This article proposes an inferential framework for comparing predictor importance in classification problems with categorical response variables. The approach is based on the categorical Gini correlation (CGC) proposed by Dang et al. (2020), a measure of dependence between numerical predictors and categorical outcomes. Predictor importance is evaluated by testing differences in CGCs across competing predictor groups. The proposed methodology accommodates predictors of arbitrary and unequal dimensions and allows for dependence between predictor groups. Asymptotic normality of the test statistic is established under both the null and alternative hypotheses, and the resulting test is shown to be consistent. In addition to deriving the asymptotic distribution, a nonparametric bootstrap procedure is developed as an alternative approach to inference. Simulation studies, along with applications to breast cancer and human activity recognition datasets, demonstrate the effectiveness of the proposed framework.

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)> .