Predictive Analytics

War Stories

Feb 13, 2015

Hobson Lane

slides.com/hobsonlane/data-analytics-war-stories/live

Choose Your Story

7707-2-TOTAL

(770) 728-6825

Only Nyquist Knows
The Meaning of Mean
Data Dearth
Question the Question
Deep Net Runs Aground
Escape the Maze

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1. Only Nyquist Knows

When your vehicle is out of control...

SMS: 7707-2-TOTAL or (770) 728-6825 MSGS: "1", "2", "3", "4", "5", or "6"

Photo by

US Secret Service

Photo by

Eric Cutright

Public Domain

Image by NASA

NASA

Public Domain

1. Only Nyquist Knows

Nav sensors (gyro., accel) are "pegged"
All you know is solar power:

How fast is the tumble?

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4 sec !

12 sec ?

1. Only Nyquist Knows

Try an Anti-Aliasing Filter

Fail: Only Nyquist Knows

12 sec

Workarounds

If Nyquist sampling (2x faster than truth) isn't possible....

Use a different sensor
- Postprocess existing signal (radio doppler)
Sample irregularly!
- Captures higher frequencies
- Lomb-Scargle to post-process

Probabilistic modeling
- Great for overwhelming data volume (IoT)

spectrum = scipy.signal.lombscargle(sample_times, samples, frequencies)

2. The Meaning of Mean

Means don't tell the whole story
Consider both and
Meaning may be found in the means for each...
- group, cluster, or class
For us we started with grouping by time of day, but that wasn't enough...

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\mu

μ

\sigma

σ

2. The Meaning of Mean

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Regression and classification required
Many "fundamental frequencies"

Mean for Each Time of Day

Classify Before Getting Mean

3. Data Dearth

Tuning a 2-DOF predictive filter for performance
More data gives algorithm more to work with
- Less Overfitting
- More Performance

Anticlined cliffs or "terraces"

More Data

Performance

($)

Conservatism

3. Data Dearth

Sometimes more of the same doesn't help
- Exogenous factors confound the smartest algorithm
Make the exogenous endogenous (new data source)

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4. Question the Question

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Correlation != Causation

(a. la. Tyler Vigen)

More sales => More returns

Normalize return rate for sales

(lag-compensated)

Multiple interracting causes

Reduce these returns surges!

4. Question the Question

Simple equation everyone can agree on

"Cost of quality"

"Customer reject rate"

"Defect rate"

But it's Wrong!

(last quarter)

And it's Late!

6\sigma

6 σ

Rejects

Sales

Reject rate

=

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4. Better "Question"

Rejects (last quarter)

Sales (qtr before last)

Reject rate

=

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Even Better

Rejects (last quarter)

Sales (estimate lagged quarter)

Reject rate

=

Correct

Rejects (last week)

Sales (integral of lagged sales)

Reject rate

=

r_r=\Sigma_k{\alpha{s_{n-k}}}

r ​ r ​ ​ = Σ ​ k ​ ​ α s ​ n - k ​ ​

"Birth-Death Process"

r_r=\Sigma_k{\alpha{s_{n-k}}}

r ​ r ​ ​ = Σ ​ k ​ ​ α s ​ n - k ​ ​

H(t,\tau)

H (t, τ)

S(t)

S (t)

R(t)

R (t)

All products "die",

Question is when

Flow rate

(Reject rate)

Product enters "pipeline" arbitrarily

Sale

Reject

Lag

And the portion that happens too soon

4. Question the Question

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Histogram reveals trend and seasonality

Sales

Month-end Surge

Rejects

4. Question the Question

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Fiscal Quarter
Geography
Diagnosis
Retailer
Salesperson
Model
Lot
Reason

Lag

Lagged Sales

Today

Predicted Returns

*

=

H(t,\tau)

H (t, τ)

S(t)

S (t)

R(t)

R (t)

Sales

Rejects

Lag Process

\div

\div

4. Analyze the Question

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You stop counting

You stop accepting returns

You stop selling

Cumulative histograms focus attention on final total

Product returns stop when...

4. Normalize & Compare

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Fiscal Quarter
Geography
Diagnosis
Retailer
Salesperson
Model
Lot
Reason

4. Analyze the Question

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Normalize histograms to compare categories

Normalize by what?
- Sales (which ones)?
- Total returns?

How are we doing this week?
- Not just this quarter

4. Question the Question

Unsupervised natural language processing?

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President inaugural speeches

Target category = political party

4. Question the Question

What are the US Presidents' political parties based on speeches?

4. Question the Question

What are the US Presidents' political parties based on speeches?

4. Question the Question

The category you're interested in will not likely be the most important "factor" in the NLP statistics
Dimension reduction (SVD, PCA) can identify factors
- Word-sets that are most significant
These represent the "themes"
- Interpretation of these "themes" is up to you
- Statistics Meaning

\ne

\neq

5. Deep Nets Run Aground

Deep net performs well!

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5. Deep Nets Run Aground

Not so fast... it's overfitting

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5. Deep Nets Run Aground

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\text{a}=\text{W}^{k}_{S^k,S^{(k+1)}}\text\ \text{p}

a = W ​ S ​ k ​ ​, S ​ (k + 1) ​ ​ ​ k ​ ​ p

\text{p}

p

\text{W}^{k}_{S^k,S^{(k+1)}}

W ​ S ​ k ​ ​, S ​ (k + 1) ​ ​ ​ k ​ ​

\text{a}

a

Conventional Hebb rule

\text{W}^{new}={W}^{old}+\text{t}_q\text{p}_q^T

W ​ n e w ​ ​ = W ​ o l d ​ ​ + t ​ q ​ ​ p ​ q ​ T ​ ​

\text{W}^{new}={W}^{old}+\alpha(\text{t}_q-\text{a}_q)\text{p}_q^T

W ​ n e w ​ ​ = W ​ o l d ​ ​ + α (t ​ q ​ ​ - a ​ q ​ ​) p ​ q ​ T ​ ​

Hebb "delta" rule

5. Shallow Data

Model degree:

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\text{a}=\text{W}^{k}_{S^k,S^{(k+1)}}\text\ \text{p}

a = W ​ S ​ k ​ ​, S ​ (k + 1) ​ ​ ​ k ​ ​ p

\text{p}

p

\text{W}^{k}_{S^k,S^{(k+1)}}

W ​ S ​ k ​ ​, S ​ (k + 1) ​ ​ ​ k ​ ​

\text{a}

a

\sum_k{{S^k}{S^{(k+1)}}}

\sum ​ k ​ ​ S ​ k ​ ​ S ​ (k + 1) ​ ​

Training data DOF:

{S}^1{S^3}N_{samples}

S ​ 1 ​ ​ S ​ 3 ​ ​ N ​ s a m p l e s ​ ​

(independent samples)

5. Shallow Data

Model degree:

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\text{a}=\text{W}^{k}_{S^k,S^{(k+1)}}\text\ \text{p}

a = W ​ S ​ k ​ ​, S ​ (k + 1) ​ ​ ​ k ​ ​ p

\text{p}

p

\text{W}^{k}_{S^k,S^{(k+1)}}

W ​ S ​ k ​ ​, S ​ (k + 1) ​ ​ ​ k ​ ​

\text{a}

a

{S^1}{S^2}+{S^2}{S^3}

S ​ 1 ​ ​ S ​ 2 ​ ​ + S ​ 2 ​ ​ S ​ 3 ​ ​

Training data DOF:

({S}^1+{S^3})N_{samples}

(S ​ 1 ​ ​ + S ​ 3 ​ ​) N ​ s a m p l e s ​ ​

(1 hidden layer)

(independent samples)

5. Bottom Line

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N_{hidden} << N_{training}

N ​ h i d d e n ​ ​ < < N ​ t r a i n i n g ​ ​

bit.ly/nntune

6. Escape the Maze

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Find Connections

(Actionable Insight)

18 databases

> 10k tables

> 100k fields

> 10M records/table

6. Escape from the Maze

Tight heuristics vital for efficient graph search
"Always turn right" is not good enough

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6. Escape from the Maze

Don't bother with "exhaustive" correlation search

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\text{complexity} \approx{O({M^2}N^2)}\approx{10}^{24}

c o m p l e x i t y \approx O (M ​ 2 ​ ​ N ​ 2 ​ ​) \approx 10 ​ 24 ​ ​

Find db relationships using meta-data
- min, max, median
- #records
- #distinct
- for reals: mean, std

\text{complexity} \approx{O({M}{N}log(N))}\approx{10}^{13}

c o m p l e x i t y \approx O (M N l o g (N)) \approx 10 ​ 13 ​ ​

10^5

1 0 ​ 5 ​ ​

10^7

1 0 ​ 7 ​ ​

Human Heuristics

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Business knowledge narrows search:
- Repair technicians
- Product designers
- Factory managers
- Suppliers
- Sales channels
- Call center

Accidental "Experiements"

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Look for differences in
- Model
- Lot
- Product
- Sales Channel
- Customer Demographic
- Region/Culture
Look for ...
- New/deleted features
- Documentation updates
- Cost-saving parts changes
- Production facilities (outsourced vs insourced)

Kruskal's Algorithm

Minimum Spanning Tree

Add lowest cost edge with new node
Repeat until all nodes accounted for

def minimum_spanning_zipcodes():
    zipcode_query_sequence = []
    G = build_graph(api.db, limit=1000000)
    for CG in nx.connected_component_subgraphs(G):
        for edge in nx.minimum_spanning_edges(CG):
            zipcode_query_sequence += [edge[2]['zipcode']]
    return zipcode_query_sequence

Produces one graph for each connected subgraph

Built into python graph library (`networkx`):

A* Algorithm

Minimum Path to Goal

from networkx.algorithms.shortest_paths import astar_path
astar_path(G, source, target, heuristic=None)

Provably optimal and optimally efficient

But typical data relationship graph has large branching factor

Built into python graph library (`networkx`)

A* Algorithm

Minimum Path to Goal

from networkx.algorithms.shortest_paths import astar_path
astar_path(G, source, target, heuristic=None)

Provably optimal and optimally efficient

Built into python graph library (`networkx`)

You better have a good heuristic!

It's Open Source!

github.com/sharplabs

Consider sample rate
Classify before mean
Explore data sources
Reject rate metric
data > nodes x inputs
Lazy correlation

Choose Your Story

7707-2-TOTAL

(770) 728-6825

Only Nyquist Knows
The Meaning of Mean
Data Dearth
Question the Question
Deep Net Runs Aground
Escape the Maze

bit.ly/pawsvote

References

"Data Driven Documents"
- 2011, Mike Bostock
"Data Science with `pug`"
- 2014, Lane, Zen, Kowalski, PDX Python U.G.
"Neural Network Design"
- 2014, Hagan, Demuth, et. al., OKSU
"Forecasting Product Returns"
- 2001, Toktay, INSEAD
`scipy.ransac`
- 2014, Andrew D. Straw
"Choose Your Own Adventure Presentation"
- 2014, Matt Makai