Within the vast body of statistical theory developed for binary classification, few meaningful results exist for imbalanced classification, in which data are dominated by samples from one of the two classes. Existing theory faces at least two main challenges. First, meaningful results must consider more complex performance measures than classification accuracy. To address this, we characterize a novel generalization of the Bayes-optimal classifier to any performance metric computed from the confusion matrix, and we use this to show how relative performance guarantees can be obtained in terms of the error of estimating the class probability function under uniform ($\mathcal{L}_\infty$) loss. Second, as we show, optimal classification performance depends on certain properties of class imbalance that have not previously been formalized. Specifically, we propose a novel sub-type of class imbalance, which we call Uniform Class Imbalance. We analyze how Uniform Class Imbalance influences optimal classifier performance and show that it necessitates different classifier behavior than other types of class imbalance. We further illustrate these two contributions in the case of $k$-nearest neighbor classification, for which we develop novel guarantees. Together, these results provide some of the first meaningful finite-sample statistical theory for imbalanced binary classification.

Spectral embedding of network adjacency matrices often produces node representations living approximately around low-dimensional submanifold structures. In particular, hidden substructure is expected to arise when the graph is generated from a latent position model. Furthermore, the presence of communities within the network might generate community-specific submanifold structures in the embedding, but this is not explicitly accounted for in most statistical models for networks. In this article, a class of models called latent structure block models (LSBM) is proposed to address such scenarios, allowing for graph clustering when community-specific one dimensional manifold structure is present. LSBMs focus on a specific class of latent space model, the random dot product graph (RDPG), and assign a latent submanifold to the latent positions of each community. A Bayesian model for the embeddings arising from LSBMs is discussed, and shown to have a good performance on simulated and real world network data. The model is able to correctly recover the underlying communities living in a one-dimensional manifold, even when the parametric form of the underlying curves is unknown, achieving remarkable results on a variety of real data.

Optimal transport maps between two probability distributions $\mu$ and $\nu$ on $\mathbb{R}^d$ have found extensive applications in both machine learning and statistics. In practice, these maps need to be estimated from data sampled according to $\mu$ and $\nu$. Plug-in estimators are perhaps most popular in estimating transport maps in the field of computational optimal transport. In this paper, we provide a comprehensive analysis of the rates of convergences for general plug-in estimators defined via barycentric projections. Our main contribution is a new stability estimate for barycentric projections which proceeds under minimal smoothness assumptions and can be used to analyze general plug-in estimators. We illustrate the usefulness of this stability estimate by first providing rates of convergence for the natural discrete-discrete and semi-discrete estimators of optimal transport maps. We then use the same stability estimate to show that, under additional smoothness assumptions of Besov type or Sobolev type, wavelet based or kernel smoothed plug-in estimators respectively speed up the rates of convergence and significantly mitigate the curse of dimensionality suffered by the natural discrete-discrete/semi-discrete estimators. As a by-product of our analysis, we also obtain faster rates of convergence for plug-in estimators of $W_2(\mu,\nu)$, the Wasserstein distance between $\mu$ and $\nu$, under the aforementioned smoothness assumptions, thereby complementing recent results in Chizat et al. (2020). Finally, we illustrate the applicability of our results in obtaining rates of convergence for Wasserstein barycenters between two probability distributions and obtaining asymptotic detection thresholds for some recent optimal-transport based tests of independence.

The common belief about the growing medium of livestreaming is that its value lies in its "live" component. In this paper, we leverage data from a large livestreaming platform to examine this belief. We are able to do this as this platform also allows viewers to purchase the recorded version of the livestream. We summarize the value of livestreaming content by estimating how demand responds to price before, on the day of, and after the livestream. We do this by proposing a generalized Orthogonal Random Forest framework. This framework allows us to estimate heterogeneous treatment effects in the presence of high-dimensional confounders whose relationships with the treatment policy (i.e., price) are complex but partially known. We find significant dynamics in the price elasticity of demand over the temporal distance to the scheduled livestreaming day and after. Specifically, demand gradually becomes less price sensitive over time to the livestreaming day and is inelastic on the livestreaming day. Over the post-livestream period, demand is still sensitive to price, but much less than the pre-livestream period. This indicates that the vlaue of livestreaming persists beyond the live component. Finally, we provide suggestive evidence for the likely mechanisms driving our results. These are quality uncertainty reduction for the patterns pre- and post-livestream and the potential of real-time interaction with the creator on the day of the livestream.

Gaussian processes (GPs) are widely used in computer experiments to emulate computationally expensive computer models for fast uncertainty quantification tasks such as uncertainty propagation, sensitivity analysis, and calibration. The popularity of GPs is attributed to their flexibility, native uncertainty incorporation, and analytical tractability for many key properties such as the likelihood function, predictive distribution and associated derivatives. However, GP models often assume stationarity, which in practice may not be adequate to capture non-stationary behaviors. A number of papers attempt to address this challenge by constructing non-stationary GP emulators. For example, the non-stationary covariance function introduced by Paciorek & Schervish (2003) could be adopted instead of a more standard stationary kernel. Bayesian treed Gaussian processes (TGP), proposed by Gramacy & Lee (2008), emulate non-stationary computer models by splitting the input space into several partitions and using independent stationary GPs to each sub-region. Ba et al. (2012) apply the composition of two stationary GPs to model both global and local details of a non-stationary computer model.

Contrastive learning applied to self-supervised representation learning has seen a resurgence in deep models. In this paper, we find that existing contrastive learning based solutions for self-supervised video recognition focus on inter-variance encoding but ignore the intra-variance existing in clips within the same video. We thus propose to learn dual representations for each clip which (i) encode intra-variance through a shuffle-rank pretext task; (ii) encode inter-variance through a temporal coherent contrastive loss. Experiment results show that our method plays an essential role in balancing inter and intra variances and brings consistent performance gains on multiple backbones and contrastive learning frameworks. Integrated with SimCLR and pretrained on Kinetics-400, our method achieves 82.0% and 51.2% downstream classification accuracy on UCF101 and HMDB51 test sets respectively and 46.1% video retrieval accuracy on UCF101, outperforming both pretext-task based and contrastive learning based counterparts.

Temperature monitoring during the life time of heat source components in engineering systems becomes essential to guarantee the normal work and the working life of these components. However, prior methods, which mainly use the interpolate estimation to reconstruct the temperature field from limited monitoring points, require large amounts of temperature tensors for an accurate estimation. This may decrease the availability and reliability of the system and sharply increase the monitoring cost. To solve this problem, this work develops a novel physics-informed deep reversible regression models for temperature field reconstruction of heat-source systems (TFR-HSS), which can better reconstruct the temperature field with limited monitoring points unsupervisedly. First, we define the TFR-HSS task mathematically, and numerically model the task, and hence transform the task as an image-to-image regression problem. Then this work develops the deep reversible regression model which can better learn the physical information, especially over the boundary. Finally, considering the physical characteristics of heat conduction as well as the boundary conditions, this work proposes the physics-informed reconstruction loss including four training losses and jointly learns the deep surrogate model with these losses unsupervisedly. Experimental studies have conducted over typical two-dimensional heat-source systems to demonstrate the effectiveness of the proposed method.

Support Vector Machine (SVM) is a supervised machine learning algorithm capable of performing classification, regression and even outlier detection. The linear SVM classifier works by drawing a straight line between two classes. This type of algorithm classifies output data and makes predictions. The output of this model is a set of visualized scattered plots separated with a straight line. You will learn the fundamental theory and practical illustrations behind Support Vector Machines and learn to fit, examine, and utilize supervised Classification models using SVM to classify data, using Python.

Different values of hyper-parameters often prove to be significant drivers of model performance and are expensive to tune and mostly task specific. Hyper-parameters play such a crucial role in modeling architectures that entire research efforts are devoted to developing efficient hyper-parameter search strategies (Bergstra et al., 2013; Nguyen et al., 2019; Henderson et al., 2018; Van Rijn and Hutter, 2018; Probst et al., 2019). The set of hyper-parameters differs for different learning algorithms. For instance, even a simple classification model like the decision tree classifier, has hyper-parameters like the maximum depth of the tree, the minimum number of samples to split an internal node and the criterion to use for estimating either the impurity at a node (gini) or the information gain (entropy) at each node. Ensemble models like random forest classifiers and gradient boosting machines also have additional parameters governing the number of estimators (trees) to include in the model.

Making predictions in a robust way is not easy for nonlinear systems. In this work, a neural network computing framework, i.e., a spatiotemporal convolutional network (STCN), was developed to efficiently and accurately render a multistep-ahead prediction of a time series by employing a spatial-temporal information (STI) transformation. The STCN combines the advantages of both the temporal convolutional network (TCN) and the STI equation, which maps the high-dimensional/spatial data to the future temporal values of a target variable, thus naturally providing the prediction of the target variable. From the observed variables, the STCN also infers the causal factors of the target variable in the sense of Granger causality, which are in turn selected as effective spatial information to improve the prediction robustness. The STCN was successfully applied to both benchmark systems and real-world datasets, all of which show 1 superior and robust performance in multistep-ahead prediction, even when the data were perturbed by noise. From both theoretical and computational viewpoints, the STCN has great potential in practical applications in artificial intelligence (AI) or machine learning fields as a model-free method based only on the observed data, and also opens a new way to explore the observed high-dimensional data in a dynamical manner for machine learning.