Quantifying variable importance is essential for answering high-stakes questions in fields like genetics, public policy, and medicine. Current methods generally calculate variable importance for a given model trained on a given dataset. However, for a given dataset, there may be many models that explain the target outcome equally well; without accounting for all possible explanations, different researchers may arrive at many conflicting yet equally valid conclusions given the same data. Additionally, even when accounting for all possible explanations for a given dataset, these insights may not generalize because not all good explanations are stable across reasonable data perturbations. We propose a new variable importance framework that quantifies the importance of a variable across the set of all good models and is stable across the data distribution. Our framework is extremely flexible and can be integrated with most existing model classes and global variable importance metrics. We demonstrate through experiments that our framework recovers variable importance rankings for complex simulation setups where other methods fail. Further, we show that our framework accurately estimates the true importance of a variable for the underlying data distribution. We provide theoretical guarantees on the consistency and finite sample error rates for our estimator. Finally, we demonstrate its utility with a real-world case study exploring which genes are important for predicting HIV load in persons with HIV, highlighting an important gene that has not previously been studied in connection with HIV. Code is available at https://github.com/jdonnelly36/Rashomon_Importance_Distribution.

We propose a conditional stochastic interpolation (CSI) approach to learning conditional distributions. CSI learns probability flow equations or stochastic differential equations that transport a reference distribution to the target conditional distribution. This is achieved by first learning the drift function and the conditional score function based on conditional stochastic interpolation, which are then used to construct a deterministic process governed by an ordinary differential equation or a diffusion process for conditional sampling. In our proposed CSI model, we incorporate an adaptive diffusion term to address the instability issues arising during the training process. We provide explicit forms of the conditional score function and the drift function in terms of conditional expectations under mild conditions, which naturally lead to an nonparametric regression approach to estimating these functions. Furthermore, we establish non-asymptotic error bounds for learning the target conditional distribution via conditional stochastic interpolation in terms of KL divergence, taking into account the neural network approximation error. We illustrate the application of CSI on image generation using a benchmark image dataset.

Numerous studies demonstrate the importance of self-regulation during learning by problem-solving. Recent work in learning analytics has largely examined students' use of SRL concerning overall learning gains. Limited research has related SRL to in-the-moment performance differences among learners. The present study investigates SRL behaviors in relationship to learners' moment-by-moment performance while working with intelligent tutoring systems for stoichiometry chemistry. We demonstrate the feasibility of labeling SRL behaviors based on AI-generated think-aloud transcripts, identifying the presence or absence of four SRL categories (processing information, planning, enacting, and realizing errors) in each utterance. Using the SRL codes, we conducted regression analyses to examine how the use of SRL in terms of presence, frequency, cyclical characteristics, and recency relate to student performance on subsequent steps in multi-step problems. A model considering students' SRL cycle characteristics outperformed a model only using in-the-moment SRL assessment. In line with theoretical predictions, students' actions during earlier, process-heavy stages of SRL cycles exhibited lower moment-by-moment correctness during problem-solving than later SRL cycle stages. We discuss system re-design opportunities to add SRL support during stages of processing and paths forward for using machine learning to speed research depending on the assessment of SRL based on transcription of think-aloud data.

We propose a new family of label randomizers for training regression models under the constraint of label differential privacy (DP). In particular, we leverage the trade-offs between bias and variance to construct better label randomizers depending on a privately estimated prior distribution over the labels. We demonstrate that these randomizers achieve state-of-the-art privacy-utility trade-offs on several datasets, highlighting the importance of reducing bias when training neural networks with label DP. We also provide theoretical results shedding light on the structural properties of the optimal unbiased randomizers.

Foundation models are a current focus of attention in both industry and academia. While they have shown their capabilities in a variety of tasks, in-depth research is required to determine their robustness to distribution shift when used as a basis for supervised machine learning. This is especially important in the context of clinical data, with particular limitations related to data accessibility, lack of pretraining materials, and limited availability of high-quality annotations. In this work, we examine the stability of models based on representations from foundation models under distribution shift. We focus on confounding by provenance, a form of distribution shift that emerges in the context of multi-institutional datasets when there are differences in source-specific language use and class distributions. Using a sampling strategy that synthetically induces varying degrees of distribution shift, we evaluate the extent to which representations from foundation models result in predictions that are inherently robust to confounding by provenance. Additionally, we examine the effectiveness of a straightforward confounding adjustment method inspired by Pearl's conception of backdoor adjustment. Results indicate that while foundation models do show some out-of-the-box robustness to confounding-by-provenance related distribution shifts, this can be considerably improved through adjustment. These findings suggest a need for deliberate adjustment of predictive models using representations from foundation models in the context of source-specific distributional differences.

Molecular abundances in protoplanetary disks are highly sensitive to the local physical conditions, including gas temperature, gas density, radiation field, and dust properties. Often multiple factors are intertwined, impacting the abundances of both simple and complex species. We present a new approach to understanding these chemical and physical interdependencies using machine learning. Specifically we explore the case of CO modeled under the conditions of a generic disk and build an explanatory regression model to study the dependence of CO spatial density on the gas density, gas temperature, cosmic ray ionization rate, X-ray ionization rate, and UV flux. Our findings indicate that combinations of parameters play a surprisingly powerful role in regulating CO compared to any singular physical parameter. Moreover, in general, we find the conditions in the disk are destructive toward CO. CO depletion is further enhanced in an increased cosmic ray environment and in disks with higher initial C/O ratios. These dependencies uncovered by our new approach are consistent with previous studies, which are more modeling intensive and computationally expensive. Our work thus shows that machine learning can be a powerful tool not only for creating efficient predictive models, but also for enabling a deeper understanding of complex chemical processes.

Yahoo's native advertising (also known as Gemini native) serves billions of ad impressions daily, reaching a yearly run-rate of many hundred of millions USD. Driving the Gemini native models that are used to predict both click probability (pCTR) and conversion probability (pCONV) is OFFSET - a feature enhanced collaborative-filtering (CF) based event prediction algorithm. \offset is a one-pass algorithm that updates its model for every new batch of logged data using a stochastic gradient descent (SGD) based approach. Since OFFSET represents its users by their features (i.e., user-less model) due to sparsity issues, rule based hard frequency capping (HFC) is used to control the number of times a certain user views a certain ad. Moreover, related statistics reveal that user ad fatigue results in a dramatic drop in click through rate (CTR). Therefore, to improve click prediction accuracy, we propose a soft frequency capping (SFC) approach, where the frequency feature is incorporated into the OFFSET model as a user-ad feature and its weight vector is learned via logistic regression as part of OFFSET training. Online evaluation of the soft frequency capping algorithm via bucket testing showed a significant 7.3% revenue lift. Since then, the frequency feature enhanced model has been pushed to production serving all traffic, and is generating a hefty revenue lift for Yahoo Gemini native. We also report related statistics that reveal, among other things, that while users' gender does not affect ad fatigue, the latter seems to increase with users' age.

Gradient boosting performs exceptionally in most prediction problems and scales well to large datasets. In this paper we prove that a ``lassoed'' gradient boosted tree algorithm with early stopping achieves faster than $n^{-1/4}$ L2 convergence in the large nonparametric space of cadlag functions of bounded sectional variation. This rate is remarkable because it does not depend on the dimension, sparsity, or smoothness. We use simulation and real data to confirm our theory and demonstrate empirical performance and scalability on par with standard boosting. Our convergence proofs are based on a novel, general theorem on early stopping with empirical loss minimizers of nested Donsker classes.

In the field of surrogate modeling, polynomial chaos expansion (PCE) allows practitioners to construct inexpensive yet accurate surrogates to be used in place of the expensive forward model simulations. For black-box simulations, non-intrusive PCE allows the construction of these surrogates using a set of simulation response evaluations. In this context, the PCE coefficients can be obtained using linear regression, which is also known as point collocation or stochastic response surfaces. Regression exhibits better scalability and can handle noisy function evaluations in contrast to other non-intrusive approaches, such as projection. However, since over-sampling is generally advisable for the linear regression approach, the simulation requirements become prohibitive for expensive forward models. We propose to leverage transfer learning whereby knowledge gained through similar PCE surrogate construction tasks (source domains) is transferred to a new surrogate-construction task (target domain) which has a limited number of forward model simulations (training data). The proposed transfer learning strategy determines how much, if any, information to transfer using new techniques inspired by Bayesian modeling and data assimilation. The strategy is scrutinized using numerical investigations and applied to an engineering problem from the oil and gas industry.

Data shift is a phenomenon present in many real-world applications, and while there are multiple methods attempting to detect shifts, the task of localizing and correcting the features originating such shifts has not been studied in depth. Feature shifts can occur in many datasets, including in multi-sensor data, where some sensors are malfunctioning, or in tabular and structured data, including biomedical, financial, and survey data, where faulty standardization and data processing pipelines can lead to erroneous features. In this work, we explore using the principles of adversarial learning, where the information from several discriminators trained to distinguish between two distributions is used to both detect the corrupted features and fix them in order to remove the distribution shift between datasets. We show that mainstream supervised classifiers, such as random forest or gradient boosting trees, combined with simple iterative heuristics, can localize and correct feature shifts, outperforming current statistical and neural network-based techniques.