We present a human-in-the-loop (HIL) approach to permutation regression, the novel task of predicting a continuous value for a given ordering of items. The model is a gradient boosted regression model that incorporates simple human-understandable constraints of the form x < y, i.e. item x has to be before item y, as binary features. The approach, HuGuR (Human Guided Regression), lets a human explore the search space of such transparent regression models. Interacting with HuGuR, users can add, remove, and refine order constraints interactively, while the coefficients are calculated on the fly. We evaluate HuGuR in a user study and compare the performance of user-built models with multiple baselines on 9 data sets. The results show that the user-built models outperform the compared methods on small data sets and in general perform on par with the other methods, while being in principle understandable for humans. On larger datasets from the same domain, machine-induced models begin to outperform the user-built models. Further work will study the trust users have in models when constructed by themselves and how the scheme can be transferred to other pattern domains, such as strings, sequences, trees, or graphs.

We propose a method to optimize language model pre-training data mixtures through efficient approximation of the cross-entropy loss corresponding to each candidate mixture via a Mixture of Data Experts (MDE). We use this approximation as a source of additional features in a regression model, trained from observations of model loss for a small number of mixtures. Experiments with Transformer decoder-only language models in the range of 70M to 1B parameters on the SlimPajama dataset show that our method achieves significantly better performance than approaches that train regression models using only the mixture rates as input features. Combining this improved optimization method with an objective that takes into account cross-entropy on end task data leads to superior performance on few-shot downstream evaluations. We also provide theoretical insights on why aggregation of data expert predictions can provide good approximations to model losses for data mixtures.

The use of machine learning (ML) has become increasingly prevalent in various domains, highlighting the importance of understanding and ensuring its safety. One pressing concern is the vulnerability of ML applications to model stealing attacks. These attacks involve adversaries attempting to recover a learned model through limited query-response interactions, such as those found in cloud-based services or on-chip artificial intelligence interfaces. While existing literature proposes various attack and defense strategies, these often lack a theoretical foundation and standardized evaluation criteria. In response, this work presents a framework called ``Model Privacy'', providing a foundation for comprehensively analyzing model stealing attacks and defenses. We establish a rigorous formulation for the threat model and objectives, propose methods to quantify the goodness of attack and defense strategies, and analyze the fundamental tradeoffs between utility and privacy in ML models. Our developed theory offers valuable insights into enhancing the security of ML models, especially highlighting the importance of the attack-specific structure of perturbations for effective defenses. We demonstrate the application of model privacy from the defender's perspective through various learning scenarios. Extensive experiments corroborate the insights and the effectiveness of defense mechanisms developed under the proposed framework.

In contrast to the standard intuition that a learner should search for a trade-off between approximation and estimation errors, researchers empirically observed that large interpolating rules may still have small test error. Moreover, when the number of parameters exceeds sample size the prediction risk of neural networks passes a U-shaped curve and decreases again [Zhang et al., 2017, Nakkiran et al., 2020]. A bit later it became clear that benign overfitting and double descent are not distinctive features of deep learning. Similar phenomena are ubiquitous for overparametrized models such as random forests and random feature models [Belkin et al., 2019, Mei and Montanari, 2022], kernel methods [Belkin et al., 2018, Liang and Rakhlin, 2020], and linear regression [Bartlett et al., 2020, Hastie et al., 2022] to name a few. In [Belkin et al., 2018], the authors reasonably suggested that we must study more tractable "shallow" methods better before diving into deep learning theory. In the present paper, we consider a classical linear regression problem, where a learner aims to estimate an unknown vector θ R d from i.i.d.

Quantum Parametric Circuits are constructed as an alternative to reduce the size of quantum circuits, meaning to decrease the number of quantum gates and, consequently, the depth of these circuits. However, determining the optimal circuit for a given problem remains an open question. Testing various combinations is challenging due to the infinite possibilities. In this work, a quantum circuit recommendation architecture for classification problems is proposed using database complexity measures. A quantum circuit is defined based on a circuit layer and the number of times this layer is iterated. Fourteen databases of varying dimensions and di fferent numbers of classes were used to evaluate six quantum circuits, each with 1, 2, 3, 4, 8, and 16-layer repetitions. Using data complexity measures from the databases, it was possible to identify the optimal circuit capable of solving all problems with up to 100% accuracy. Furthermore, with a mean absolute error of 0.80 2.17, one determined the appropriate number of layer repetitions, allowing for an error margin of up to three additional layers. Sixteen distinct machine learning models were employed for the selection of quantum circuits, alongside twelve classical regressor models to dynamically define the number of layers. Introduction Quantum computing (QC) leverages principles from quantum mechanics to perform information processing. In addition to exploring intrinsically quantum phenomena such as superposition and entanglement [1], QC becomes even more relevant as the miniaturization of electronic components reaches the atomic level, and the laws of quantum mechanics come into play to operate them.

Because of the global need to increase power production from renewable energy resources, developments in the online monitoring of the associated infrastructure is of interest to reduce operation and maintenance costs. However, challenges exist for data-driven approaches to this problem, such as incomplete or limited histories of labelled damage-state data, operational and environmental variability, or the desire for the quantification of uncertainty to support risk management. This work first introduces a probabilistic regression model for predicting wind-turbine power, which adjusts for wake effects learnt from data. Spatial correlations in the learned model parameters for different tasks (turbines) are then leveraged in a hierarchical Bayesian model (an approach to multi-task learning) to develop a "metamodel", which can be used to make power-predictions which adjust for turbine location - including on previously unobserved turbines not included in the training data. The results show that the metamodel is able to outperform a series of benchmark models, and demonstrates a novel strategy for making efficient use of data for inference in populations of structures, in particular where correlations exist in the variable(s) of interest (such as those from wind-turbine wake-effects).

Birth weight serves as a fundamental indicator of neonatal health, closely linked to both early medical interventions and long-term developmental risks. Traditional predictive models, often constrained by limited feature selection and incomplete datasets, struggle to achieve overlooking complex maternal and fetal interactions in diverse clinical settings. This research explores machine learning to address these limitations, utilizing a structured methodology that integrates advanced imputation strategies, supervised feature selection techniques, and predictive modeling. Given the constraints of the dataset, the research strengthens the role of data preprocessing in improving the model performance. Among the various methodologies explored, tree-based feature selection methods demonstrated superior capability in identifying the most relevant predictors, while ensemble-based regression models proved highly effective in capturing non-linear relationships and complex maternal-fetal interactions within the data. Beyond model performance, the study highlights the clinical significance of key physiological determinants, offering insights into maternal and fetal health factors that influence birth weight, offering insights that extend over statistical modeling. By bridging computational intelligence with perinatal research, this work underscores the transformative role of machine learning in enhancing predictive accuracy, refining risk assessment and informing data-driven decision-making in maternal and neonatal care. Keywords: Birth weight prediction, maternal-fetal health, MICE, BART, Gradient Boosting, neonatal outcomes, Clinipredictive.

Predicting missing segments in partially observed functions is challenging due to infinite-dimensionality, complex dependence within and across observations, and irregular noise. These challenges are further exacerbated by the existence of two distinct sources of variation in functional data, termed amplitude (variation along the $y$-axis) and phase (variation along the $x$-axis). While registration can disentangle them from complete functional data, the process is more difficult for partial observations. Thus, existing methods for functional data prediction often ignore phase variation. Furthermore, they rely on strong parametric assumptions, and require either precise model specifications or computationally intensive techniques, such as bootstrapping, to construct prediction intervals. To tackle this problem, we propose a unified registration and prediction approach for partially observed functions under the conformal prediction framework, which separately focuses on the amplitude and phase components. By leveraging split conformal methods, our approach integrates registration and prediction while ensuring exchangeability through carefully constructed predictor-response pairs. Using a neighborhood smoothing algorithm, the framework produces pointwise prediction bands with finite-sample marginal coverage guarantees under weak assumptions. The method is easy to implement, computationally efficient, and suitable for parallelization. Numerical studies and real-world data examples clearly demonstrate the effectiveness and practical utility of the proposed approach.

Causal discovery aims to infer causal graphs from observational or experimental data. Methods such as the popular PC algorithm are based on conditional independence testing and utilize enabling assumptions, such as the faithfulness assumption, for their inferences. In practice, these assumptions, as well as the functional assumptions inherited from the chosen conditional independence test, are typically taken as a given and not further tested for their validity on the data. In this work, we propose internal coherency scores that allow testing for assumption violations and finite sample errors, whenever detectable without requiring ground truth or further statistical tests. We provide a complete classification of erroneous results, including a distinction between detectable and undetectable errors, and prove that the detectable erroneous results can be measured by our scores. We illustrate our coherency scores on the PC algorithm with simulated and real-world datasets, and envision that testing for internal coherency can become a standard tool in applying constraint-based methods, much like a suite of tests is used to validate the assumptions of classical regression analysis.

Adversarial robustness of machine learning models is critical to ensuring reliable performance under data perturbations. Recent progress has been on point estimators, and this paper considers distributional predictors. First, using the link between exponential families and Bregman divergences, we formulate an adversarial Bregman divergence loss as an adversarial negative log-likelihood. Using the geometric properties of Bregman divergences, we compute the adversarial perturbation for such models in closed-form. Second, under such losses, we introduce \emph{adversarially robust posteriors}, by exploiting the optimization-centric view of generalized Bayesian inference. Third, we derive the \emph{first} rigorous generalization certificates in the context of an adversarial extension of Bayesian linear regression by leveraging the PAC-Bayesian framework. Finally, experiments on real and synthetic datasets demonstrate the superior robustness of the derived adversarially robust posterior over Bayes posterior, and also validate our theoretical guarantees.