social services

health and welfare

Does China have good social services / health care? Nope. China has social services, but not ready for large increase in demand.

China well behind:

• nurses and midwives
• ICU beds
• low public spending for education (below average)
• half of South Afria in healthcare

China’s countryside: 27% anemia, 20% uncorrected poor vision, 33% intestinal worms.

projections of needed increase

• level of benefits is still modest
• eligible population is still limited

As population ages and household decline, demand for higher coverage and spending will increase.

China stuck with their debt strategy even despite things going badly.

Deleveraging

• Simplest method: kick the bucket down the can—roll over current debt
• Hard approach: curtail credit in sectors with excess capacity, such as real estate

The second approach became destabilizing, and made local government debt even worse.

Real Estate

Goverment is generally happy to have demand re:

• public works
• railway stations
• railway lines
• container ports

etc.

BUT! Real estate’s purchasing is market driven unlike public works; thus failure of real-estate firms affects millions of households and businesses.

levels of interp

• probes: no causality
• attribution (i.e. integrated gradient): no interpretation

methods of causal interventions

activation patching / interchange interventions

Record the activation, and swap the activations (can thus find the output)

distributed alignment search

Features are not axis aligned. Find equality task efficiently after (a rotation?)

three worlds of casual interventions

…as interp

“can we find interpretable causal mechanisms?” That is, “searching for a rotation” and then run interchange interventions.

constituents

Functions is self-concordant if:

\begin{align} \mid f’’’\qty(x)\mid \leq 2f’’\qty(x)^{\frac{3}{2}}, \forall x \in \text{dom } f \end{align}

and \(f\) is self-concordant if \(g\qty(t) = f\qty(x+tv)\) is self concordant for all \(x \in \text{dom } f\).

requirements

Convergence analysis! There exists \(\eta \in (0, \frac{1}{4}]\), \(\gamma > 0\) such that:

• if \(\lambda \qty(x) > \eta\), then \(f\qty(x^{(k+1)}) - f\qty(x^{(k)}) \leq -y\)
• if \(\lambda \qty(x) \leq \eta\), then \(2\lambda \qty(x^{(k+1)}) \leq \qty(2 \lambda \qty(x^{(k)}))^{2}\)

and \(\eta, \gamma\) depends only on backtracking line search parameters. This gives bounds:

Descent methods are generally of shape:

\begin{align} x^{(k+1)} = x^{(k)} + t^{(k)} \delta x^{(k)} \end{align}

choosing these is a matter of which descent method you choose. The Hessian thus exposes:

\begin{align} \qty {x + v \mid v^{T} \nabla^{2} f\qty(x) v \leq 1} \end{align}

line search

backtracking line search

A first-order Taylor line in \(t\), centered about \(x\):

\begin{align} f\qty(x) + t \nabla f\qty(x)^{T} \Delta x \end{align}

We can degrade this to raise it to be slightly higher: