Stochastic gradient descent (SGD) has emerged as the quintessential method in a data scientist's toolbox. Much progress has been made in the last two decades toward understanding the iteration complexity of SGD (in expectation and high-probability) in the learning theory and optimization literature. However, using SGD for high-stakes applications requires careful quantification of the associated uncertainty. Toward that end, in this work, we establish high-dimensional Central Limit Theorems (CLTs) for linear functionals of online least-squares SGD iterates under a Gaussian design assumption. Our main result shows that a CLT holds even when the dimensionality is of order exponential in the number of iterations of the online SGD, thereby enabling high-dimensional inference with online SGD. Our proof technique involves leveraging Berry-Esseen bounds developed for martingale difference sequences and carefully evaluating the required moment and quadratic variation terms through recent advances in concentration inequalities for product random matrices. We also provide an online approach for estimating the variance appearing in the CLT (required for constructing confidence intervals in practice) and establish consistency results in the high-dimensional setting.

Growing materials data and data-driven informatics drastically promote the discovery and design of materials. While there are significant advancements in data-driven models, the quality of data resources is less studied despite its huge impact on model performance. In this work, we focus on data bias arising from uneven coverage of materials families in existing knowledge. Observing different diversities among crystal systems in common materials databases, we propose an information entropy-based metric for measuring this bias. To mitigate the bias, we develop an entropy-targeted active learning (ET-AL) framework, which guides the acquisition of new data to improve the diversity of underrepresented crystal systems. We demonstrate the capability of ET-AL for bias mitigation and the resulting improvement in downstream machine learning models. This approach is broadly applicable to data-driven materials discovery, including autonomous data acquisition and dataset trimming to reduce bias, as well as data-driven informatics in other scientific domains.

The essential difficulty of gradient-based bilevel optimization using implicit differentiation is to estimate the inverse Hessian vector product with respect to neural network parameters. This paper proposes to tackle this problem by the Nystrom method and the Woodbury matrix identity, exploiting the low-rankness of the Hessian. Compared to existing methods using iterative approximation, such as conjugate gradient and the Neumann series approximation, the proposed method avoids numerical instability and can be efficiently computed in matrix operations without iterations. As a result, the proposed method works stably in various tasks and is faster than iterative approximations. Throughout experiments including large-scale hyperparameter optimization and meta learning, we demonstrate that the Nystrom method consistently achieves comparable or even superior performance to other approaches. The source code is available from https://github.com/moskomule/hypergrad.

Businesses and customers can gain valuable information from product reviews. The sheer number of reviews often necessitates ranking them based on their potential helpfulness. However, only a few reviews ever receive any helpfulness votes on online marketplaces. Sorting all reviews based on the few existing votes can cause helpful reviews to go unnoticed because of the limited attention span of readers. The problem of review helpfulness prediction is even more important for higher review volumes, and newly written reviews or launched products. In this work we compare the use of RoBERTa and XLM-R language models to predict the helpfulness of online product reviews. The contributions of our work in relation to literature include extensively investigating the efficacy of state-of-the-art language models -- both monolingual and multilingual -- against a robust baseline, taking ranking metrics into account when assessing these approaches, and assessing multilingual models for the first time. We employ the Amazon review dataset for our experiments. According to our study on several product categories, multilingual and monolingual pre-trained language models outperform the baseline that utilizes random forest with handcrafted features as much as 23% in RMSE. Pre-trained language models reduce the need for complex text feature engineering. However, our results suggest that pre-trained multilingual models may not be used for fine-tuning only one language. We assess the performance of language models with and without additional features. Our results show that including additional features like product rating by the reviewer can further help the predictive methods.

We consider the problem of minimizing a non-convex objective while preserving the privacy of the examples in the training data. Building upon the previous variance-reduced algorithm SpiderBoost, we introduce a new framework that utilizes two different kinds of gradient oracles. The first kind of oracles can estimate the gradient of one point, and the second kind of oracles, less precise and more cost-effective, can estimate the gradient difference between two points. SpiderBoost uses the first kind periodically, once every few steps, while our framework proposes using the first oracle whenever the total drift has become large and relies on the second oracle otherwise. This new framework ensures the gradient estimations remain accurate all the time, resulting in improved rates for finding second-order stationary points. Moreover, we address a more challenging task of finding the global minima of a non-convex objective using the exponential mechanism. Our findings indicate that the regularized exponential mechanism can closely match previous empirical and population risk bounds, without requiring smoothness assumptions for algorithms with polynomial running time. Furthermore, by disregarding running time considerations, we show that the exponential mechanism can achieve a good population risk bound and provide a nearly matching lower bound.

In this work, the novel task of detecting and classifying table tennis strokes solely using the ball trajectory has been explored. A single camera setup positioned in the umpire's view has been employed to procure a dataset consisting of six stroke classes executed by four professional table tennis players. Ball tracking using YOLOv4, a traditional object detection model, and TrackNetv2, a temporal heatmap based model, have been implemented on our dataset and their performances have been benchmarked. A mathematical approach developed to extract temporal boundaries of strokes using the ball trajectory data yielded a total of 2023 valid strokes in our dataset, while also detecting services and missed strokes successfully. The temporal convolutional network developed performed stroke recognition on completely unseen data with an accuracy of 87.155%. Several machine learning and deep learning based model architectures have been trained for stroke recognition using ball trajectory input and benchmarked based on their performances. While stroke recognition in the field of table tennis has been extensively explored based on human action recognition using video data focused on the player's actions, the use of ball trajectory data for the same is an unexplored characteristic of the sport. Hence, the motivation behind the work is to demonstrate that meaningful inferences such as stroke detection and recognition can be drawn using minimal input information.

While machine learning models rapidly advance the state-of-the-art on various real-world tasks, out-of-domain (OOD) generalization remains a challenging problem given the vulnerability of these models to spurious correlations. We propose a balanced mini-batch sampling strategy to transform a biased data distribution into a spurious-free balanced distribution, based on the invariance of the underlying causal mechanisms for the data generation process. We argue that the Bayes optimal classifiers trained on such balanced distribution are minimax optimal across a diverse enough environment space. We also provide an identifiability guarantee of the latent variable model of the proposed data generation process, when utilizing enough train environments. Experiments are conducted on DomainBed, demonstrating empirically that our method obtains the best performance across 20 baselines reported on the benchmark.

The inability to guarantee robustness is one of the major obstacles to the application of deep learning models in security-demanding domains. We identify that the most commonly used cross-entropy (CE) loss does not guarantee robust boundary for neural networks. CE loss sharpens the neural network at the decision boundary to achieve a lower loss, rather than pushing the boundary to a more robust position. A robust boundary should be kept in the middle of samples from different classes, thus maximizing the margins from the boundary to the samples. We think this is due to the fact that CE loss has no stationary point. In this paper, we propose a family of new losses, called stationary point (SP) loss, which has at least one stationary point on the correct classification side. We proved that robust boundary can be guaranteed by SP loss without losing much accuracy. With SP loss, larger perturbations are required to generate adversarial examples. We demonstrate that robustness is improved under a variety of adversarial attacks by applying SP loss. Moreover, robust boundary learned by SP loss also performs well on imbalanced datasets.

This paper focuses on multi-enrollment speaker recognition which naturally occurs in the task of online speaker clustering, and studies the properties of different scoring back-ends in this scenario. First, we show that popular cosine scoring suffers from poor score calibration with a varying number of enrollment utterances. Second, we propose a simple replacement for cosine scoring based on an extremely constrained version of probabilistic linear discriminant analysis (PLDA). The proposed model improves over the cosine scoring for multi-enrollment recognition while keeping the same performance in the case of one-to-one comparisons. Finally, we consider an online speaker clustering task where each step naturally involves multi-enrollment recognition. We propose an online clustering algorithm allowing us to take benefits from the PLDA model such as the ability to handle uncertainty and better score calibration. Our experiments demonstrate the effectiveness of the proposed algorithm.

The emergence of Quantum Machine Learning (QML) to enhance traditional classical learning methods has seen various limitations to its realisation. There is therefore an imperative to develop quantum models with unique model hypotheses to attain expressional and computational advantage. In this work we extend the linear quantum support vector machine (QSVM) with kernel function computed through quantum kernel estimation (QKE), to form a decision tree classifier constructed from a decision directed acyclic graph of QSVM nodes - the ensemble of which we term the quantum random forest (QRF). To limit overfitting, we further extend the model to employ a low-rank Nystr\"{o}m approximation to the kernel matrix. We provide generalisation error bounds on the model and theoretical guarantees to limit errors due to finite sampling on the Nystr\"{o}m-QKE strategy. In doing so, we show that we can achieve lower sampling complexity when compared to QKE. We numerically illustrate the effect of varying model hyperparameters and finally demonstrate that the QRF is able obtain superior performance over QSVMs, while also requiring fewer kernel estimations.