Lattices of continuous monotonic functions

Lattices of Continuous Functions

Fast and Flexible Monotonic Functions with Ensembles of Lattices

For many machine learning problems, there are some inputs that are known to be positively (or negatively) related to the output, and in such cases training the model to respect that monotonic relationship can provide regularization, and makes the model more interpretable. However, flexible monotonic functions are computationally challenging to learn beyond a few features. We break through this ...

Completion of Lattices of Semi-continuous Functions

If U and V are topologies on an abstract set X, then the triple (X, U, V) is a bitopological space. Using the theorem of Priestley on the representation of distributive lattices, results of Dilworth concerning the normal completion of the lattice of bounded, continuous, realvalued functions on a topological space are extended to include the lattice of bounded, semi-continuous, real-valued funct...

Noncommutative Lattices and the Algebras of Their Continuous Functions

Recently a new kind of approximation to continuum topological spaces has been introduced, the approximating spaces being partially ordered sets (posets) with a finite or at most a countable number of points. The partial order endows a poset with a nontrivial non-Hausdorff topology. Their ability to reproduce important topological information of the continuum has been the main motivation for the...

Learning Monotonic Linear Functions

Learning probabilities (p-concepts [13]) and other real-valued concepts (regression) is an important role of machine learning. For example, a doctor may need to predict the probability of getting a disease P [y|x], which depends on a number of risk factors. Generalized additive models [9] are a well-studied nonparametric model in the statistics literature, usually with monotonic link functions....