New Model

China would need to shift to new growth model… Since 1980, it relied on:

1. mobilization on two mechanisms
2. shift in control of resources to state to private

There may be thus diminishing returns.

a new growth model

• China’s capacity outstrips global demand
• incomes no longerr rising as rapidly
• foreign direct investment is slowing

Expansion of credit

China bank access accounts for a large percentage of global GDP; thus bad debt can accumulate and hurt. Banks is thus driving the infrastructure drive via credit. Credit growth comes up, GDP growdth comes down; bad state! Yet, almost 20% of enterprises are loosing money.

Supervised learning (also known as behavioral cloning) if the agent is learning what to do in an observe-act cycle) is a type of decision making method.

constituents

• input space: \(\mathcal{X}\)
• output space: \(\mathcal{Y}\)
• hypothesis/model/prediction: \(h : \mathcal{X} \to \mathcal{Y}\)

requirements

Our ultimate goal is to learn a good model \(h\) from the training set:

• what “good” means is hard to define
• we generally want to use the model on new data, not just the training set

continuous \(\mathcal{Y}\) is then called a regression problem; discrete \(\mathcal{Y}\) is called a classification problem.

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Technology: RTIC Outback Bottle 40oz

Description: Black Water Bottle

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motivation

Consider Generic Maximum Likelihood Estimate.

• parametric distribution estimation: suppose you have a family of densities \(p_{x}\qty(y)\), with parameter \(x\)
• we take \(p_{x}\qty(y) = 0\) for invalid values of \(x\)

maximum likelihood estimation: choose \(x\) to maximize \(p_{x}\qty(y)\) given some dataset \(y\).

linear measurement with IID noise

Suppose you have some kind of linear noise model:

\begin{equation} y_{i} = a_{i}^{T}x + v_{i} \end{equation}

where \(v_{i}\) is IID noise, and \(a^{T}_{i}\) is the model. We can write \(y\) probabilistically as:

Consider an error minimization task \(\min \norm{Ax - b}\) (\(Ax\) as the “predictions”, and \(b\) is the “data”). Some interpretation—

• approximation: \(Ax^{*}\) is the best approximation of the vector \(b\) by linear combinations of columns of \(A\)
• geometric: \(Ax^{*}\) is a point in \(\mathcal{R}\qty(A)\) closest to \(b\)
• estimation: linear measurement model \(y = Ax + v\)
  • you took a measurement \(y\), \(A\) is the theoretical measurement, \(v\) is the measurement error
  • implausibility of making \(v\) error is \(\norm{v}\)
  • given \(y = b\) (what you measured), most plausible \(x\) is \(x^{*}\)
• optimal design: \(x\) are design variables, \(Ax\) is the result; \(x^{*}\) is the design that best approximates desired \(b\)

Penalty Function Approximation

Suppose you are optimizing some design \(x\) with respect to some dynamics \(A\). Suppose your design residual is \(r = Ax - b\). And you have some kind of penalty function to describe how comfortable you are with various errors: \(\phi\qty(r_1) + … + \phi\qty(r_{n})\).