We propose a novel family of decision-aware surrogate losses, called Perturbation Gradient (PG) losses, for the predict-then-optimize framework. These losses directly approximate the downstream decision loss and can be optimized using off-the-shelf gradient-based methods. Importantly, unlike existing surrogate losses, the approximation error of our PG losses vanishes as the number of samples grows. This implies that optimizing our surrogate loss yields a best-in-class policy asymptotically, even in misspecified settings. This is the first such result in misspecified settings and we provide numerical evidence confirming our PG losses substantively outperform existing proposals when the underlying model is misspecified and the noise is not centrally symmetric. Insofar as misspecification is commonplace in practice -- especially when we might prefer a simpler, more interpretable model -- PG losses offer a novel, theoretically justified, method for computationally tractable decision-aware learning.

Lexicase selection has been shown to provide advantages over other selection algorithms in several areas of evolutionary computation and machine learning. In its standard form, lexicase selection filters a population or other collection based on randomly ordered training cases that are considered one at a time. This iterated filtering process can be time-consuming, particularly in settings with large numbers of training cases. In this paper, we propose a new method that is nearly equivalent to lexicase selection in terms of the individuals that it selects, but which does so significantly more quickly. The new method, called DALex (for Diversely Aggregated Lexicase), selects the best individual with respect to a weighted sum of training case errors, where the weights are randomly sampled. This allows us to formulate the core computation required for selection as matrix multiplication instead of recursive loops of comparisons, which in turn allows us to take advantage of optimized and parallel algorithms designed for matrix multiplication for speedup. Furthermore, we show that we can interpolate between the behavior of lexicase selection and its "relaxed" variants, such as epsilon or batch lexicase selection, by adjusting a single hyperparameter, named "particularity pressure," which represents the importance granted to each individual training case. Results on program synthesis, deep learning, symbolic regression, and learning classifier systems demonstrate that DALex achieves significant speedups over lexicase selection and its relaxed variants while maintaining almost identical problem-solving performance. Under a fixed computational budget, these savings free up resources that can be directed towards increasing population size or the number of generations, enabling the potential for solving more difficult problems.

This work proposes $\mu$GUIDE: a general Bayesian framework to estimate posterior distributions of tissue microstructure parameters from any given biophysical model or MRI signal representation, with exemplar demonstration in diffusion-weighted MRI. Harnessing a new deep learning architecture for automatic signal feature selection combined with simulation-based inference and efficient sampling of the posterior distributions, $\mu$GUIDE bypasses the high computational and time cost of conventional Bayesian approaches and does not rely on acquisition constraints to define model-specific summary statistics. The obtained posterior distributions allow to highlight degeneracies present in the model definition and quantify the uncertainty and ambiguity of the estimated parameters.

In clinical practice, one often needs to identify whether a patient is at high risk of adverse outcomes after some key medical event; for example, the short-term risk of death after an admission for heart failure. This task is challenging due to the complexity, variability, and heterogeneity of longitudinal medical data, especially for individuals suffering from chronic diseases like heart failure. In this paper, we introduce Event-Based Contrastive Learning (EBCL), a method for learning embeddings of heterogeneous patient data that preserves temporal information before and after key index events. We demonstrate that EBCL produces models that yield better fine-tuning performance on critical downstream tasks for a heart failure cohort, including 30-day readmission, 1-year mortality, and 1-week length of stay, relative to other pretraining methods. Our findings also reveal that EBCL pretraining alone can effectively cluster patients with similar mortality and readmission risks, offering valuable insights for clinical decision-making and personalized patient care.

Robustness to distribution shift has become a growing concern for text and image models as they transition from research subjects to deployment in the real world. However, high-quality benchmarks for distribution shift in tabular machine learning tasks are still lacking despite the widespread real-world use of tabular data and differences in the models used for tabular data in comparison to text and images. As a consequence, the robustness of tabular models to distribution shift is poorly understood. To address this issue, we introduce TableShift, a distribution shift benchmark for tabular data. TableShift contains 15 binary classification tasks in total, each with an associated shift, and includes a diverse set of data sources, prediction targets, and distribution shifts. The benchmark covers domains including finance, education, public policy, healthcare, and civic participation, and is accessible using only a few lines of Python code via the TableShift API. We conduct a large-scale study comparing several state-of-the-art tabular data models alongside robust learning and domain generalization methods on the benchmark tasks. Our study demonstrates (1) a linear trend between in-distribution (ID) and out-of-distribution (OOD) accuracy; (2) domain robustness methods can reduce shift gaps but at the cost of reduced ID accuracy; (3) a strong relationship between shift gap (difference between ID and OOD performance) and shifts in the label distribution. The benchmark data, Python package, model implementations, and more information about TableShift are available at https://github.com/mlfoundations/tableshift and https://tableshift.org .

We present a comprehensive examination of learning methodologies employed for the structural identification of dynamical systems. These techniques are designed to elucidate emergent phenomena within intricate systems of interacting agents. Our approach not only ensures theoretical convergence guarantees but also exhibits computational efficiency when handling high-dimensional observational data. The methods adeptly reconstruct both first- and second-order dynamical systems, accommodating observation and stochastic noise, intricate interaction rules, absent interaction features, and real-world observations in agent systems. The foundational aspect of our learning methodologies resides in the formulation of tailored loss functions using the variational inverse problem approach, inherently equipping our methods with dimension reduction capabilities.

Vertical federated learning has garnered significant attention as it allows clients to train machine learning models collaboratively without sharing local data, which protects the client's local private data. However, existing VFL methods face challenges when dealing with heterogeneous local models among participants, which affects optimization convergence and generalization. To address this challenge, this paper proposes a novel approach called Vertical federated learning for training multiple Heterogeneous models (VFedMH). VFedMH focuses on aggregating the local embeddings of each participant's knowledge during forward propagation. To protect the participants' local embedding values, we propose an embedding protection method based on lightweight blinding factors. In particular, participants obtain local embedding using local heterogeneous models. Then the passive party, who owns only features of the sample, injects the blinding factor into the local embedding and sends it to the active party. The active party aggregates local embeddings to obtain global knowledge embeddings and sends them to passive parties. The passive parties then utilize the global embeddings to propagate forward on their local heterogeneous networks. However, the passive party does not own the sample labels, so the local model gradient cannot be calculated locally. To overcome this limitation, the active party assists the passive party in computing its local heterogeneous model gradients. Then, each participant trains their local model using the heterogeneous model gradients. The objective is to minimize the loss value of their respective local heterogeneous models. Extensive experiments are conducted to demonstrate that VFedMH can simultaneously train multiple heterogeneous models with heterogeneous optimization and outperform some recent methods in model performance.

Bayesian Optimization (BO) is typically used to optimize an unknown function $f$ that is noisy and costly to evaluate, by exploiting an acquisition function that must be maximized at each optimization step. Even if provably asymptotically optimal BO algorithms are efficient at optimizing low-dimensional functions, scaling them to high-dimensional spaces remains an open problem, often tackled by assuming an additive structure for $f$. By doing so, BO algorithms typically introduce additional restrictive assumptions on the additive structure that reduce their applicability domain. This paper contains two main contributions: (i) we relax the restrictive assumptions on the additive structure of $f$ without weakening the maximization guarantees of the acquisition function, and (ii) we address the over-exploration problem for decentralized BO algorithms. To these ends, we propose DuMBO, an asymptotically optimal decentralized BO algorithm that achieves very competitive performance against state-of-the-art BO algorithms, especially when the additive structure of $f$ comprises high-dimensional factors.

Most commonly used $f$-divergences of measures, e.g., the Kullback-Leibler divergence, are subject to limitations regarding the support of the involved measures. A remedy consists of regularizing the $f$-divergence by a squared maximum mean discrepancy (MMD) associated with a characteristic kernel $K$. In this paper, we use the so-called kernel mean embedding to show that the corresponding regularization can be rewritten as the Moreau envelope of some function in the reproducing kernel Hilbert space associated with $K$. Then, we exploit well-known results on Moreau envelopes in Hilbert spaces to prove properties of the MMD-regularized $f$-divergences and, in particular, their gradients. Subsequently, we use our findings to analyze Wasserstein gradient flows of MMD-regularized $f$-divergences. Finally, we consider Wasserstein gradient flows starting from empirical measures and provide proof-of-the-concept numerical examples with Tsallis-$\alpha$ divergences.

Knowledge of the effect of interventions, called the treatment effect, is paramount for decision-making. Approaches to estimating this treatment effect, e.g. by using Conditional Average Treatment Effect (CATE) estimators, often only provide a point estimate of this treatment effect, while additional uncertainty quantification is frequently desired instead. Therefore, we present a novel method, the Conformal Monte Carlo (CMC) meta-learners, leveraging conformal predictive systems, Monte Carlo sampling, and CATE meta-learners, to instead produce a predictive distribution usable in individualized decision-making. Furthermore, we show how specific assumptions on the noise distribution of the outcome heavily affect these uncertainty predictions. Nonetheless, the CMC framework shows strong experimental coverage while retaining small interval widths to provide estimates of the true individual treatment effect.