Key Insights

1. Does China have a modern form of government?
2. China’s National Government as a Hierarchy: is it centralized? Meritocratic?

Forms of Government

1. Modern Government Model (“European Model”—Enlightenment English/Scottish/French): state should adjudicate interests in a fair and legitimate fashion
   • US Government Model: hybrid, constitutional, late 18th entry design (i.e. “government is designed to stop things”)
2. Alternative Model (“Developer Model”): State’s purpose is to push national progress through economic and military strength (i.e. “the government pushes things forward)
   • China
   • Axis Powers

Modern Government

We typical define a modern government as a liberal democratic government. But China’s system is in some sense much newer than liberal democracy—invented by the Soviets.

Chen’s Talk.

1. start with function \(f\) gives as expression
2. build parse tree for expression (leaves and variables / constants, nodes are functions of child expressions)
3. apply general composition rule that preserve convexity

Greedy parses may fail, such as in the case of logsumexp.

line

All points of the form \(x = \theta x_{1} + \qty(1-\theta) x_{2}\), with \(\theta \in \mathbb{R}\) is a “line through \(x_1\), \(x_2\)”.

affine set

For set \(G\), for all two points \(x_1, x_2 \in G\), all points lying on the line \(x_1, x_2 \in G\). For instance, the solution set of a set of linear equations \(\qty {x \mid A x = b}\).

convex set

convex set,

line segment

all points form \(x = \theta x_{1} + \qty(1-\theta)x_{2}\), with \(0 \leq \theta \leq 1\).

Sorta like “distribution-based k-means clustering”. guarantees convergence (i.e. each parameter will converge to the maximum possible parameter).

constituents

A Gaussian mixture model!

requirements

Two steps:

e-step

“guess the value of \(z^{(i)}\); soft guesses of cluster assignments”

\begin{align} w_{j}^{(i)} &= p\qty(z^{(i)} = j | x^{(i)} ; \phi, \mu, \Sigma) \\ &= \frac{p\qty(x^{(i)} | z^{(i)}=j) p\qty(z^{(i)}=j))}{\sum_{l=1}^{k}p\qty(x^{(i)} | z^{(i)}=l) p\qty(z^{(i)}=l))} \end{align}

Where we have:

• \(p\qty(x^{(i)} |z^{(i)}=j)\) from the Gaussian distribution, where we have \(\Sigma_{j}\) and \(\mu_{j}\) for the parameters of our Gaussian \(j\).
• \(p\qty(z^{(i)} =j)\) is just \(\phi_{j}\) which we are learning

These weights \(w_{j}\) are how much the model believes it belongs to each cluster.