Understandable Artificial Intelligence

Sept 2019

# Stochastic Gradient Descent

©2019 Economic Data Sciences

### What Is It?

• Often referred to  as SGD
• This method is an iterative approach to optimization
• This approach can be traced back to at least 1951
• Two parts:
• Stochastic = random starting position
• Gradient Descent = the approach used to optimize
• This method is so popular it is a default tool in Microsoft Excel

# Basic Gradient Descent

©2019 Economic Data Sciences

### Assumes All Trade-Offs Are Smooth

• A seeker finds the most benefit per unit of uncertainty
• It does this by 'rolling' along the line

Yup, found the best

# Stochastic Gradient Descent

©2019 Economic Data Sciences

### Why Does this Matter? Part I: Rough Trade-offs

• The real world isn't like theory, it's messier
• SGD sends several 'seekers' to find the best option given the complexities of the real world

I'm The Best!

I'm The Best!

I'm The Best!

I'm The Best!

I'm The Best!

Only This is Truly The Best

# Stochastic Gradient Descent

©2019 Economic Data Sciences

### Why Does this Matter? Part II: Many Different Risks & Goals

• Risk, uncertainty, and opportunities come in many different forms
• A technique like SGD is needed to consider all of these simultaneously

# Does It Work?

©2019 Economic Data Sciences

### Proof Is In The Pudding

• Forgetting about all of these details the important question is:
• Does it work?
• EDS has now conduct 30+ projects
• In 100% of cases, improvements have been made after the analysis
• How?
• In essence, the ability to consider more factors and information leads to more informed decisions
• Simply, more informed decision making leads to better outcomes

# Why Doesn't Everyone Do It?

©2019 Economic Data Sciences

### A Natural Question is to Ask Why Haven't You Seen This Before

• The simple answer is many have tried
• Using SGD means it is difficult to be 'sure' the solution is best
• Past solutions haven't been able to solve this issue
• In short, it is easy to do poorly
• Only the EDS technology can provide consistent and confident results
• Our distributed approach coordinates a single problem across a cluster of computers

# What Is So Special About EDS?

©2019 Economic Data Sciences

### Distributed, Coordinated, & Informed

• A real world problem usually includes:
• 100s of important factors
• Qualitative & Quantitative
• 1000s of potential investments
• EDS's technology has three key pillars for success:
1. Distributed: Only distributed systems can handle problems of this size
2. Coordinated: Working with a distributed system means that all of the distributed workers must be coordinated
3. Informed: Keeping a memory of what solutions work best means EDS can solve these problems faster

©2019 Economic Data Sciences

# On The Shoulders Of Giants

\small Utility = \underbrace{\small \mu}_{\text{\tiny Return}} - \underbrace{\small \lambda \tiny 1 \small \cdot \sigma}_{\text{\tiny Variance}} - \underbrace{\small \lambda \tiny 2 \small \cdot TEV}_{\text{\tiny Tracking Error}} - \underbrace{\small \lambda \tiny 3 \small \cdot TFS}_{\text{\tiny Factor Sensitivity}} ...
• Building on current methods adds interpretability and transparency
• Extendable frameworks allow inclusions from other models and insights
• Tail-Risk, Diversification Ratio, Black-Litterman, etc.

1950s

1980s

2010s

An Extendable

Framework

### EDS's mathematical insights extend current best practices

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