Understanding the effects of interventions is central to scientific progress, with randomized controlled trials (RCTs) regarded as the gold standard for causal inference in many applied fields. However, RCTs are costly, time-consuming, and often constrained by ethical or practical limitations, motivating the need for causal methods able to draw conclusions from observational data. While such data is collected at ever larger scale, making its use for causal inference is often hindered by the fact that not all variables affecting treatment allocation and the outcome are observed - an issue known as unobserved confounding. In this paper, we introduce a new study design called confounder detection via treatment intent. The idea is to query a human expert who makes treatment decisions, and ask them to compare pairs of units proposed by a principled matching strategy, with the goal of eliciting unobserved variables that explain why treatment decisions differ. We provide a theoretical basis for such a procedure, ascertaining conditions under which such a study design may elicit unobserved confounders. Building on this newly established foundations, we study treatment effects of interventions in the intensive care unit (ICU). First, we show empirical evidence strongly indicating that electronic health records (EHRs) collected in ICUs are subject to unobserved confounding. By using clinical text notes as a proxy for physicians' knowledge and leveraging natural language processing, we provide a proof of concept for our methodology in a semi-synthetic environment with a known ground truth.

Reproducibility319 The backbone recommendation model, DLRM by Naumov et al. [2019], has an open-source PyTorch320 implementation available on Github which includes an implementation of CE. For CCE you need a321 fast library for K-means. We recommend the open-sourced implementation by Johnson et al. [2019]322 for better performance, but you can also use the implementation in Scikit-learn [Pedregosa et al.,323 2011]. The baseline result should be straightforward to reproduce as we closely follow the instructions324 provided by Naumov et al. [2019]. For the CE methods, we only need to change two functions in325 the code: create_emband apply_emb. We suggest using a class for each CE method; see Figure 3.326 For the random hash function, one could use a universal hash function or numpy.random.randint.327

Maximizing the area under the receiver operating characteristic curve (AUC) is a popular approach to imbalanced binary classification problems. Existing AUC maximization methods usually assume that training and test distributions are identical. However, this assumption is often violated in practice due to {\it a positive distribution shift}, where the negative-conditional density does not change but the positive-conditional density can vary. This shift often occurs in imbalanced classification since positive data are often more diverse and time-varying than negative data. To deal with this shift, we theoretically show that the AUC on the test distribution can be expressed by using the positive and marginal training densities and the marginal test density. Based on this result, we can maximize the AUC on the test distribution by using positive and unlabeled data in the training distribution and unlabeled data in the test distribution. The proposed method requires only positive labels in the training distribution as supervision. Moreover, the derived AUC has a simple form and thus is easy to implement. The effectiveness of the proposed method is shown with four real-world datasets.

A.1 Proof Sketch We first introduce the following lemma: Lemma 1. Lemma 2. For matrices A,B 2Mn, if A B, then we have min(A) min(B)and max(A) max(B), where max() (resp., min()) denotes taking the maximum (resp., minimum) eigenvalue.. Proof of Lemma 2. For any matrix P 2Mn with P> = P, we have max(P) = max We first consider the condition number of ˆH when X is in a locally convex area. By equations 3 and 4, we have M1 H M2. Rearranging the terms yields H M1 0 and M2 H 0. Therefore, for any vector x 2RM, we have We next consider the minimum singular value of H and ˆH with min(H)= p min(H2) and min(ˆH)= q min(ˆH2) in any case. Under Assumption 1 and equation 4, we have H M2. Similarly, we can obtain H M2. By Lemma 2, we further have max(H) max(M2)= nmax 2 C.1 kr ˆf(ˆX) k2 vs. krf(X) k2 In this section, we explain why we use kr ˆf(ˆX) k2 rather than kr f(X) k2 to characterize the convergence rate. In general, it is hard to develop a convergence rate for objective values. However, when the global model is in a locally convex area of f, we can obtain the relationship between the gradient and the local optimum.

This paper reorganizes the current manuscript around the DPO versus DDO-RM preference-optimization project and focuses on two parts: the algorithmic view and the preliminary held-out benchmark. The benchmark asks a narrow question: even in a minimal pairwise chosen-versus-rejected setting, can a reward-guided decision-distribution update outperform a direct pairwise objective? We compare Direct Preference Optimization (DPO) against DDO-RM on EleutherAI/pythia-410m using HuggingFaceH4/ultrafeedback\_binarized, evaluate on the held-out test\_prefs split, and report results for seeds 42, 13, and 3407. Algorithmically, DDO-RM treats each prompt as a finite decision problem over candidate responses. Instead of optimizing only a binary chosen-rejected relation, it forms a policy distribution over candidates, centers reward-model scores under that distribution, and distills a reward-guided target distribution back into the policy. In the current public benchmark, DDO-RM improves mean pair accuracy from 0.5238 to 0.5602, AUC from 0.5315 to 0.5382, and mean margin from 0.1377 to 0.5353 relative to DPO. These are encouraging but still preliminary results: the study covers one model family, one dataset, one held-out evaluation split, and three seeds.

Objective. We establish a principled method for inferring mental health related psychometric variables from neural and behavioral data using the Implicit Association Test (IAT) as the data generation engine, aiming to overcome the limited predictive performance (typically under 0.7 AUC) of the gold-standard D-score method, which relies solely on reaction times. Approach. We propose a sparse hierarchical Bayesian model that leverages multi-modal data to predict experiences related to mental illness symptoms in new participants. The model is a multivariate generalization of the D-score with trainable parameters, engineered for parameter efficiency in the small-cohort regime typical of IAT studies. Data from two IAT variants were analyzed: a suicidality-related E-IAT ($n=39$) and a psychosis-related PSY-IAT ($n=34$). Main Results. Our approach overcomes a high inter-individual variability and low within-session effect size in the dataset, reaching AUCs of 0.73 (E-IAT) and 0.76 (PSY-IAT) in the best modality configurations, though corrected 95% confidence intervals are wide ($\pm 0.18$) and results are marginally significant after FDR correction ($q=0.10$). Restricting the E-IAT to MDD participants improves AUC to 0.79 $[0.62, 0.97]$ (significant at $q=0.05$). Performance is on par with the best reference methods (shrinkage LDA and EEGNet) for each task, even when the latter were adapted to the task, while the proposed method was not. Accuracy was substantially above near-chance D-scores (0.50-0.53 AUC) in both tasks, with more consistent cross-task performance than any single reference method. Significance. Our framework shows promise for enhancing IAT-based assessment of experiences related to entrapment and psychosis, and potentially other mental health conditions, though further validation on larger and independent cohorts will be needed to establish clinical utility.

Many practical settings call for the reconstruction of temporal signals from corrupted or missing data. Classic examples include decoding, tracking, signal enhancement and denoising.