Inductive randomness predictors: beyond conformal
- URL: http://arxiv.org/abs/2503.02803v2
- Date: Mon, 07 Jul 2025 15:47:24 GMT
- Title: Inductive randomness predictors: beyond conformal
- Authors: Vladimir Vovk,
- Abstract summary: This paper introduces inductive randomness predictors, which form a proper superset of inductive conformal predictors.<n>It turns out that every non-trivial inductive conformal predictor is strictly dominated by an inductive randomness predictor.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This paper introduces inductive randomness predictors, which form a proper superset of inductive conformal predictors but have the same principal property of validity under the assumption of randomness (i.e., of IID data). It turns out that every non-trivial inductive conformal predictor is strictly dominated by an inductive randomness predictor, although the improvement is not great, at most a factor of $\mathrm{e}\approx2.72$ in the case of e-prediction. The dominating inductive randomness predictors are more complicated and more difficult to compute; besides, an improvement by a factor of $\mathrm{e}$ is rare. Therefore, this paper does not suggest replacing inductive conformal predictors by inductive randomness predictors and only calls for a more detailed study of the latter.
Related papers
- Universality of conformal prediction under the assumption of randomness [0.0]
Conformal predictors provide set or functional predictions that are valid under the assumption of randomness.<n>The question is whether there are predictors that are valid in the same sense under the assumption of randomness and that are more efficient than conformal predictors.<n>The answer is that the class of conformal predictors is universal in that only limited gains in predictive efficiency are possible.
arXiv Detail & Related papers (2025-02-26T16:00:42Z) - Randomness, exchangeability, and conformal prediction [0.0]
It introduces new kinds of confidence predictors, including randomness predictors and exchangeability predictors.<n>The main result implies that both are close to conformal predictors and quantifies the difference between randomness prediction and conformal prediction.
arXiv Detail & Related papers (2025-01-20T19:14:26Z) - Conformal Generative Modeling with Improved Sample Efficiency through Sequential Greedy Filtering [55.15192437680943]
Generative models lack rigorous statistical guarantees for their outputs.
We propose a sequential conformal prediction method producing prediction sets that satisfy a rigorous statistical guarantee.
This guarantee states that with high probability, the prediction sets contain at least one admissible (or valid) example.
arXiv Detail & Related papers (2024-10-02T15:26:52Z) - Random features models: a way to study the success of naive imputation [0.0]
Constant (naive) imputation is still widely used in practice as this is a first easy-to-use technique to deal with missing data.
Recent works suggest that this bias is low in the context of high-dimensional linear predictors.
This paper confirms the intuition that the bias is negligible and that surprisingly naive imputation also remains relevant in very low dimension.
arXiv Detail & Related papers (2024-02-06T09:37:06Z) - Variational Prediction [95.00085314353436]
We present a technique for learning a variational approximation to the posterior predictive distribution using a variational bound.
This approach can provide good predictive distributions without test time marginalization costs.
arXiv Detail & Related papers (2023-07-14T18:19:31Z) - Creating Probabilistic Forecasts from Arbitrary Deterministic Forecasts
using Conditional Invertible Neural Networks [0.19573380763700712]
We use a conditional Invertible Neural Network (cINN) to learn the underlying distribution of the data and then combine the uncertainty from this distribution with an arbitrary deterministic forecast.
Our approach enables the simple creation of probabilistic forecasts without complicated statistical loss functions or further assumptions.
arXiv Detail & Related papers (2023-02-03T15:11:39Z) - On Second-Order Scoring Rules for Epistemic Uncertainty Quantification [8.298716599039501]
We show that there seems to be no loss function that provides an incentive for a second-order learner to faithfully represent its uncertainty.
As a main mathematical tool to prove this result, we introduce the generalised notion of second-order scoring rules.
arXiv Detail & Related papers (2023-01-30T08:59:45Z) - Exact and Approximate Conformal Inference for Multi-Output Regression [0.0]
Conformal inference is used in machine learning to quantify uncertainty associated with predictions.
In this paper, we explore multi-output regression, delivering exact derivations of conformal inference $p$-values.
We also provide both theoretical and empirical evidence of the effectiveness of these methods using both real-world and simulated data.
arXiv Detail & Related papers (2022-10-31T15:41:13Z) - Predictive Inference with Feature Conformal Prediction [80.77443423828315]
We propose feature conformal prediction, which extends the scope of conformal prediction to semantic feature spaces.
From a theoretical perspective, we demonstrate that feature conformal prediction provably outperforms regular conformal prediction under mild assumptions.
Our approach could be combined with not only vanilla conformal prediction, but also other adaptive conformal prediction methods.
arXiv Detail & Related papers (2022-10-01T02:57:37Z) - On the Difficulty of Epistemic Uncertainty Quantification in Machine
Learning: The Case of Direct Uncertainty Estimation through Loss Minimisation [8.298716599039501]
Uncertainty quantification has received increasing attention in machine learning.
The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify.
We show that loss minimisation does not work for second-order predictors.
arXiv Detail & Related papers (2022-03-11T17:26:05Z) - Robust uncertainty estimates with out-of-distribution pseudo-inputs
training [0.0]
We propose to explicitly train the uncertainty predictor where we are not given data to make it reliable.
As one cannot train without data, we provide mechanisms for generating pseudo-inputs in informative low-density regions of the input space.
With a holistic evaluation, we demonstrate that this yields robust and interpretable predictions of uncertainty while retaining state-of-the-art performance on diverse tasks.
arXiv Detail & Related papers (2022-01-15T17:15:07Z) - CovarianceNet: Conditional Generative Model for Correct Covariance
Prediction in Human Motion Prediction [71.31516599226606]
We present a new method to correctly predict the uncertainty associated with the predicted distribution of future trajectories.
Our approach, CovariaceNet, is based on a Conditional Generative Model with Gaussian latent variables.
arXiv Detail & Related papers (2021-09-07T09:38:24Z) - DEUP: Direct Epistemic Uncertainty Prediction [56.087230230128185]
Epistemic uncertainty is part of out-of-sample prediction error due to the lack of knowledge of the learner.
We propose a principled approach for directly estimating epistemic uncertainty by learning to predict generalization error and subtracting an estimate of aleatoric uncertainty.
arXiv Detail & Related papers (2021-02-16T23:50:35Z) - Sequential prediction under log-loss and misspecification [47.66467420098395]
We consider the question of sequential prediction under the log-loss in terms of cumulative regret.
We show that cumulative regrets in the well-specified and misspecified cases coincideally.
We provide an $o(1)$ characterization of the distribution-free or PAC regret.
arXiv Detail & Related papers (2021-01-29T20:28:23Z) - The Hidden Uncertainty in a Neural Networks Activations [105.4223982696279]
The distribution of a neural network's latent representations has been successfully used to detect out-of-distribution (OOD) data.
This work investigates whether this distribution correlates with a model's epistemic uncertainty, thus indicating its ability to generalise to novel inputs.
arXiv Detail & Related papers (2020-12-05T17:30:35Z) - Learnable Uncertainty under Laplace Approximations [65.24701908364383]
We develop a formalism to explicitly "train" the uncertainty in a decoupled way to the prediction itself.
We show that such units can be trained via an uncertainty-aware objective, improving standard Laplace approximations' performance.
arXiv Detail & Related papers (2020-10-06T13:43:33Z) - The Vector Poisson Channel: On the Linearity of the Conditional Mean
Estimator [82.5577471797883]
This work studies properties of the conditional mean estimator in vector Poisson noise.
The first result shows that the conditional mean estimator cannot be linear when the dark current parameter of the Poisson noise is non-zero.
The second result produces a quantitative refinement of the first result.
arXiv Detail & Related papers (2020-03-19T18:21:33Z) - De-randomized PAC-Bayes Margin Bounds: Applications to Non-convex and
Non-smooth Predictors [21.59277717031637]
We present a family of de-randomized PACes for deterministic non-smooth predictors, e.g., ReLU-nets.
We also present empirical results of our bounds over changing set size and in labels.
arXiv Detail & Related papers (2020-02-23T17:54:07Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.