Related papers: Calibrated Adaptive Probabilistic ODE Solvers
Machine learning models deployed in real-world applications are often evaluated with precision-based metrics such as F1-score or AUC-PR (Area Under the Curve of Precision Recall). Heavily dependent on the class prior, such metrics make it…
Response calibration is the process of inferring how much the measured data depend on the signal one is interested in. It is essential for any quantitative signal estimation on the basis of the data. Here, we investigate self-calibration…
Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…
Reliable uncertainty estimation is crucial for perception systems in safe autonomous driving. Recently, many methods have been proposed to model uncertainties in deep learning based object detectors. However, the estimated probabilities are…
Propensity scores are commonly used to estimate treatment effects from observational data. We argue that the probabilistic output of a learned propensity score model should be calibrated -- i.e., a predictive treatment probability of 90%…
The output of predictive models is routinely recalibrated by reconciling low-level predictions with known derived quantities defined at higher levels of aggregation. For example, models predicting turnout probabilities at the individual…
We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…
We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
Implicit methods for the numerical solution of initial-value problems may admit multiple solutions at any given time step. Accordingly, their nonlinear solvers may converge to any of these solutions. Below a critical timestep, exactly one…
We consider a step search method for continuous optimization under a stochastic setting where the function values and gradients are available only through inexact probabilistic zeroth- and first-order oracles. Unlike the stochastic gradient…
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…
GPT-3 can perform numerous tasks when provided a natural language prompt that contains a few training examples. We show that this type of few-shot learning can be unstable: the choice of prompt format, training examples, and even the order…
Making good predictions of a physical system using a computer code requires the inputs to be carefully specified. Some of these inputs called control variables have to reproduce physical conditions whereas other inputs, called parameters,…
Overconfidence and underconfidence in machine learning classifiers is measured by calibration: the degree to which the probabilities predicted for each class match the accuracy of the classifier on that prediction. How one measures…
We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…
Neural differential equations may be trained by backpropagating gradients via the adjoint method, which is another differential equation typically solved using an adaptive-step-size numerical differential equation solver. A proposed step is…
Uncertainty estimates must be calibrated (i.e., accurate) and sharp (i.e., informative) in order to be useful. This has motivated a variety of methods for recalibration, which use held-out data to turn an uncalibrated model into a…
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…