A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
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 when margin losses can be proper composite losses, explicitly show how to determ…
The goal of online prediction with expert advice is to find a decision strategy which will perform almost as well as the best expert in a given pool of experts, on any sequence of outcomes. This problem has been widely studied and O(T) and O(logT) regret bounds can be achieved for convex losses (\cite{zin…
The problem of bipartite ranking, where instances are labeled positive or negative and the goal is to learn a scoring function that minimizes the probability of mis-ranking a pair of positive and negative instances (or equivalently, that maximizes the area under the ROC curve), has been widely studied in recent years. …
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 the implications. We also show how the separation of concerns afforded by using …
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules via the proper-composite representation, in which predictions are mapped to probab…
We study strictly proper scoring rules in the Reproducing Kernel Hilbert Space. We propose a general Kernel Scoring rule and associated Kernel Divergence. We consider conditions under which the Kernel Score is strictly proper. We then demonstrate that the Kernel Score includes the Maximum Mean Discrepancy as a special …
The paper argues that uncertainty quantification in ML is application-specific and proposes a flexible family of measures.
problem The need for proper uncertainty quantification in machine learning for safety-critical applications.
method A flexible family of uncertainty measures tailored to specific applications, using proper scoring rules to control characteristics.
result Different uncertainty measures are more suitable for different tasks (e.g., selective prediction, out-of-distribution detection, active learning).
The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space interpretation and reformulated into the underlying data distribution setting where connections to maximal marginal diver…
The last few years have seen a staggering number of empirical studies of the robustness of neural networks in a model of adversarial perturbations of their inputs. Most rely on an adversary which carries out local modifications within prescribed balls. None however has so far questioned the broader picture: how to fram…
This paper argues against using calibration metrics for assessing posterior probabilities and proposes expected proper scoring rules instead.
problem The assessment of posterior probabilities generated by machine learning classifiers using calibration metrics is flawed and should be replaced with expected proper scoring rules.
method The paper reviews proper scoring rules from a practical perspective, explains why expected PSRs are a principled measure of posterior quality, and introduces a new calibration metric called calibration loss.
result Calibration loss is superior to expected calibration error and expected score divergence calibration metrics for assessing posterior probabilities.
Boosted ensemble of decision tree (DT) classifiers are extremely popular in international competitions, yet to our knowledge nothing is formally known on how to make them \textit{also} differential private (DP), up to the point that random forests currently reign supreme in the DP stage. Our paper starts with the proof…
We develop efficient algorithms to train ℓ1-regularized linear classifiers with large dimensionality d of the feature space, number of classes k, and sample size n. Our focus is on a special class of losses that includes, in particular, the multiclass hinge and logistic losses. Our approach combines several…
We unify f-divergences, Bregman divergences, surrogate loss bounds (regret bounds), proper scoring rules, matching losses, cost curves, ROC-curves and information. We do this by systematically studying integral and variational representations of these objects and in so doing identify their primitives which all are rela…