DSL

import metametric.dsl as mm

Auto

mm.auto[X] derives an automatic metric for type X. This is the default behavior of the @metametric decorator.

Discrete similarity

mm.discrete[X] constructs a discrete similarity metric for type X. That is, given that type X has method __eq__, the metric returns 1.0 if two objects of type X are equal, and 0.0 otherwise.

\[ \text{sim}(x, y) = \begin{cases} 1 & \text{if } x = y \\ 0 & \text{otherwise} \end{cases} \]

Custom similarity

mm.from_func(f) constructs a metric from a function f: Callable[[X, X], float] that takes two arguments of the same type and returns a float.

\[ \text{sim}(x, y) = f(x, y) \]

With preprocessing

mm.preprocess(g, M) is a metric that first applies a preprocessing function g: Callable[[X], Y] to both arguments, then applies a metric f: Metric[Y] to the results. This is the contramap operation of the metric type.

\[ \text{sim}(x, y) = f(g(x), g(y)) \]

Product (dataclass) similarity

mm.dataclass[X](M) constructs a metric for a dataclass X by taking the product of the metrics for each of its fields defined in M: Dict[str, Metric[Any]].

\[ \text{sim}(x, y) = \prod_{(f, m_f) \in M} m_f(x.\!f, y.\!f) \]

Sum (union) similarity

mm.union[X](M) constructs a metric for a union type X by a dictionary of each case of the union defined in M: Dict[type, Metric[Any]].

\[ \text{sim}(x, y) = \sum_{(t, m_t) \in M} \mathbb{1}_{x \in t} \mathbb{1}_{y \in t} m_t(x, y) \]

Set matching similarity

mm.set_matching[X, ◇, N](f) constructs a set matching metric between two objects of type Set[X], with \(\diamond \in \{\leftrightarrow, \to, \leftarrow, \sim\}\) as the matching constraint, and N as the normalizer.

\[ \Sigma^{\diamond}[f](x, y) = \max_{M^\diamond} \sum_{(u, v) \in M^\diamond} f(u, v) \]

\[ \textrm{sim}(x, y) = \mathsf{N}(\Sigma^{\diamond}[f](x, y)) \]

See here for a description of matching constraints.

Latent set matching similarity

mm.latet_set_matching[X, ◇, N](f) constructs a latent set matching metric between two objects of type Set[X] where X has Variables.

\[ \Sigma(X, Y) = \max_{M^{\leftrightarrow}_V, M^\diamond} \sum_{(u, v) \in M^\diamond} \phi_T(u, v) \]

where \(M^\diamond\) is a matching between \(X\) and \(Y\) according to the specified matching constraint, and \(M^\leftrightarrow_V\) is a one-to-one matching between the variables in \(X\) and \(Y\).

mm.latet_set_matching[X, ◇, N](f) constructs a latent set matching metric between two objects of type Set[X] where X has Variables.

\[ \Sigma(X, Y) = \max_{M^{\leftrightarrow}_V, M^\diamond} \sum_{(u, v) \in M^\diamond} \phi_T(u, v) \]

where \(M^\diamond\) is a matching between \(X\) and \(Y\) according to the specified matching constraint, and \(M^\leftrightarrow_V\) is a one-to-one matching between the variables in \(X\) and \(Y\).

Sequence matching similarity

Coming soon!

Graph matching similarity

Coming soon!