New concept of proper-calibeating extends classic calibrated forecasts to proper scoring rules.
problem Defining and extending calibrated forecasts to proper scoring rules.
method Extending the concepts of calibrated and calibeating forecasts to proper scoring rules and proving their properties.
result Proper-calibration always implies calibration, but proper-calibeating does not necessarily imply calibeating.
The article reviews scoring rules for estimating and evaluating forecasts.
problem Evaluating probabilistic forecasts and estimating probability distributions.
method Mathematical foundations and characterization of scoring rules.
result Important families of scoring rules and their applications in statistics and machine learning.
Prior-weighted logistic regression has become a standard tool for calibration in speaker recognition. Logistic regression is the optimization of the expected value of the logarithmic scoring rule. We generalize this via a parametric family of proper scoring rules. Our theoretical analysis shows how different members of…
Survival regression method improves log-likelihood scores.
problem Improper scoring rules in survival regression models.
method SurvivalMonotonic-net (SuMo-net) with monotonic neural networks.
result SuMo-net achieves state-of-the-art log-likelihood scores.
Critiques binary classification evaluation methods, advocating for proper scoring rules.
problem The dominance of top-K metrics and fixed-threshold evaluations in machine learning.
method Introduces a decision-theoretic framework mapping evaluation metrics to their use cases, and implements a clipped Brier score variant.
result Demonstrates the clinical utility of proper scoring rules through a Python package, exttt{briertools}.
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 …
Proposes measures for uncertainty quantification using proper scoring rules.
problem Uncertainty quantification for prediction tasks.
method Decomposes proper scoring rules into divergence and entropy components, tailoring uncertainty quantification to specific tasks.
result Flexibility in uncertainty quantification improves performance in selective prediction and active learning.
There has been much recent interest in application of the pool-adjacent-violators (PAV) algorithm for the purpose of calibrating the probabilistic outputs of automatic pattern recognition and machine learning algorithms. Special cost functions, known as proper scoring rules form natural objective functions to judge the…
New scoring rules improve probabilistic classification model evaluation.
problem Traditional scoring rules misalign with the preference for correct classifications.
method Introduces Penalized Brier Score (PBS) and Penalized Logarithmic Loss (PLL) to modify proper scoring rules.
result PBS and PLL better identify optimal checkpoints and early stopping points, leading to superior F1 scores.
Study compares multivariate scoring rules for distribution forecasts.
problem Evaluating the discrimination ability of multivariate scoring rules.
method Simulation study comparing energy and variogram scores using historical data.
result Variogram score with p=0.5 outperforms other scores.
We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results achieved by other investigators.
Estimates proper calibration errors and refinement terms in probabilistic predictions.
problem Lack of a general estimator for proper calibration errors and refinement terms with known statistical properties.
method Proposes a method for consistent, asymptotically unbiased estimation of proper calibration errors and refinement terms.
result Proves the relation between refinement and f-divergences, implying information monotonicity in neural networks.
Conditional forecasts improve performative prediction accuracy.
problem Performative predictions undermine standard forecasting methods.
method Condition forecasts on covariates to make them forecast-invariant.
result Proper scoring rules fail under conditioning, but two solutions are identified.
This paper explores how to choose scoring rules for estimating properties with parametric assumptions.
problem Indirect elicitation of properties with parametric assumptions.
method Developed a framework for choosing proper scoring rules for indirect elicitation, considering constraints and optimal solutions.
result The optimal estimation of the target property changes monotonically with the increase of each weight, and often setting some weights as zero yields the best configuration.
Improves generative models for cost-sensitive decisions.
problem Generative models lack awareness of decision costs.
method Integrates a decision loss into the training objective.
result Improves cost-sensitive forecast accuracy.
New scoring rules compare probabilistic top lists in classification.
problem Evaluation of probabilistic top lists in classification.
method Elicitability through symmetric proper scoring rules.
result Brier score provides a well-suited metric for comparison.
New findings show second-order scoring rules can't accurately represent epistemic uncertainty.
problem Lack of epistemic uncertainty representation in second-order learners.
method Generalised second-order scoring rules introduced to prove theoretical limitations.
result No loss function incentivizes second-order learners to accurately represent epistemic uncertainty.
The paper introduces new measures for quantifying uncertainty in machine learning.
problem Uncertainty representation and quantification in machine learning.
method Proper scoring rules for aleatoric and epistemic uncertainty quantification.
result Established a natural bridge between credal set and second-order distribution representations of uncertainty.
Study identifies regions where scoring rules reliably detect forecast errors.
problem Insufficient reliability of scoring rules in evaluating multivariate probabilistic forecasts.
method Systematic finite-sample analysis of proper scoring rules on synthetic and real-world data.
result Identified regions of reliability for scoring rules in time-series forecasting.
Improving Bayesian filtering with strictly proper scoring rules
problem Bayesian filtering of partially and noisily observed dynamical systems
method Proper scoring ensemble filter (PSEF)
result Accurate approximation of challenging filtering distributions
Robust scatter estimation is a fundamental task in statistics. The recent discovery on the connection between robust estimation and generative adversarial nets (GANs) by Gao et al. (2018) suggests that it is possible to compute depth-like robust estimators using similar techniques that optimize GANs. In this paper, we …
Model selection for time series forecasting can be biased by the distribution of scores.
problem Model selection for probabilistic forecasting on time series data.
method Using proper scoring rules to aggregate scores across multiple time series.
result The mean score is immune to the skewness of the score distribution.
Estimates uncertainty in bounding box regression for object detection.
problem Reliable deployment of deep object detectors in safety-critical tasks.
method Training variance networks with energy score as a proper scoring rule.
result Energy score leads to better calibrated and lower entropy predictive distributions.
SurvivalBoost improves prediction of event times in competing risks scenarios.
problem Predicting event times in scenarios with multiple possible outcomes.
method Developed a strictly proper censoring-adjusted scoring rule for stochastic optimization of competing risks.
result SurvivalBoost outperforms 12 state-of-the-art models across various metrics.
In recent years, probabilistic forecasting is an emerging topic, which is why there is a growing need of suitable methods for the evaluation of multivariate predictions. We analyze the sensitivity of the most common scoring rules, especially regarding quality of the forecasted dependency structures. Additionally, we pr…
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.
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…
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).
New tree splitting criteria improve probabilistic predictions.
problem Improving tree-based nonparametric predictive distributions.
method Using proper scoring rules for tree splitting criteria.
result Trees with new splitting criteria produce better predictive distributions.
This work introduces a bias-variance decomposition for proper scores, improving uncertainty estimation in predictive models.
problem Reliable uncertainty estimation for predictions in safety-critical applications, especially under domain drift.
method Developed a general bias-variance decomposition for proper scores, introducing the Bregman Information as the variance term.
result The decomposition provides novel formulations for different predictive tasks, including classification and model ensembles.
Signature kernel scoring rule improves weather forecasting by capturing temporal and spatial dependencies.
problem Lack of suitable scoring rules for probabilistic weather forecasting.
method Reframe weather variables as continuous paths using iterated integrals (signature kernels) to capture temporal and spatial dependencies.
result Signature kernel scoring rule outperforms conventional methods in weather forecasting, especially for long-term forecasts.
Study optimizes scoring rules for incentivizing agent's information gathering in online settings.
problem Optimizing incentives for agents to acquire information in online settings.
method Designing a sample-efficient algorithm that tailors the UCB algorithm to the strategic agent's model.
result Achieves sublinear T2/3-regret after T iterations, independent of the number of states. Generative Cross-Entropy improves classification with fewer labels.
problem Limited sample efficiency of cross-entropy loss in data-scarce scenarios.
method Proposes Generative Cross-Entropy (GenCE), a new loss function that incorporates generative principles into a standard discriminative network.
result Generative Cross-Entropy outperforms traditional cross-entropy loss across various datasets and conditions.
EnScale learns to downscale climate models efficiently, capturing both spatial and temporal consistency.
problem Downscaling climate models from coarse to high-resolution data is computationally expensive and challenging.
method EnScale uses generative models and proper scoring rules to map GCM data to RCM data, reducing computational cost.
result EnScale achieves competitive performance and computational efficiency in downscaling multiple climate variables.
ProSMIN improves representation quality through probabilistic self-supervised learning.
problem Improving representation quality in self-supervised learning.
method ProSMIN uses two neural networks, online and target, to learn diverse representations through knowledge distillation and a modified scoring rule loss function.
result ProSMIN achieves superior accuracy and calibration on various downstream tasks.
Decision-alignment evaluates uncertainty quantification for decision-relevant UQ
problem Evaluation of uncertainty quantification metrics
method Introduce decision-alignment
result Proper scoring rules align with decision utility
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…
This research focuses on invariant probabilistic predictions, showing they are not robust under distribution shifts.
problem The challenge of creating robust probabilistic predictions that remain consistent under distribution shifts.
method A causality-inspired framework to investigate invariance and robustness of probabilistic predictions with respect to proper scoring rules.
result Arbitrary distribution shifts do not admit invariant and robust probabilistic predictions, unlike point predictions.
A novel framework quantifies uncertainty using proper scores for various tasks.
problem Uncertainty quantification in machine learning for reliable applications.
method Proposes a general framework based on proper scores for epistemic, aleatoric uncertainty, and model calibration.
result Achieves state-of-the-art uncertainty estimation for large language models and generative models.
ForesightFlow detects informed trading on prediction markets using an information leakage score.
problem Detecting informed trading on decentralized prediction markets.
method Developed an Information Leakage Score (ILS) framework to quantify the fraction of terminal information move priced in before public news events.
result The score connects label generation to proper-scoring-rule literature and reveals systematic biases in insider trading documentation.
Recently, several new pari-mutuel mechanisms have been introduced to organize markets for contingent claims. Hanson introduced a market maker derived from the logarithmic scoring rule, and later Chen and Pennock developed a cost function formulation for the market maker. On the other hand, the SCPM model of Peters et a…
DistPred provides a fast, distribution-free method for regression and forecasting.
problem Deterministic point estimates in regression and prediction tasks.
method Transforming proper scoring rules into a differentiable form and using it as a loss function.
result Achieved state-of-the-art performance and significantly improved computational efficiency.
We present a simple theoretical framework, and corresponding practical procedures, for comparing probabilistic models on real data in a traditional machine learning setting. This framework is based on the theory of proper scoring rules, but requires only basic algebra and probability theory to understand and verify. Th…
Unified framework for estimating density ratios across multiple distributions.
problem Binary density ratio estimation for multiple distributions.
method Unified framework based on Bregman divergence minimization.
result Generalization of binary DRE methods to multiple distributions.
Paper refines InfoNCE for accurate mutual information estimation.
problem Indirect connection of InfoNCE to mutual information estimation.
method Introduces InfoNCE-anchor with an auxiliary anchor class for consistent density ratio estimation.
result InfoNCE-anchor yields a plug-in MI estimator with significantly reduced bias.
Improves model calibration for deep neural networks using proper scores.
problem Calibration errors in deep neural networks are often biased and inconsistent.
method Introduces proper calibration errors related to proper scores.
result Demonstrates the superiority of proper scores over common estimators.
A test assesses the calibration of set-based epistemic uncertainty representations.
problem Evaluating the accuracy of set-based representations of epistemic uncertainty in machine learning.
method Proposes a novel statistical test to determine if a convex combination of predictions is calibrated, allowing instance-level variability.
result Demonstrates the benefits of capturing instance-level variability on synthetic and real-world experiments.
No policy can simultaneously be fully autonomous, optimally calibrated, and helpful, proving a trilemma.
problem Proving impossibility of a policy achieving maximum helpfulness, optimal calibration, and full autonomy.
method Geometric proof showing that adding any non-affine autonomy incentive to a strictly proper scoring rule destroys strict properness.
result The Behavioral Credibility Trilemma: no policy can achieve all three goals simultaneously.