Industrial prognostic aims to predict the failure time of machines by utilizing their degradation signals. This is typically achieved by establishing a statistical learning model that maps the degradation signals of machines to their time-to-failure (TTFs) [1, 2]. Similar to that of many other statistical learning models, the implementation of prognostic models usually consists of two steps: model training and real-time monitoring (also known as model testing or deployment). Model training focuses on using a historical dataset that comprises the degradation signals and TTFs of some failed machines to estimate the parameters of the prognostic model; real-time monitoring feeds the real-time degradation signals from a partially degraded onsite machine into the prognostic model trained earlier to predict its TTF or TTF distribution. Most existing prognostic models assume that a historical dataset from a decent number of failed machines is available for model training [3, 4, 5, 6, 7]. In reality, however, the amount of historical data owned by a single organization (e.g., a company, a university lab, a factory, etc.) might be small or not large enough to train a reliable prognostic model.

Compared to "black-box" models, like random forests and deep neural networks, explainable boosting machines (EBMs) are considered "glass-box" models that can be competitively accurate while also maintaining a higher degree of transparency and explainability. However, EBMs become readily less transparent and harder to interpret in high-dimensional settings with many predictor variables; they also become more difficult to use in production due to increases in scoring time. We propose a simple solution based on the least absolute shrinkage and selection operator (LASSO) that can help introduce sparsity by reweighting the individual model terms and removing the less relevant ones, thereby allowing these models to maintain their transparency and relatively fast scoring times in higher-dimensional settings. In short, post-processing a fitted EBM with many (i.e., possibly hundreds or thousands) of terms using the LASSO can help reduce the model's complexity and drastically improve scoring time. We illustrate the basic idea using two real-world examples with code.

Machine learning is currently undergoing an explosion in capability, popularity, and sophistication. However, one of the major barriers to widespread acceptance of machine learning (ML) is trustworthiness: most ML models operate as black boxes, their inner workings opaque and mysterious, and it can be difficult to trust their conclusions without understanding how those conclusions are reached. Explainability is therefore a key aspect of improving trustworthiness: the ability to better understand, interpret, and anticipate the behaviour of ML models. To this end, we propose SMILE, a new method that builds on previous approaches by making use of statistical distance measures to improve explainability while remaining applicable to a wide range of input data domains.

Quadratic programming is a ubiquitous prototype in convex programming. Many combinatorial optimizations on graphs and machine learning problems can be formulated as quadratic programming; for example, Support Vector Machines (SVMs). Linear and kernel SVMs have been among the most popular models in machine learning over the past three decades, prior to the deep learning era. Generally, a quadratic program has an input size of $\Theta(n^2)$, where $n$ is the number of variables. Assuming the Strong Exponential Time Hypothesis ($\textsf{SETH}$), it is known that no $O(n^{2-o(1)})$ algorithm exists (Backurs, Indyk, and Schmidt, NIPS'17). However, problems such as SVMs usually feature much smaller input sizes: one is given $n$ data points, each of dimension $d$, with $d \ll n$. Furthermore, SVMs are variants with only $O(1)$ linear constraints. This suggests that faster algorithms are feasible, provided the program exhibits certain underlying structures. In this work, we design the first nearly-linear time algorithm for solving quadratic programs whenever the quadratic objective has small treewidth or admits a low-rank factorization, and the number of linear constraints is small. Consequently, we obtain a variety of results for SVMs: * For linear SVM, where the quadratic constraint matrix has treewidth $\tau$, we can solve the corresponding program in time $\widetilde O(n\tau^{(\omega+1)/2}\log(1/\epsilon))$; * For linear SVM, where the quadratic constraint matrix admits a low-rank factorization of rank-$k$, we can solve the corresponding program in time $\widetilde O(nk^{(\omega+1)/2}\log(1/\epsilon))$; * For Gaussian kernel SVM, where the data dimension $d = \Theta(\log n)$ and the squared dataset radius is small, we can solve it in time $O(n^{1+o(1)}\log(1/\epsilon))$. We also prove that when the squared dataset radius is large, then $\Omega(n^{2-o(1)})$ time is required.

We present a methodology for using unlabeled data to design semi supervised learning (SSL) methods that improve the prediction performance of supervised learning for regression tasks. The main idea is to design different mechanisms for integrating the unlabeled data, and include in each of them a mixing parameter $\alpha$, controlling the weight given to the unlabeled data. Focusing on Generalized Linear Models (GLM) and linear interpolators classes of models, we analyze the characteristics of different mixing mechanisms, and prove that in all cases, it is invariably beneficial to integrate the unlabeled data with some nonzero mixing ratio $\alpha>0$, in terms of predictive performance. Moreover, we provide a rigorous framework to estimate the best mixing ratio $\alpha^*$ where mixed SSL delivers the best predictive performance, while using the labeled and unlabeled data on hand. The effectiveness of our methodology in delivering substantial improvement compared to the standard supervised models, in a variety of settings, is demonstrated empirically through extensive simulation, in a manner that supports the theoretical analysis. We also demonstrate the applicability of our methodology (with some intuitive modifications) to improve more complex models, such as deep neural networks, in real-world regression tasks.

Moreover, models and develop generalization bounds for having generalization bounds not only contributes to the theoretical models based on the Wasserstein distance and understanding of GANs themselves, but also to the the total variation distance. Our first result on understanding of the structure of real-life datasets, if those the Wasserstein distance assumes the instance can be provably approximated by GAN-generated data. In space is bounded, while our second result takes addition, given that GANs are used for data-augmentation advantage of dimensionality reduction. Our results in fields such as medical image classification (see e.g. Frid-naturally apply to Wasserstein GANs and Adar et al., 2018), theoretical guarantees can substantiate Energy-Based GANs, and our bounds provide the soundness of such applications.

Existing generalization bounds fail to explain crucial factors that drive the generalization of modern neural networks. Since such bounds often hold uniformly over all parameters, they suffer from over-parametrization and fail to account for the strong inductive bias of initialization and stochastic gradient descent. As an alternative, we propose a novel optimal transport interpretation of the generalization problem. This allows us to derive instance-dependent generalization bounds that depend on the local Lipschitz regularity of the learned prediction function in the data space. Therefore, our bounds are agnostic to the parametrization of the model and work well when the number of training samples is much smaller than the number of parameters. With small modifications, our approach yields accelerated rates for data on low-dimensional manifolds and guarantees under distribution shifts. We empirically analyze our generalization bounds for neural networks, showing that the bound values are meaningful and capture the effect of popular regularization methods during training.

Deep learning has shown impressive results in a variety of time series forecasting tasks, where modeling the conditional distribution of the future given the past is the essence. However, when this conditional distribution is non-stationary, it poses challenges for these models to learn consistently and to predict accurately. In this work, we propose a new method to model non-stationary conditional distributions over time by clearly decoupling stationary conditional distribution modeling from non-stationary dynamics modeling. Our method is based on a Bayesian dynamic model that can adapt to conditional distribution changes and a deep conditional distribution model that handles multivariate time series using a factorized output space. Our experimental results on synthetic and real-world datasets show that our model can adapt to non-stationary time series better than state-of-the-art deep learning solutions.

Segmentation has emerged as a fundamental field of computer vision and natural language processing, which assigns a label to every pixel/feature to extract regions of interest from an image/text. To evaluate the performance of segmentation, the Dice and IoU metrics are used to measure the degree of overlap between the ground truth and the predicted segmentation. In this paper, we establish a theoretical foundation of segmentation with respect to the Dice/IoU metrics, including the Bayes rule and Dice-/IoU-calibration, analogous to classification-calibration or Fisher consistency in classification. We prove that the existing thresholding-based framework with most operating losses are not consistent with respect to the Dice/IoU metrics, and thus may lead to a suboptimal solution. To address this pitfall, we propose a novel consistent ranking-based framework, namely RankDice/RankIoU, inspired by plug-in rules of the Bayes segmentation rule. Three numerical algorithms with GPU parallel execution are developed to implement the proposed framework in large-scale and high-dimensional segmentation. We study statistical properties of the proposed framework. We show it is Dice-/IoU-calibrated, and its excess risk bounds and the rate of convergence are also provided. The numerical effectiveness of RankDice/mRankDice is demonstrated in various simulated examples and Fine-annotated CityScapes, Pascal VOC and Kvasir-SEG datasets with state-of-the-art deep learning architectures.

Machine learning (ML) may be oblivious to human bias but it is not immune to its perpetuation. Marginalisation and iniquitous group representation are often traceable in the very data used for training, and may be reflected or even enhanced by the learning models. In the present work, we aim at clarifying the role played by data geometry in the emergence of ML bias. We introduce an exactly solvable high-dimensional model of data imbalance, where parametric control over the many bias-inducing factors allows for an extensive exploration of the bias inheritance mechanism. Through the tools of statistical physics, we analytically characterise the typical properties of learning models trained in this synthetic framework and obtain exact predictions for the observables that are commonly employed for fairness assessment. Despite the simplicity of the data model, we retrace and unpack typical unfairness behaviour observed on real-world datasets. We also obtain a detailed analytical characterisation of a class of bias mitigation strategies. We first consider a basic loss-reweighing scheme, which allows for an implicit minimisation of different unfairness metrics, and quantify the incompatibilities between some existing fairness criteria. Then, we consider a novel mitigation strategy based on a matched inference approach, consisting in the introduction of coupled learning models. Our theoretical analysis of this approach shows that the coupled strategy can strike superior fairness-accuracy trade-offs.