Related papers: A Geometric Proof of Calibration
The field of algorithms with predictions incorporates machine learning advice in the design of online algorithms to improve real-world performance. A central consideration is the extent to which predictions can be trusted -- while existing…
Reachability computations that rely on learned or estimated models require calibration in order to uphold confidence about their guarantees. Calibration generally involves sampling scenarios inside the reachable set. However, producing…
We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…
In this paper, we develop the notion of presentability in the parametrised homotopy theory framework of Barwick-Dotto-Glasman-Nardin-Shah over orbital categories. We formulate and prove a characterisation of parametrised presentable…
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
We give a geometric proof of the Affability Theorem of T. Giordano, H. Matui, I. Putnam and C. Skau for aperiodic and repetitive planar tilings.
We show that including degrees of a particular kind of provability in the search target for any theorem-prover in sufficiently powerful formal systems over finite-sized statements preserves well-definition and a sufficient consistency while…
In safety-critical applications a probabilistic model is usually required to be calibrated, i.e., to capture the uncertainty of its predictions accurately. In multi-class classification, calibration of the most confident predictions only is…
We prove a quantitative version of the Gibbard-Satterthwaite theorem. We show that a uniformly chosen voter profile for a neutral social choice function f of $q \ge 4$ alternatives and n voters will be manipulable with probability at least…
A goodness-of-fit test for the fitting of a parametric model to data obtained from a detector with finite resolution and limited acceptance is proposed. The parameters of the model are found by minimization of a statistic that is used for…
Obvious strategyproofness (OSP) is an appealing concept as it allows to maintain incentive compatibility even in the presence of agents that are not fully rational, e.g., those who struggle with contingent reasoning [Li, 2015]. However, it…
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…
We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First we identify the conditions under which propositional probability…
A set of probabilistic forecasts is calibrated if each prediction of the forecaster closely approximates the empirical distribution of outcomes on the subset of timesteps where that prediction was made. We study the fundamental problem of…
We propose a learning framework for calibrating predictive models to make loss-controlling prediction for exchangeable data, which extends our recently proposed conformal loss-controlling prediction for more general cases. By comparison,…
We consider a trader who wants to direct his portfolio towards a set of acceptable wealths given by a convex risk measure. We propose a black-box algorithm, whose inputs are the joint law of stock prices and the convex risk measure, and…
Calibration$\unicode{x2014}$the problem of ensuring that predicted probabilities align with observed class frequencies$\unicode{x2014}$is a basic desideratum for reliable prediction with machine learning systems. Calibration error is…