Related papers: The Geometry and Calculus of Losses
Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…
Traditionally Bayesian decision-theoretic design of experiments proceeds by choosing a design to minimise expectation of a given loss function over the space of all designs. The loss function encapsulates the aim of the experiment, and the…
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…
Classification is the most important process in data analysis. However, due to the inherent non-convex and non-smooth structure of the zero-one loss function of the classification model, various convex surrogate loss functions such as hinge…
We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…
Coreset of a given dataset and loss function is usually a small weighed set that approximates this loss for every query from a given set of queries. Coresets have shown to be very useful in many applications. However, coresets construction…
Simultaneous segmentation of multiple organs from different medical imaging modalities is a crucial task as it can be utilized for computer-aided diagnosis, computer-assisted surgery, and therapy planning. Thanks to the recent advances in…
The earth system is exceedingly complex and often chaotic in nature, making prediction incredibly challenging: we cannot expect to make perfect predictions all of the time. Instead, we look for specific states of the system that lead to…
In the prospect theory, value function is typically concave for gains, commonly convex for losses, with losses usually having a steeper slope than gains. The neural system largely differs from the loss and gains sides. Five new studies on…
Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization…
This paper studies loss functions for finite sets. For a given finite set $S$, we give sum-of-square type loss functions of minimum degree. When $S$ is the vertex set of a standard simplex, we show such loss functions have no spurious…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
The geometric problem of estimating an unknown compact convex set from evaluations of its support function arises in a range of scientific and engineering applications. Traditional approaches typically rely on estimators that minimize the…
Most classification models can be considered as the process of matching templates. However, when intra-class uncertainty/variability is not considered, especially for datasets containing unbalanced classes, this may lead to classification…
Though learning has become a core component of modern information processing, there is now ample evidence that it can lead to biased, unsafe, and prejudiced systems. The need to impose requirements on learning is therefore paramount,…
We study loss functions that measure the accuracy of a prediction based on multiple data points simultaneously. To our knowledge, such loss functions have not been studied before in the area of property elicitation or in machine learning…
This paper shows that a wide class of effective learning rules -- those that improve a scalar performance measure over a given time window -- can be rewritten as natural gradient descent with respect to a suitably defined loss function and…
This paper explores connections between margin-based loss functions and consistency in binary classification and regression applications. It is shown that a large class of margin-based loss functions for binary classification/regression…
In machine learning, a loss function measures the difference between model predictions and ground-truth (or target) values. For neural network models, visualizing how this loss changes as model parameters are varied can provide insights…
Loss functions are one of the crucial ingredients in deep learning-based medical image segmentation methods. Many loss functions have been proposed in existing literature, but are studied separately or only investigated with few other…