EMBRACING THE BLESSING OF DIMENSIONALITY TO DETERMINE SPECIES’ PROVENANCE

Kevin Cazelles KCazelles

Emelia Myles-Gonzalez, Tyler Zemlak, Kevin S. McCann @McCannLab

QCBS Annual symposium, Montreal

December 18th, 2019

KevCaz/fightingNoise

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ContextThe push for provenance2 / 64

The push for provenance

Consumers are become increasingly aware of, and interested in, the origins of their seafood, particularly as issues such as environmental sustainability, impacts on endangered species, toxin accumulations, incidents of illegal, unregulated and unreported (IUU) fishing, quality assurances and human rights abuses are better understood.

Roebuck, K. et al. (2017) Canadian's Eating in the Dark: A Report Card of International Seafood Labelling Requirements

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The push for provenance

Roebuck, K. et al. (2017) Canadian's Eating in the Dark: A Report Card of International Seafood Labelling Requirements

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Sockeye salmon (Oncorhynchus nerka)

Crawford, S.S. & Muir, A.M. (2008). Global introductions of salmon and trout in the genus Oncorhynchus: 1870–2007. Reviews in Fish Biology and Fisheries.

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The push for provenance

1. We need regulations

e.g. Country of Origin Labelling (COOL) in USA

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The push for provenance

1. We need regulations

e.g. Country of Origin Labelling (COOL) in USA

2. We need tools to authenticate the provenance

What this talk is about!

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Biotracers to create spatial fingerprints

Bio + tracer

- trace elements

- stable isotopes

- fatty acids

- DNA

- gut contents

- etc.

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Vertical vs horizontal strategies

The future of food authentication and food quality assurance critically depends on combining chemometrics, computational analytical methods, and bioinformatics in processing and interpreting the data obtained through analytical technique.

Danezis, G. P., et al. (2016) Food authentication: state of the art and prospects. Current Opinion in Food Science

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Why develop horizontal strategies?

Chen, Dong, et al. (2013) Blessing of Dimensionality: High-Dimensional Feature and Its Efficient Compression for Face Verification. 2013 IEEE Conference on Computer Vision and Pattern Recognition.

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HOW TO COMBINE BIO-TRACERS TO DETERMINE SPECIES PROVENANCE?

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A Bayesian framework12 / 64

Where does this sample come from?

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Where does this sample come from?

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A Naive Bayes classifier15 / 64

A Naive Bayes classifier

- A priori knowledge

- Sample (observations)

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A Naive Bayes classifier

- A priori knowledge

- Sample (observations)

- Quantity, quality, heterogeneity

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A Naive Bayes classifier

- A priori knowledge

- Sample (observations)

- Quantity, quality, heterogeneity

- Statistical model

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Origins and distributions

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Where does this sample come from?

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Problem

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Problem

O₁ | Sample ?

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Problem

O₁ | Sample ?

Sample | O₁ & Sample | O₂ known!

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A bayesian approach

Assumptions

1. sample from one of the areas considered

2. no mixture

$[O_1|S_{n}] = \frac{[S_{n}|O_1][O_1]}{\sum_j [S_{n}|O_j][O_j]}$

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Similarity & authentication

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Similarity & authentication

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Similarity & authentication

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Similarity & authentication

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Similarity & authentication

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Similarity & authentication

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Similarity & authentication

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Dimensionality & authentication

Assumption: Bio-tracers ~ N(μ, Σ)

just as in a Linear Discriminant Analysis (LDA)

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Dimensionality & authentication

Assumption: Bio-tracers ~ N(μ, Σ)

just as in a Linear Discriminant Analysis (LDA)

μ: means - fixed

Σ: covariance matrix

diagonal (variances) fixed

off-diagonal terms (symmetric) vary:

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Dimensionality & authentication

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Dimensionality & authentication

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Dimensionality & authentication

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Dimensionality & authentication

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Dimensionality & authentication

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Dimensionality & authentication

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Dimensionality & authentication

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Dimensionality & authentication

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Dimensionality & authentication

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Dimensionality & authentication

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Dimensionality & authentication

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Dimensionality & authentication

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Dimensionality & authentication

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Dimensionality & authentication

Blessing of dimensionality!

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So

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So

1. the more dissimilar the distributions the better

2. the higher the dimensionality the better

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So

1. the more dissimilar the distributions the better

2. the higher the dimensionality the better

3. Assuming extra bio-tracers enhance 1. or 2. (or both)

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So

1. the more dissimilar the distributions the better

2. the higher the dimensionality the better

3. Assuming extra bio-tracers enhance 1. or 2. (or both)

THE MORE BIO-TRACERS THE BETTER

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Using the framework52 / 64

Data

- Sockeye Salmon

- 3 regions

- 30 individuals/region

- bio-tracers:

3 stable isotopes

14 fatty acids

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How?

- A priori knowledge 20 individuals | test on 10 individuals

- All combinations of bio-tracers

- Custom Bayes classifier / LDA / Deep Learning

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How?

- A priori knowledge 20 individuals | test on 10 individuals

- All combinations of bio-tracers

- Custom Bayes classifier / LDA / Deep Learning

cor(RU, US) > cor(CA, US) = cor(CA, RU)

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Results - increasing sample size

3 bio-tracers

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Results - increasing dimensionality

sample size = 1

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Perspectives58 / 64

Perspectives

Limits

Unpack results about correlation structure

Mixture problem

Temporal variations

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Perspectives

Future

Let's think vertical

Can we use this to create reliable maps of probabilities of origin?

Magozzi, S., et al. (2017) Using ocean models to predict spatial and temporal variation in marine carbon isotopes. Ecosphere

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Many thanks to

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Many thanks to

My co-authors and the McCann Lab

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Many thanks to

My co-authors and the McCann Lab

Food From Thought

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THE END64 / 64

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EMBRACING THE BLESSING OF DIMENSIONALITY TO DETERMINE SPECIES’ PROVENANCE

Kevin Cazelles KCazelles

Emelia Myles-Gonzalez, Tyler Zemlak, Kevin S. McCann @McCannLab

QCBS Annual symposium, Montreal

December 18th, 2019

Context

The push for provenance

The push for provenance

The push for provenance

Sockeye salmon (Oncorhynchus nerka)

The push for provenance

1. We need regulations

e.g. Country of Origin Labelling (COOL) in USA

The push for provenance

1. We need regulations

e.g. Country of Origin Labelling (COOL) in USA

2. We need tools to authenticate the provenance

Biotracers to create spatial fingerprints

Bio + tracer

- trace elements

- stable isotopes

- fatty acids

- DNA

- gut contents

- etc.

Vertical vs horizontal strategies

Why develop horizontal strategies?

A Bayesian framework

Where does this sample come from?

Where does this sample come from?

A Naive Bayes classifier

A Naive Bayes classifier

- A priori knowledge

- Sample (observations)

A Naive Bayes classifier

- A priori knowledge

- Sample (observations)

- Quantity, quality, heterogeneity

A Naive Bayes classifier

- A priori knowledge

- Sample (observations)

- Quantity, quality, heterogeneity

- Statistical model

Origins and distributions

Where does this sample come from?

Problem

Problem

O1 | Sample ?

Problem

O1 | Sample ?

Sample | O1 & Sample | O2 known!

A bayesian approach

1. sample from one of the areas considered

2. no mixture

Similarity & authentication

Similarity & authentication

Similarity & authentication

Similarity & authentication

Similarity & authentication

Similarity & authentication

Similarity & authentication

Dimensionality & authentication

Assumption: Bio-tracers ~ N(μ, Σ)

just as in a Linear Discriminant Analysis (LDA)

Dimensionality & authentication

Assumption: Bio-tracers ~ N(μ, Σ)

just as in a Linear Discriminant Analysis (LDA)

μ: means - fixed

Σ: covariance matrix

diagonal (variances) fixed

off-diagonal terms (symmetric) vary:

Dimensionality & authentication

Dimensionality & authentication

Dimensionality & authentication

Dimensionality & authentication

Dimensionality & authentication

Dimensionality & authentication

Dimensionality & authentication

Dimensionality & authentication

Dimensionality & authentication

O₁ | Sample ?

O₁ | Sample ?

Sample | O₁ & Sample | O₂ known!