Real-world clinical decision making is a complex process that involves balancing the risks and benefits of treatments. Quality-adjusted lifetime is a composite outcome that combines patient quantity and quality of life, making it an attractive outcome in clinical research. We propose methods for constructing optimal treatment length strategies to maximize this outcome. Existing methods for estimating optimal treatment strategies for survival outcomes cannot be applied to a quality-adjusted lifetime due to induced informative censoring. We propose a weighted estimating equation that adjusts for both confounding and informative censoring. We also propose a nonparametric estimator of the mean counterfactual quality-adjusted lifetime survival curve under a given treatment length strategy, where the weights are estimated using an undersmoothed sieve-based estimator. We show that the estimator is asymptotically linear and provide a data-dependent undersmoothing criterion. We apply our method to obtain the optimal time for percutaneous endoscopic gastrostomy insertion in patients with amyotrophic lateral sclerosis.

In the evolving landscape of machine learning (ML), Federated Learning (FL) presents a paradigm shift towards decentralized model training while preserving user data privacy. This paper introduces the concept of ``privacy drift", an innovative framework that parallels the well-known phenomenon of concept drift. While concept drift addresses the variability in model accuracy over time due to changes in the data, privacy drift encapsulates the variation in the leakage of private information as models undergo incremental training. By defining and examining privacy drift, this study aims to unveil the nuanced relationship between the evolution of model performance and the integrity of data privacy. Through rigorous experimentation, we investigate the dynamics of privacy drift in FL systems, focusing on how model updates and data distribution shifts influence the susceptibility of models to privacy attacks, such as membership inference attacks (MIA). Our results highlight a complex interplay between model accuracy and privacy safeguards, revealing that enhancements in model performance can lead to increased privacy risks. We provide empirical evidence from experiments on customized datasets derived from CIFAR-100 (Canadian Institute for Advanced Research, 100 classes), showcasing the impact of data and concept drift on privacy. This work lays the groundwork for future research on privacy-aware machine learning, aiming to achieve a delicate balance between model accuracy and data privacy in decentralized environments.

One key ingredient of image restoration is to define a realistic prior on clean images to complete the missing information in the observation. State-of-the-art restoration methods rely on a neural network to encode this prior. Moreover, typical image distributions are invariant to some set of transformations, such as rotations or flips. However, most deep architectures are not designed to represent an invariant image distribution. Recent works have proposed to overcome this difficulty by including equivariance properties within a Plug-and-Play paradigm. In this work, we propose a unified framework named Equivariant Regularization by Denoising (ERED) based on equivariant denoisers and stochastic optimization. We analyze the convergence of this algorithm and discuss its practical benefit.

Transformer models have continuously expanded into all machine learning domains convertible to the underlying sequence-to-sequence representation, including tabular data. However, while ubiquitous, this representation restricts their extension to the more general case of relational databases. In this paper, we introduce a modular neural message-passing scheme that closely adheres to the formal relational model, enabling direct end-to-end learning of tabular Transformers from database storage systems. We address the challenges of appropriate learning data representation and loading, which are critical in the database setting, and compare our approach against a number of representative models from various related fields across a significantly wide range of datasets. Our results demonstrate a superior performance of this newly proposed class of neural architectures.

Given a budget on total model size, one must decide whether to train a single, large neural network or to combine the predictions of many smaller networks. We study this trade-off for ensembles of random-feature ridge regression models. We prove that when a fixed number of trainable parameters are partitioned among K independently trained models, K = 1 achieves optimal performance, provided the ridge parameter is optimally tuned. We then derive scaling laws which describe how the test risk of an ensemble of regression models decays with its total size. We identify conditions on the kernel and task eigenstructure under which ensembles can achieve near-optimal scaling laws. Training ensembles of deep convolutional neural networks on CIFAR-10 and a transformer architecture on C4, we find that a single large network outperforms any ensemble of networks with the same total number of parameters, provided the weight decay and feature-learning strength are tuned to their optimal values. Ensembling methods are a well-established tool in machine learning for reducing the variance of learned predictors. While traditional ensemble approaches like random forests (Breiman, 2001) and XGBoost (Chen & Guestrin, 2016) combine many weak predictors, the advent of deep neural networks has shifted the state of the art toward training a single large predictor (LeCun et al., 2015). However, deep neural networks still suffer from various sources of variance, such as finite datasets and random initialization (Atanasov et al., 2022; Adlam & Pennington, 2020; Lin & Dobriban, 2021; Atanasov et al., 2024).

Traditional neural networks (multi-layer perceptrons) have become an important tool in data science due to their success across a wide range of tasks. However, their performance is sometimes unsatisfactory, and they often require a large number of parameters, primarily due to their reliance on the linear combination structure. Meanwhile, additive regression has been a popular alternative to linear regression in statistics. In this work, we introduce novel deep neural networks that incorporate the idea of additive regression. Our neural networks share architectural similarities with Kolmogorov-Arnold networks but are based on simpler yet flexible activation and basis functions. Additionally, we introduce several hybrid neural networks that combine this architecture with that of traditional neural networks. We derive their universal approximation properties and demonstrate their effectiveness through simulation studies and a real-data application. The numerical results indicate that our neural networks generally achieve better performance than traditional neural networks while using fewer parameters.

Access to large-scale high-quality healthcare databases is key to accelerate medical research and make insightful discoveries about diseases. However, access to such data is often limited by patient privacy concerns, data sharing restrictions and high costs. To overcome these limitations, synthetic patient data has emerged as an alternative. However, synthetic data generation (SDG) methods typically rely on machine learning (ML) models trained on original data, leading back to the data scarcity problem. We propose an approach to generate synthetic tabular patient data that does not require access to the original data, but only a description of the desired database. We leverage prior medical knowledge and in-context learning capabilities of large language models (LLMs) to generate realistic patient data, even in a low-resource setting. We quantitatively evaluate our approach against state-of-the-art SDG models, using fidelity, privacy, and utility metrics. Our results show that while LLMs may not match the performance of state-of-the-art models trained on the original data, they effectively generate realistic patient data with well-preserved clinical correlations. An ablation study highlights key elements of our prompt contributing to high-quality synthetic patient data generation. This approach, which is easy to use and does not require original data or advanced ML skills, is particularly valuable for quickly generating custom-designed patient data, supporting project implementation and providing educational resources.

A key problem in deep learning and computational neuroscience is relating the geometrical properties of neural representations to task performance. Here, we consider this problem for continuous decoding tasks where neural variability may affect task precision. Using methods from statistical mechanics, we study the average-case learning curves for $\varepsilon$-insensitive Support Vector Regression ($\varepsilon$-SVR) and discuss its capacity as a measure of linear decodability. Our analysis reveals a phase transition in the training error at a critical load, capturing the interplay between the tolerance parameter $\varepsilon$ and neural variability. We uncover a double-descent phenomenon in the generalization error, showing that $\varepsilon$ acts as a regularizer, both suppressing and shifting these peaks. Theoretical predictions are validated both on toy models and deep neural networks, extending the theory of Support Vector Machines to continuous tasks with inherent neural variability.

We propose a novel method for measuring the discrepancy between a set of samples and a desired posterior distribution for Bayesian inference. Classical methods for assessing sample quality like the effective sample size are not appropriate for scalable Bayesian sampling algorithms, such as stochastic gradient Langevin dynamics, that are asymptotically biased. Instead, the gold standard is to use the kernel Stein Discrepancy (KSD), which is itself not scalable given its quadratic cost in the number of samples. The KSD and its faster extensions also typically suffer from the curse-of-dimensionality and can require extensive tuning. To address these limitations, we develop the polynomial Stein discrepancy (PSD) and an associated goodness-of-fit test. While the new test is not fully convergence-determining, we prove that it detects differences in the first r moments in the Bernstein-von Mises limit. We empirically show that the test has higher power than its competitors in several examples, and at a lower computational cost. Finally, we demonstrate that the PSD can assist practitioners to select hyper-parameters of Bayesian sampling algorithms more efficiently than competitors.

In Location-Based Services (LBS), such as food delivery, a fundamental task is segmenting Areas of Interest (AOIs), aiming at partitioning the urban geographical spaces into non-overlapping regions. Traditional AOI segmentation algorithms primarily rely on road networks to partition urban areas. While promising in modeling the geo-semantics, road network-based models overlooked the service-semantic goals (e.g., workload equality) in LBS service. In this paper, we point out that the AOI segmentation problem can be naturally formulated as a Markov Decision Process (MDP), which gradually chooses a nearby AOI for each grid in the current AOI's border. Based on the MDP, we present the first attempt to generalize Deep Reinforcement Learning (DRL) for AOI segmentation, leading to a novel DRL-based framework called DRL4AOI. The DRL4AOI framework introduces different service-semantic goals in a flexible way by treating them as rewards that guide the AOI generation. To evaluate the effectiveness of DRL4AOI, we develop and release an AOI segmentation system. We also present a representative implementation of DRL4AOI - TrajRL4AOI - for AOI segmentation in the logistics service. It introduces a Double Deep Q-learning Network (DDQN) to gradually optimize the AOI generation for two specific semantic goals: i) trajectory modularity, i.e., maximize tightness of the trajectory connections within an AOI and the sparsity of connections between AOIs, ii) matchness with the road network, i.e., maximizing the matchness between AOIs and the road network. Quantitative and qualitative experiments conducted on synthetic and real-world data demonstrate the effectiveness and superiority of our method. The code and system is publicly available at https://github.com/Kogler7/AoiOpt.