We propose a method for non-parametric conditional distribution estimation based on partitioning covariate-sorted observations into contiguous bins and using the within-bin empirical CDF as the predictive distribution. Bin boundaries are chosen to minimise the total leave-one-out Continuous Ranked Probability Score (LOO-CRPS), which admits a closed-form cost function with $O(n^2 \log n)$ precomputation and $O(n^2)$ storage; the globally optimal $K$-partition is recovered by a dynamic programme in $O(n^2 K)$ time. Minimisation of within-sample LOO-CRPS turns out to be inappropriate for selecting $K$ as it results in in-sample optimism. We instead select $K$ by $K$-fold cross-validation of test CRPS, which yields a U-shaped criterion with a well-defined minimum. Having selected $K^*$ and fitted the full-data partition, we form two complementary predictive objects: the Venn prediction band and a conformal prediction set based on CRPS as the nonconformity score, which carries a finite-sample marginal coverage guarantee at any prescribed level $\varepsilon$. The conformal prediction is transductive and data-efficient, as all observations are used for both partitioning and p-value calculation, with no need to reserve a hold-out set. On real benchmarks against split-conformal competitors (Gaussian split conformal, CQR, CQR-QRF, and conformalized isotonic distributional regression), the method produces substantially narrower prediction intervals while maintaining near-nominal coverage.

Classical Monte Carlo methods for pricing catastrophe insurance tail risk converge at order reciprocal root N, requiring large simulation budgets to resolve upper-tail percentiles of the loss distribution. This sample-sparsity problem can lead to AI models trained on impoverished tail data, producing poorly calibrated risk estimates where insolvency risk is greatest. Quantum Amplitude Estimation (QAE), following Montanaro, achieves convergence approaching order reciprocal N in oracle queries - a quadratic speedup that, at scale, would enable high-resolution tail estimation within practical budgets. We validate this advantage empirically using a Qiskit Aer simulator with genuine Grover amplification. A complete pipeline encodes fitted lognormal catastrophe distributions into quantum oracles via amplitude encoding, producing small readout probabilities that enable safe Grover amplification with up to k=16 iterations. Seven experiments on synthetic and real (NOAA Storm Events, 58,028 records) data yield three main findings: an oracle-model advantage, that strong classical baselines win when analytical access is available, and that discretisation, not estimation, is the current bottleneck.

Real-world image recognition is often challenged by the variability of visual styles including object textures, lighting conditions, filter effects, etc. Although these variations have been deemed to be implicitly handled by more training data and deeper networks, recent advances in image style transfer suggest that it is also possible to explicitly manipulate the style information. Extending this idea to general visual recognition problems, we present Batch-Instance Normalization (BIN) to explicitly normalize unnecessary styles from images. Considering certain style features play an essential role in discriminative tasks, BIN learns to selectively normalize only disturbing styles while preserving useful styles. The proposed normalization module is easily incorporated into existing network architectures such as Residual Networks, and surprisingly improves the recognition performance in various scenarios. Furthermore, experiments verify that BIN effectively adapts to completely different tasks like object classification and style transfer, by controlling the trade-off between preserving and removing style variations. BIN can be implemented with only a few lines of code using popular deep learning frameworks.

Similarly,thetexture ofacloth mayconfuse classifying clothing categories (shirts vs. skirts), but it is crucial for classifying fashion attributes (spottedvs.

Acommon modification, motivatedbyPACagnostic learning, assumes thatf isclosetoanatural distribution classC, and tries to find the distribution inC closest tof.

Nevertheless, it encounters challenges related to ill-posed problems, resulting in deviations between single model predictions and ground-truths. Ensemble learning, as a powerful machine learning technique, aims to address these deviations by combining the predictions of multiple base models.

Machine learning (ML) algorithms can often differ in performance across domains.

This makes CDE particularly useful in critical application domains. However, interpretable CDE methods are understudied.

In machine learning, model calibration and predictive inference are essential for producing reliable predictions and quantifying uncertainty to support decision-making.