Data Science as 9 problems

A gentle-yet-focussed introduction

(was 2) Regression/value estimation

Instance:

a collection (dataset) of numerical $<\mathbf{x}, y>$ datapoints
a regressor (independent) value x

Solution: a regressand (dependent) value y that complements x

Measure: error over the collection

(was 1) Classification and class probability

Instance:

a collection (dataset) of datapoints from $\mathbf{X}$
a classification system $C = \{c_1, c_2, \dots c_k\}$

Solution: classification function $\gamma: \mathbf{X} \rightarrow C$

Measure: misclassification

[PF] “classification predicts whether something will happen, whereas regr. predicts how much something will happen.”

false_positives_and_negatives

Similarity

Identify similar individuals based on data known about them.

Instance:

a collection (dataset) of datapoints from $\mathbf{X}$ , e.g., $\mathbb{R}^n$
(distance functions for some of the dimensions)

Solution: similarity function $\sigma: \mathbf{X} \rightarrow \mathbb{R}$

[Measure: error]

Clustering (segmentation)

group individuals in a population together by their similarity (but not driven by any specific purpose)

Instance:

a collection (dataset) $\mathbf{D}$ of datapoints from $\mathbf{X}$ , e.g., $\mathbb{R}^n$
a relational structure on $\mathbf{X}$ (a graph)
a small integer $k$

Solution: a partition of $\mathbf{D}$ into $\mathcal{C_1}, \dots \mathcal{C_k}$

Measure: network modularity Q: proportion of the relational structure that respects the clusters.

Detection version: $k$ is part of the output.

Example research work (by yours truly):

Co-occurence (frequent itemset mining)

similarity of objects based on their appearing together in transactions.

Instance:

a collection (dataset) $\mathbf{T}$ of itemssets (subsets of $\mathbf{X}$ ) or sequences
a theshold $\tau$

Solution: All frequent patterns: subsets that appear in $\mathbf{T}$ above $\tau$

Detection version: $\tau$ is part of the output.

Market-basket analysis, (some) recommendation systems

Profiling (behaviour description)

Instance:

a user description $\mathbf{u}$ drawn from a $\mathbf{D}$ collection
a stimulus $a\in \mathbf{A}$
a set of possible responses $\mathbf{R}$

Solution: a functional reaction of u to a, i.e., $\rho: \mathbf{U} \times \mathbf{A} \rightarrow \mathbf{R}$

Application: anomaly/fraud detection.

Example research work on Social media profiling:

Link prediction

Instance:

a dynamical graph $\mathbf{G}$ , i.e., a sequence $<V, E>$ , $<V, E^\prime=E+\{(u,v)\}>$ , $<V, E^{\prime\prime}=E^\prime+\{(r,s)\}>\dots$

Question

what is the next link to be created?

What YouTube video will you watch next?

Alternatives: predict the strenght of the new link; l. deletion.

Data reduction

Instance:

a collection (dataset) $\mathbf{D}$ of datapoints from $\mathbf{X}$ , e.g., $\mathbb{R}^m$
[a distinct indipendent variable $x_i$ ]

Solution: a projection of $\mathbf{D}$ onto $\mathbb{R}^n$ , $n < m$

Measure: error in the estimation of $x_i$

Example: genre identification in consumer behaviour analysis

Causal modelling

Instance:

a collection (dataset) $\mathbf{D}$ of datapoints from $\mathbf{X}$ , e.g., $\mathbb{R}^m$
a distinct indipendent variable $x_i$

Solution: a variable $x_j$ of $\mathbf{D}$ that controls $x_i$

Measure: effectiveness of $x_j$ tuning to tune $x_i$

Example: Exactly What food causes you to put on weight?

Controlled clinical trials, A/B testing.

Data Science as 9 problems

Data Science as 9 problems

A gentle-yet-focussed introduction

[Un]Supervision

Supervised Data Science

Supervised

Could be either

(mostly) unsupervised