Generalized Low-Rank Update: Model Parameter Bounds for Low-Rank Training Data Modifications

In this study, we have developed an incremental machine learning (ML) method that efficiently obtains the optimal model when a small number of instances or features are added or removed. This problem holds practical importance in model selection, such as cross-validation (CV) and feature selection. Among the class of ML methods known as linear estimators, there exists an efficient model update framework called the low-rank update that can effectively handle changes in a small number of rows and columns within the data matrix. However, for ML methods beyond linear estimators, there is currently no comprehensive framework available to obtain knowledge about the updated solution within a specific computational complexity. In light of this, our study introduces a method called the Generalized Low-Rank Update (GLRU) which extends the low-rank update framework of linear estimators to ML methods formulated as a certain class of regularized empirical risk minimization, including commonly used methods such as SVM and logistic regression. The proposed GLRU method not only expands the range of its applicability but also provides information about the updated solutions with a computational complexity proportional to the amount of dataset changes. To demonstrate the effectiveness of the GLRU method, we conduct experiments showcasing its efficiency in performing cross-validation and feature selection compared to other baseline methods.

Human-In-the-Loop for Bayesian Autonomous Materials Phase Mapping

Autonomous experimentation (AE) combines machine learning and research hardware automation in a closed loop, guiding subsequent experiments toward user goals. As applied to materials research, AE can accelerate materials exploration, reducing time and cost compared to traditional Edisonian studies. Additionally, integrating knowledge from diverse sources including theory, simulations, literature, and domain experts can boost AE performance. Domain experts may provide unique knowledge addressing tasks that are difficult to automate. Here, we present a set of methods for integrating human input into an autonomous materials exploration campaign for composition-structure phase mapping. The methods are demonstrated on x-ray diffraction data collected from a thin film ternary combinatorial library. At any point during the campaign, the user can choose to provide input by indicating regions-of-interest, likely phase regions, and likely phase boundaries based on their prior knowledge (e.g., knowledge of the phase map of a similar material system), along with quantifying their certainty. The human input is integrated by defining a set of probabilistic priors over the phase map. Algorithm output is a probabilistic distribution over potential phase maps, given the data, model, and human input. We demonstrate a significant improvement in phase mapping performance given appropriate human input.

Adaptive Defective Area Identification in Material Surface Using Active Transfer Learning-based Level Set Estimation

In material characterization, identifying defective areas on a material surface is fundamental. The conventional approach involves measuring the relevant physical properties point-by-point at the predetermined mesh grid points on the surface and determining the area at which the property does not reach the desired level. To identify defective areas more efficiently, we propose adaptive mapping methods in which measurement resources are used preferentially to detect the boundaries of defective areas. We interpret this problem as an active-learning (AL) of the level set estimation (LSE) problem. The goal of AL-based LSE is to determine the level set of the physical property function defined on the surface with as small number of measurements as possible. Furthermore, to handle the situations in which materials with similar specifications are repeatedly produced, we introduce a transfer learning approach so that the information of previously produced materials can be effectively utilized. As a proof-of-concept, we applied the proposed methods to the red-zone estimation problem of silicon wafers and demonstrated that we could identify the defective areas with significantly lower measurement costs than those of conventional methods.

Latent Reconstruction-Aware Variational Autoencoder

Variational Autoencoders (VAEs) have become increasingly popular in recent years due to their ability to generate new objects such as images and texts from a given dataset. This ability has led to a wide range of applications. While standard tasks often require sampling from high-density regions in the latent space, there are also tasks that require sampling from low-density regions, such as Morphing and Latent Space Bayesian Optimization (LS-BO). These tasks are becoming increasingly important in fields such as de novo molecular design, where the ability to generate diverse and high-quality chemical compounds is essential. In this study, we investigate the issue of low-quality objects generated from low-density regions in VAEs. To address this problem, we propose a new VAE model, the Latent Reconstruction-Aware VAE (LRA-VAE). The LRA-VAE model takes into account what we refer to as the Latent Reconstruction Error (LRE) of the latent variables. We evaluate our proposal using Morphing and LS-BO experiments, and show that LRA-VAE can improve the quality of generated objects over the other approaches, making it a promising solution for various generation tasks that involve sampling from low-density regions.

Distributionally Robust Multi-objective Bayesian Optimization under Uncertain Environments

In this study, we address the problem of optimizing multi-output black-box functions under uncertain environments. We formulate this problem as the estimation of the uncertain Pareto-frontier (PF) of a multi-output Bayesian surrogate model with two types of variables: design variables and environmental variables. We consider this problem within the context of Bayesian optimization (BO) under uncertain environments, where the design variables are controllable, whereas the environmental variables are assumed to be random and not controllable. The challenge of this problem is to robustly estimate the PF when the distribution of the environmental variables is unknown, that is, to estimate the PF when the environmental variables are generated from the worst possible distribution. We propose a method for solving the BO problem by appropriately incorporating the uncertainties of the environmental variables and their probability distribution. We demonstrate that the proposed method can find an arbitrarily accurate PF with high probability in a finite number of iterations. We also evaluate the performance of the proposed method through numerical experiments.

Valid P-Value for Deep Learning-Driven Salient Region

Various saliency map methods have been proposed to interpret and explain predictions of deep learning models. Saliency maps allow us to interpret which parts of the input signals have a strong influence on the prediction results. However, since a saliency map is obtained by complex computations in deep learning models, it is often difficult to know how reliable the saliency map itself is. In this study, we propose a method to quantify the reliability of a salient region in the form of p-values. Our idea is to consider a salient region as a selected hypothesis by the trained deep learning model and employ the selective inference framework. The proposed method can provably control the probability of false positive detections of salient regions. We demonstrate the validity of the proposed method through numerical examples in synthetic and real datasets. Furthermore, we develop a Keras-based framework for conducting the proposed selective inference for a wide class of CNNs without additional implementation cost.

Transformer-based Personalized Attention Mechanism (PersAM) for Medical Images with Clinical Records

In medical image diagnosis, identifying the attention region, i.e., the region of interest for which the diagnosis is made, is an important task. Various methods have been developed to automatically identify target regions from given medical images. However, in actual medical practice, the diagnosis is made based not only on the images but also on a variety of clinical records. This means that pathologists examine medical images with some prior knowledge of the patients and that the attention regions may change depending on the clinical records. In this study, we propose a method called the Personalized Attention Mechanism (PersAM), by which the attention regions in medical images are adaptively changed according to the clinical records. The primary idea of the PersAM method is to encode the relationships between the medical images and clinical records using a variant of Transformer architecture. To demonstrate the effectiveness of the PersAM method, we applied it to a large-scale digital pathology problem of identifying the subtypes of 842 malignant lymphoma patients based on their gigapixel whole slide images and clinical records.

A Confidence Machine for Sparse High-Order Interaction Model

In predictive modeling for high-stake decision-making, predictors must be not only accurate but also reliable. Conformal prediction (CP) is a promising approach for obtaining the confidence of prediction results with fewer theoretical assumptions. To obtain the confidence set by so-called full-CP, we need to refit the predictor for all possible values of prediction results, which is only possible for simple predictors. For complex predictors such as random forests (RFs) or neural networks (NNs), split-CP is often employed where the data is split into two parts: one part for fitting and another to compute the confidence set. Unfortunately, because of the reduced sample size, split-CP is inferior to full-CP both in fitting as well as confidence set computation. In this paper, we develop a full-CP of sparse high-order interaction model (SHIM), which is sufficiently flexible as it can take into account high-order interactions among variables. We resolve the computational challenge for full-CP of SHIM by introducing a novel approach called homotopy mining. Through numerical experiments, we demonstrate that SHIM is as accurate as complex predictors such as RF and NN and enjoys the superior statistical power of full-CP.

A Low-Cost Robot Science Kit for Education with Symbolic Regression for Hypothesis Discovery and Validation

The next generation of physical science involves robot scientists - autonomous physical science systems capable of experimental design, execution, and analysis in a closed loop. Such systems have shown real-world success for scientific exploration and discovery, including the first discovery of a best-in-class material. To build and use these systems, the next generation workforce requires expertise in diverse areas including ML, control systems, measurement science, materials synthesis, decision theory, among others. However, education is lagging. Educators need a low-cost, easy-to-use platform to teach the required skills. Industry can also use such a platform for developing and evaluating autonomous physical science methodologies. We present the next generation in science education, a kit for building a low-cost autonomous scientist. The kit was used during two courses at the University of Maryland to teach undergraduate and graduate students autonomous physical science. We discuss its use in the course and its greater capability to teach the dual tasks of autonomous model exploration, optimization, and determination, with an example of autonomous experimental "discovery" of the Henderson-Hasselbalch equation.

Benchmarking Active Learning Strategies for Materials Optimization and Discovery

Autonomous physical science is revolutionizing materials science. In these systems, machine learning controls experiment design, execution, and analysis in a closed loop. Active learning, the machine learning field of optimal experiment design, selects each subsequent experiment to maximize knowledge toward the user goal. Autonomous system performance can be further improved with implementation of scientific machine learning, also known as inductive bias-engineered artificial intelligence, which folds prior knowledge of physical laws (e.g., Gibbs phase rule) into the algorithm. As the number, diversity, and uses for active learning strategies grow, there is an associated growing necessity for real-world reference datasets to benchmark strategies. We present a reference dataset and demonstrate its use to benchmark active learning strategies in the form of various acquisition functions. Active learning strategies are used to rapidly identify materials with optimal physical properties within a ternary materials system. The data is from an actual Fe-Co-Ni thin-film library and includes previously acquired experimental data for materials compositions, X-ray diffraction patterns, and two functional properties of magnetic coercivity and the Kerr rotation. Popular active learning methods along with a recent scientific active learning method are benchmarked for their materials optimization performance. We discuss the relationship between algorithm performance, materials search space complexity, and the incorporation of prior knowledge.