Intelligent System ↔ Data Science

1955 → The first Dartmouth college summer AI conference

1997 → Deep Blue chess machine

There are many problems in which we have data but we do not have models.

Example: economics, physics

Machine learning as subset of statistics but with many other disciplines (deployment, HPC, etc... ).

Statistical Learning Theory

Speaker: Lorenzo Rosasco

Supervised Learning Problem

Decision Boundary → $f(x)=0$

$f(x_{new})= b_{new}$

• $X \times Y$ is a probability space with measure $\rho$
• Data sampled from the distribution independently wrt each other.
• $L: X \times Y \rightarrow [0, +\infty)$: measurable loss function.
• Expected risk:

$$ \mathcal{E}(f) = \int_{X \times Y} L(y, f(x)) d\rho(x,y) $$

The expected risk is the expected value of the loss function under the joint distribution of X and Y. We want to minimize the expected risk:

$$ \min_{f: X \rightarrow Y} \mathcal{E}(f) $$

Given only training samples and not the whole distribution $\rho$, that is unknown.

Input Space