, $\theta$, would conflict with the symbol for our parameter vector.

Can we arrange that PDF into an exponential family form? Spoiler: yes.

Here, we demonstrate that a Gamma PDF given two unknown parameters, $\beta$ and $k$, is an exponential family.

$f(x|k,\beta) = \frac{1}{\Gamma(k)\beta(k)}x^{k-1}e^{-\frac{x}{\beta}}$
$ = \frac{1}{\Gamma(k)\beta(k)}e^{(k-1)\ln(x)}e^{-\frac{x}{\beta}}$
$ = \frac{1}{\Gamma(k)\beta(k)}e^{(k-1)\ln(x) – \frac{x}{\beta}}$

The log identity $x^b = e^{b\ln(x)}$ is a very useful logarithmic identity to remember when trying to arrange PDFs into exponential family form.

We observe:
$h(x) = I_{x>0}(x)$ (If you see that h(x) = 1, that is a cue to use an indicator function that ranges through the support of $x$.)
$c(k,\beta) = \frac{1}{\Gamma(k)\beta(k)}$
$w_1(k,\beta) = k – 1$
$w_2(k,\beta) = -\frac{1}{\beta}$
$t_1(x) = \ln(x)$
$t_2(x) = x$

Hence, the Gamma distribution given unknown parameters $\beta$ and $k$ is an exponential family with a two-dimensional parameter vector $\theta$.

A similar process will apply for showing that a Gamma PDF with one unknown parameter, $\beta$ or $k$ is an exponential family.