Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has emerged as a rapidly growing alternative framework that is particularly well suited to modern applications involving high-dimensional data and complex machine learning models. Its appeal stems from being both distribution-free -- relying mainly on symmetry assumptions such as exchangeability -- and model-agnostic, treating the learning algorithm as a black box. Even under such limited assumptions, conformal prediction provides exact finite-sample guarantees, though these are typically of a marginal nature that requires careful interpretation. This paper explains the core ideas of conformal prediction and reviews selected methods. Rather than offering an exhaustive survey, it aims to provide a clear conceptual entry point and a pedagogical overview of the field.

Instead, we apply powerful machine learning models for one-class (Moya et al., 1993) or

We provide both theoretical analysis and experimental results to validate the effectiveness of our proposed algorithm.

The original MuZero did not use sticky actions (Machado et al., 2017) (a 25% chance that the selected action is ignored and that instead the previous action is repeated) for Atari experiments. For all experiments in this work we used a network architecture based on the one introduced by MuZero(Schrittwieser etal.,2020), To implement the network, we used the modules provided by the Haiku neural network library (Henniganetal.,2020). We did not observe any benefit from using a Gaussian mixture, so instead inallourexperiments weusedasingle Gaussian withdiagonal covariance. All experiments used the Adam optimiser (Kingma & Ba, 2015) with decoupled weight decay (Loshchilov & Hutter, 2017) for training.

This paper identifies astructural property of data distributions that enables deep neural networks to learn hierarchically.

Misalignedrewards can lead to suboptimal behaviors [Ngo et al., 2022], undermining the potential benefits of RL in practical scenarios.

Theorem D.2.Assumetheconditionsin Lemma D.1 and Assumption 4.1 hold. Proof.DenoterandommatrixXi = (si,ai) (si,ai)> .

Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraintsislarge.