Controllable Depth-of-Field (DoF) imaging commonly produces amazing visual effects based on heavy and expensive high-end lenses. However, confronted with the increasing demand for mobile scenarios, it is desirable to achieve a lightweight solution with Minimalist Optical Systems (MOS). This work centers around two major limitations of MOS, i.e., the severe optical aberrations and uncontrollable DoF, for achieving single-lens controllable DoF imaging via computational methods. A Depth-aware Controllable DoF Imaging (DCDI) framework is proposed equipped with All-in-Focus (AiF) aberration correction and monocular depth estimation, where the recovered image and corresponding depth map are utilized to produce imaging results under diverse DoFs of any high-end lens via patch-wise convolution. To address the depth-varying optical degradation, we introduce a Depth-aware Degradation-adaptive Training (DA2T) scheme. At the dataset level, a Depth-aware Aberration MOS (DAMOS) dataset is established based on the simulation of Point Spread Functions (PSFs) under different object distances. Additionally, we design two plug-and-play depth-aware mechanisms to embed depth information into the aberration image recovery for better tackling depth-aware degradation. Furthermore, we propose a storage-efficient Omni-Lens-Field model to represent the 4D PSF library of various lenses. With the predicted depth map, recovered image, and depth-aware PSF map inferred by Omni-Lens-Field, single-lens controllable DoF imaging is achieved. Comprehensive experimental results demonstrate that the proposed framework enhances the recovery performance, and attains impressive single-lens controllable DoF imaging results, providing a seminal baseline for this field. The source code and the established dataset will be publicly available at https://github.com/XiaolongQian/DCDI.

In this paper we present a new machine learning workflow with unsupervised learning techniques to identify domains within atomic force microscopy images obtained from polymer films. The goal of the workflow is to identify the spatial location of the two types of polymer domains with little to no manual intervention and calculate the domain size distributions which in turn can help qualify the phase separated state of the material as macrophase or microphase ordered or disordered domains. We briefly review existing approaches used in other fields, computer vision and signal processing that can be applicable for the above tasks that happen frequently in the field of polymer science and engineering. We then test these approaches from computer vision and signal processing on the AFM image dataset to identify the strengths and limitations of each of these approaches for our first task. For our first domain segmentation task, we found that the workflow using discrete Fourier transform or discrete cosine transform with variance statistics as the feature works the best. The popular ResNet50 deep learning approach from computer vision field exhibited relatively poorer performance in the domain segmentation task for our AFM images as compared to the DFT and DCT based workflows. For the second task, for each of 144 input AFM images, we then used an existing porespy python package to calculate the domain size distribution from the output of that image from DFT based workflow. The information and open source codes we share in this paper can serve as a guide for researchers in the polymer and soft materials fields who need ML modeling and workflows for automated analyses of AFM images from polymer samples that may have crystalline or amorphous domains, sharp or rough interfaces between domains, or micro or macrophase separated domains.

Training machine learning models is an often expensive process, especially in large data settings. Not only is there significant cost in the fitting of individual models, but even more importantly, the best model must be chosen from a set of candidates parameterized by a set of "hyperparameters" indexing the models, and each of these models must be fitted and evaluated in order to make the optimal selection. As a result, model selection, also called hyperparameter tuning, tends to be the most computationally expensive part of the machine learning pipeline. In order to evaluate models, we typically need to set aside unseen "holdout" data to estimate the risk of the model on new samples from the training distribution. When we have an abundance of training samples, such as in the millions or billions, we can afford to set aside a modest holdout set of tens of thousands of examples without compromising model performance.

Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization under suitable high-dimensional settings. However, a fundamental question -- for what kinds of high-dimensional learning problems SGD and its accelerated variants can achieve optimality has yet to be well studied. This paper investigates SGD with two essential components in practice: exponentially decaying step size schedule and momentum. We establish the convergence upper bound for momentum accelerated SGD (ASGD) and propose concrete classes of learning problems under which SGD or ASGD achieves min-max optimal convergence rates. The characterization of the target function is based on standard power-law decays in (functional) linear regression. Our results unveil new insights for understanding the learning bias of SGD: (i) SGD is efficient in learning ``dense'' features where the corresponding weights are subject to an infinity norm constraint; (ii) SGD is efficient for easy problem without suffering from the saturation effect; (iii) momentum can accelerate the convergence rate by order when the learning problem is relatively hard. To our knowledge, this is the first work to clearly identify the optimal boundary of SGD versus ASGD for the problem under mild settings.

One thread of empirical work in social science focuses on decomposing group differences in outcomes into unexplained components and components explained by observable factors. In this paper, we study gender wage decompositions, which require estimating the portion of the gender wage gap explained by career histories of workers. Classical methods for decomposing the wage gap employ simple predictive models of wages which condition on a small set of simple summaries of labor history. The problem is that these predictive models cannot take advantage of the full complexity of a worker's history, and the resulting decompositions thus suffer from omitted variable bias (OVB), where covariates that are correlated with both gender and wages are not included in the model. Here we explore an alternative methodology for wage gap decomposition that employs powerful foundation models, such as large language models, as the predictive engine. Foundation models excel at making accurate predictions from complex, high-dimensional inputs. We use a custom-built foundation model, designed to predict wages from full labor histories, to decompose the gender wage gap. We prove that the way such models are usually trained might still lead to OVB, but develop fine-tuning algorithms that empirically mitigate this issue. Our model captures a richer representation of career history than simple models and predicts wages more accurately. In detail, we first provide a novel set of conditions under which an estimator of the wage gap based on a fine-tuned foundation model is $\sqrt{n}$-consistent. Building on the theory, we then propose methods for fine-tuning foundation models that minimize OVB. Using data from the Panel Study of Income Dynamics, we find that history explains more of the gender wage gap than standard econometric models can measure, and we identify elements of history that are important for reducing OVB.

Federated learning holds great potential for enabling large-scale healthcare research and collaboration across multiple centres while ensuring data privacy and security are not compromised. Although numerous recent studies suggest or utilize federated learning based methods in healthcare, it remains unclear which ones have potential clinical utility. This review paper considers and analyzes the most recent studies up to May 2024 that describe federated learning based methods in healthcare. After a thorough review, we find that the vast majority are not appropriate for clinical use due to their methodological flaws and/or underlying biases which include but are not limited to privacy concerns, generalization issues, and communication costs. As a result, the effectiveness of federated learning in healthcare is significantly compromised. To overcome these challenges, we provide recommendations and promising opportunities that might be implemented to resolve these problems and improve the quality of model development in federated learning with healthcare.

Machine unlearning algorithms aim to efficiently remove data from a model without retraining it from scratch, in order to enforce data privacy, remove corrupted or outdated data, or respect a user's ``right to be forgotten." Certified machine unlearning is a strong theoretical guarantee that quantifies the extent to which data is erased from the model weights. Most prior works in certified unlearning focus on models trained on convex or strongly convex loss functions, which benefit from convenient convergence guarantees and the existence of global minima. For nonconvex objectives, existing algorithms rely on limiting assumptions and expensive computations that hinder practical implementations. In this work, we propose a simple first-order algorithm for unlearning on general nonconvex loss functions which unlearns by ``rewinding" to an earlier step during the learning process and then performs gradient descent on the loss function of the retained data points. Our algorithm is black-box, in that it can be directly applied to models pretrained with vanilla gradient descent with no prior consideration of unlearning. We prove $(\epsilon, \delta)$ certified unlearning and performance guarantees that establish the privacy-utility-complexity tradeoff of our algorithm, with special consideration for nonconvex functions that satisfy the Polyak-Lojasiewicz inequality.

As an example, when the density function of π( | y) is available (up to a constant), Markov chain Monte Carlo (MCMC, Meyn and Tweedie, 2009) methods are popular and generic algorithms widely used. The MCMC algorithms simulate a Markov chain that leaves the target distribution invariant. The drawback is that this often makes the algorithms computationally and statistically inefficient for high-dimensional problems. In this article, we discuss an emerging class of samplers that leverage generative diffusions (see, e.g., Benton et al., 2024; Song et al., 2021), which have empirically worked well for many Bayesian inverse problems. At the heart, the generative diffusions aim to find a continuos-time Markov process (e.g., stochastic differential equation) that bridges the target distribution and a reference measure, so that sampling the target simplifies to sample the reference and the Markov process. In contrast to traditional samplers such as MCMC which use the target's density function to build statistically exact samplers, the generative diffusions use the data to approximate a sampler akin to normalising flow (Chen et al., 2018; Papamakarios et al., 2021) and flow matching (Lipman et al., 2023). This comes with at least three benefits compared to MCMC: 1) scalability of the problem dimension (after the training time), 2) no need to explicitly know the target density function, 3) and the resulting samplers are embarrassingly differentiable (see a use case in Watson et al., 2022). However, the generative diffusion framework (for unconditional sampling) is not immediately applicable to conditional sampling, since we do not have the conditional data samples from π( | y) required to train the generative samplers.

We propose a novel approach to select the best model of the data. Based on the exclusive properties of the nested models, we find the most parsimonious model containing the risk minimizer predictor. We prove the existence of probable approximately correct (PAC) bounds on the difference of the minimum empirical risk of two successive nested models, called successive empirical excess risk (SEER). Based on these bounds, we propose a model order selection method called nested empirical risk (NER). By the sorted NER (S-NER) method to sort the models intelligently, the minimum risk decreases. We construct a test that predicts whether expanding the model decreases the minimum risk or not. With a high probability, the NER and S-NER choose the true model order and the most parsimonious model containing the risk minimizer predictor, respectively. We use S-NER model selection in the linear regression and show that, the S-NER method without any prior information can outperform the accuracy of feature sorting algorithms like orthogonal matching pursuit (OMP) that aided with prior knowledge of the true model order. Also, in the UCR data set, the NER method reduces the complexity of the classification of UCR datasets dramatically, with a negligible loss of accuracy.

Interpretability studies often involve tracing the flow of information through machine learning models to identify specific model components that perform relevant computations for tasks of interest. Prior work quantifies the importance of a model component on a particular task by measuring the impact of performing ablation on that component, or simulating model inference with the component disabled. We propose a new method, optimal ablation (OA), and show that OA-based component importance has theoretical and empirical advantages over measuring importance via other ablation methods. We also show that OA-based component importance can benefit several downstream interpretability tasks, including circuit discovery, localization of factual recall, and latent prediction.