We propose a flexible ensemble classification framework, Random Subspace Ensemble (RaSE), for sparse classification. In the RaSE algorithm, we aggregate many weak learners, where each weak learner is a base classifier trained in a subspace optimally selected from a collection of random subspaces. To conduct subspace selection, we propose a new criterion, ratio information criterion (RIC), based on weighted Kullback-Leibler divergence. The theoretical analysis includes the risk and Monte-Carlo variance of RaSE classifier, establishing the screening consistency and weak consistency of RIC, and providing an upper bound for the misclassification rate of RaSE classifier. In addition, we show that in a high-dimensional framework, the number of random subspaces needs to be very large to guarantee that a subspace covering signals is selected. Therefore, we propose an iterative version of RaSE algorithm and prove that under some specific conditions, a smaller number of generated random subspaces are needed to find a desirable subspace through iteration. An array of simulations under various models and real-data applications demonstrate the effectiveness and robustness of the RaSE classifier and its iterative version in terms of low misclassification rate and accurate feature ranking. The RaSE algorithm is implemented in the R package RaSEn on CRAN.

This work presents a review of the current state of research in data-driven turbulence closure modeling. It offers a perspective on the challenges and open issues, but also on the advantages and promises of machine learning methods applied to parameter estimation, model identification, closure term reconstruction and beyond, mostly from the perspective of Large Eddy Simulation and related techniques. We stress that consistency of the training data, the model, the underlying physics and the discretization is a key issue that needs to be considered for a successful ML-augmented modeling strategy. In order to make the discussion useful for non-experts in either field, we introduce both the modeling problem in turbulence as well as the prominent ML paradigms and methods in a concise and self-consistent manner. Following, we present a survey of the current data-driven model concepts and methods, highlight important developments and put them into the context of the discussed challenges.

As an instance of sequential decision-making problems, the multi-armed bandit (MAB) algorithms have attracted significant attention in various applications, such as ad optimization, personalized medicine, search engines, and recommendation systems. Recently, various methods for evaluating a new policy using historical data obtained via the MAB algorithms (Beygelzimer & Langford, 2009; Li et al., 2010) have emerged. The goal of off-policy evaluation (OPE) is to evaluate a new policy by estimating the expected reward obtained from the new policy (Dudík et al., 2011; Wang et al., 2017; Narita et al., 2019; Bibaut et al., 2019; Kallus & Uehara, 2019; Oberst & Sontag, 2019). Although an OPE algorithm estimates the expected reward from a new policy, most existing studies presume that the samples are independent and identically distributed (i.i.d.). However, the MAB algorithm policy updates the probability of choosing an action based on past observations, and samples are not i.i.d.

Although the expectation maximisation (EM) algorithm was introduced in 1970, it remains somewhat inaccessible to machine learning practitioners due to its obscure notation, terse proofs and lack of concrete links to modern machine learning techniques like autoencoded variational Bayes. This has resulted in gaps in the AI literature concerning the meaning of such concepts like ``latent variables'' and ``variational lower bound,'' which are frequently used but often not clearly explained. The roots of these ideas lie in the EM algorithm. We first give a tutorial presentation of the EM algorithm for estimating the parameters of a $K$-component mixture density. The Gaussian mixture case is presented in detail using $K$-ary scalar hidden (or latent) variables rather than the more traditional binary valued $K$-dimenional vectors. This presentation is motivated by mixture modelling from the target tracking literature. In a similar style to Bishop's 2009 book, we present variational Bayesian inference as a generalised EM algorithm stemming from the variational (or evidential) lower bound, as well as the technique of mean field approximation (or product density transform). We continue the evolution from EM to variational autoencoders, developed by Kingma & Welling in 2014. In so doing, we establish clear links between the EM algorithm and its variational counterparts, hence clarifying the meaning of ``latent variables.'' We provide a detailed coverage of the ``reparametrisation trick'' and focus on how the AEVB differs from conventional variational Bayesian inference. Throughout the tutorial, consistent notational conventions are used. This unifies the narrative and clarifies the concepts. Some numerical examples are given to further illustrate the algorithms.

Ensembling is now recognized as an effective approach for increasing the predictive performance and calibration of deep networks. We introduce a new approach, Parameter Ensembling by Perturbation (PEP), that constructs an ensemble of parameter values as random perturbations of the optimal parameter set from training by a Gaussian with a single variance parameter. The variance is chosen to maximize the log-likelihood of the ensemble average ($\mathbb{L}$) on the validation data set. Empirically, and perhaps surprisingly, $\mathbb{L}$ has a well-defined maximum as the variance grows from zero (which corresponds to the baseline model). Conveniently, calibration level of predictions also tends to grow favorably until the peak of $\mathbb{L}$ is reached. In most experiments, PEP provides a small improvement in performance, and, in some cases, a substantial improvement in empirical calibration. We show that this "PEP effect" (the gain in log-likelihood) is related to the mean curvature of the likelihood function and the empirical Fisher information. Experiments on ImageNet pre-trained networks including ResNet, DenseNet, and Inception showed improved calibration and likelihood. We further observed a mild improvement in classification accuracy on these networks. Experiments on classification benchmarks such as MNIST and CIFAR-10 showed improved calibration and likelihood, as well as the relationship between the PEP effect and overfitting; this demonstrates that PEP can be used to probe the level of overfitting that occurred during training. In general, no special training procedure or network architecture is needed, and in the case of pre-trained networks, no additional training is needed.

We study dropout in two-layer neural networks with rectified linear unit (ReLU) activations. Under mild overparametrization and assuming that the limiting kernel can separate the data distribution with a positive margin, we show that dropout training with logistic loss achieves $\epsilon$-suboptimality in test error in $O(1/\epsilon)$ iterations.

It has been hypothesized that label smoothing can reduce overfitting and improve generalization, and current empirical evidence seems to corroborate these effects. However, there is a lack of mathematical understanding of when and why such empirical improvements occur. In this paper, as a step towards understanding why label smoothing is effective, we propose a theoretical framework to show how label smoothing provides in controlling the generalization loss. In particular, we show that this benefit can be precisely formulated and identified in the label noise setting, where the training is partially mislabeled. Our theory also predicts the existence of an optimal label smoothing point, a single value for the label smoothing hyperparameter that minimizes generalization loss. Extensive experiments are done to confirm the predictions of our theory. We believe that our findings will help both theoreticians and practitioners understand label smoothing, and better apply them to real-world datasets.

A key to causal inference with observational data is achieving balance in predictive features associated with each treatment type. Recent literature has explored representation learning to achieve this goal. In this work, we discuss the pitfalls of these strategies - such as a steep trade-off between achieving balance and predictive power - and present a remedy via the integration of balancing weights in causal learning. Specifically, we theoretically link balance to the quality of propensity estimation, emphasize the importance of identifying a proper target population, and elaborate on the complementary roles of feature balancing and weight adjustments. Using these concepts, we then develop an algorithm for flexible, scalable and accurate estimation of causal effects. Finally, we show how the learned weighted representations may serve to facilitate alternative causal learning procedures with appealing statistical features. We conduct an extensive set of experiments on both synthetic examples and standard benchmarks, and report encouraging results relative to state-of-the-art baselines.

The recent and remarkable emergence of machine learning (ML) methods, and in particular deep learning (DL), can be explained by several factors, among which (i) the increasing computational capabilities, (ii) the access to large datasets for training, and (iii) the development of efficient and user-friendly libraries (LeCun et al., 2015; Goodfellow et al., 2016; Chollet, 2018). Impressive results have been obtained in a wide range of problems using DL to the extent that DL has become state-of-the-art for many different applications: computer vision, natural language processing, signal processing, etc... In numerical weather prediction, even if the physical laws governing the system dynamics are reasonably well known, the numerical models are affected by errors. This model error could come, for example, from misrepresented physical processes or from unresolved small-scale processes. It is legitimate to wonder whether ML methods can make use of the large amount of Earth observations, available in particular through remote sensing, to try and provide better numerical models. This question is the topic of numerous studies in the geosciences, whose objective is to construct a dynamical model using only observations of a physical system. The output dynamical model is often called the surrogate model to emphasise its difference with the (true) dynamical model. Several ML methods have already been tested to construct a surrogate model for low-order chaotic systems.

We formulate a new problem at the intersectionof semi-supervised learning and contextual bandits,motivated by several applications including clini-cal trials and ad recommendations. We demonstratehow Graph Convolutional Network (GCN), a semi-supervised learning approach, can be adjusted tothe new problem formulation. We also propose avariant of the linear contextual bandit with semi-supervised missing rewards imputation. We thentake the best of both approaches to develop multi-GCN embedded contextual bandit. Our algorithmsare verified on several real world datasets.