[PPT] - Basic Concepts Overview First Principle Models Most of science and PowerPoint Presentation

SLIDE 1

Scientific Method

Basic Concepts Overview

Complex Systems

models

– automobile exhaust temperature – employee performance based on survey answers – the daily precipitation in Portland

– Collect data under all normal operating conditions – Construct a model from the data

First Principle Models

– Kirchhoff’s laws – Newton’s laws of mechanics – Maxwell’s laws

– Used to verify the underlying first-principle models – Used to estimate unkown parameters (e.g. acceleration of gravity)

SLIDE 2

Five Problems for this Class

determine whether they have different statistical properties (e.g., mean, standard deviation, pdf, etc.)?

a model?

the distribution from which the data was drawn?

set of classes, how do you classify unlabeled data?

parameters, how do you adjust the parameters to maximize performance?

Data-based (Nonparametric) Models

– Data acquisition systems are becoming cheaper – Computational power is increasing – Methods of generating models from data are improving

becoming increasingly important

– What can be done with it? – What information is “contained in” the data?

Approach

statistics

(neural networks)

process

Technology-Centered vs. Problem Centered

– Neural networks – Genetic algorithms – Fuzzy logic – Evolutionary computing

applications

– Given a problem, what are reasonable and accepted solutions

SLIDE 3

Experimental Process Comments

Experimental Process Drawing conclusions from data usually requires the following general experimental procedure

have a meaningful problem statement.

generated? What is measured? How accurate are the measurements?

Causality

c d c+1 z

caused by the inputs

– Input: exhaust temperature – Output: air/fuel ratio of engine input

temperature?

Experimental Process Continued

inputs and output. Goal: accurate prediction (generalization).

the model find in the data? How accurately can the models predict? Which inputs are most important? Which are irrelevant?

SLIDE 4

Causality Continued 3

– Outputs may causally depend on the observed inputs – Inputs may causally depend on the observed outputs – Input-output dependency may be caused by other (unobserved) factors – Input-output correlation is non-causal

“knowledge discovery”

is meaningful

Causality Continued

c d c+1 z

– Input: price of competitor’s stock – Output: your price/earnings ratio

p(y|x) = probability of output, given the input

Variable Types There are five types of variables that we will encounter in examples and in your projects

Causality Continued 2

variables for causality – Married men live longer than single men – Bush is president, the economy is plummeting – Height vs. weight – Florida is warm, Florida has a higher fraction of older people than any other state – “Standard & Poor’s 500 index [dropped] to its lowest close since late October 1998, as investors buckled under another heap of corporate profit warnings and steep job cuts.”

alone

statistical analysis

SLIDE 5

Variable Types Continued

ratios of numbers are meaningful and there is a natural interpretation of 0. Includes most real-valued cases.

Frequentist vs. Bayesian Interpretations

statistical distribution

apriori knowledge of the problem

– An economist predicts 80% chance of recession in 3 months

is better