Until now, no tabular method has consistently outperformed classical supervised learning, which ignores these shifts.

Whole slide image (WSI) analysis is gaining prominence within the medical imaging field.

Note that we don't validate the inner-loop'sλ at every outer-loop iteration, but keep changing it on-the-fly at each validation cycle.

Proof of Lemma 2. Let U be the data set associated to ν. Proof of Lemma 3. First, we prove that the property holds for the root node. We wish to prove the property for some unexplored leaf after the iteration. This is trivial if the leaf ν is not expanded in that iteration. Suppose the leaf ν is expanded. Proof of Lemma 5. From Lemma 2, we note that Q Consider any path from the root to a leaf whose length is mK for some integer K > 0. We note that for each node ν and any of its children ν (Lemma 5).

In this section, we provide proofs for Proposition 2.1.B. Inthe proof, we inherit the notations that weuseforprovingTheorem2.1. The instance normalization that we incorporate into the DGM is not the same as the instance normalization that is typically used in image stylization [35]. CNN-F-5 significantly improves the robustness of CNN. CNN-F achieves higher accuracy on MNIST than CNN for under both standard training and adversarial training.

Large-scale AI evaluation increasingly relies on aggregating binary judgments from $K$ annotators, including LLMs used as judges. Most classical methods, e.g., Dawid-Skene or (weighted) majority voting, assume annotators are conditionally independent given the true label $Y\in\{0,1\}$, an assumption often violated by LLM judges due to shared data, architectures, prompts, and failure modes. Ignoring such dependencies can yield miscalibrated posteriors and even confidently incorrect predictions. We study label aggregation through a hierarchy of dependence-aware models based on Ising graphical models and latent factors. For class-dependent Ising models, the Bayes log-odds is generally quadratic in votes; for class-independent couplings, it reduces to a linear weighted vote with correlation-adjusted parameters. We present finite-$K$ examples showing that methods based on conditional independence can flip the Bayes label despite matching per-annotator marginals. We prove separation results demonstrating that these methods remain strictly suboptimal as the number of judges grows, incurring nonvanishing excess risk under latent factors. Finally, we evaluate the proposed method on three real-world datasets, demonstrating improved performance over the classical baselines.

We analyze sources of error in prediction market forecasts in order to bound the difference between a security's price and the ground truth it estimates.