Related papers: Proper-Composite Loss Functions in Arbitrary Dimen…

We propose a general approach for supervised learning with structured output spaces, such as combinatorial and polyhedral sets, that is based on minimizing estimated conditional risk functions. Given a loss function defined over pairs of…

We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore…

Estimating the ratio of two probability densities from a finite number of observations is a central machine learning problem. A common approach is to construct estimators using binary classifiers that distinguish observations from the two…

In Constraint Programming, constraints are usually represented as predicates allowing or forbidding combinations of values. However, some algorithms exploit a finer representation: error functions. Their usage comes with a price though: it…

We study losses for binary classification and class probability estimation and extend the understanding of them from margin losses to general composite losses which are the composition of a proper loss with a link function. We characterise…

Virtually all machine learning tasks are characterized using some form of loss function, and "good performance" is typically stated in terms of a sufficiently small average loss, taken over the random draw of test data. While optimizing for…

Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is…

Statistical decision problems lie at the heart of statistical machine learning. The simplest problems are binary and multiclass classification and class probability estimation. Central to their definition is the choice of loss function,…

The curse of dimensionality in the realm of association rules is twofold. Firstly, we have the well known exponential increase in computational complexity with increasing item set size. Secondly, there is a \emph{related curse} concerned…

We address the statistical estimation of composite functionals which may be nonlinear in the probability measure. Our study is motivated by the need to estimate coherent measures of risk, which become increasingly popular in finance,…

Learning systems match predicted scores to observations over some domain. Often, it is critical to produce accurate predictions in some subset (or region) of the domain, yet less important to accurately predict in other regions. We…

We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…

Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…

We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…

As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…

In this work we study loss functions for learning and evaluating probability distributions over large discrete domains. Unlike classification or regression where a wide variety of loss functions are used, in the distribution learning and…

Given a prediction task, understanding when one can and cannot design a consistent convex surrogate loss, particularly a low-dimensional one, is an important and active area of machine learning research. The prediction task may be given as…

We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…

Set prediction is about learning to predict a collection of unordered variables with unknown interrelations. Training such models with set losses imposes the structure of a metric space over sets. We focus on stochastic and underdefined…

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of…